Structure of Motor Symptoms of Parkinson Disease

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STRUCTURE OF MOTOR SYMPTOMS OF PARKINSON'S DISEASE

A Dissertation Submitted to the Faculty of

Physical Education and Sport

Charles University

In Partial Fulfillment of the

Requirements for the Degree

of

Doctor of Philosophy

Kinanthropology

by

Jan tochl

Prague, Czech Republic

September 2005


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ACKNOWLEDGEMENTS

This thesis has been completed with the help and effort of many people. First,

would like to thank to Professor Petr Blahu for his patience and support during m

doctoral study. His unreserved approachability, useful lectures and encouragement we

crucial for the final realization of the thesis.

I am also very grateful to the University of Groningen for having me stay and f

arranging my stay comfortably and unforgettably. I would like to especially recogni

and thank Dr. Anne Boomsma and Dr. Marijtje A. J. van Duijn for their great suppo

constructive criticism and valuable lectures. Special thanks to I. Kohoutov for hhelpful comments to the manuscript.

Sincere appreciation is due to Prof. R ika for his patient assistance in getting

the data and correcting the manuscripts. Individual thanks to Prof. Leenders for his eff

and help with data gathering. Many thanks also to doctors Jan Roth, Petr Me , Robert

Jech, Tereza Serranov, and Olga Ulmanov who performed some of the UPDRS testin

Last but not least, I am grateful to my family and friends, especially to Ondra

Cipis, Zmijk, Ross, Mra and Elika for their constant support, encouragement an

friendship. Individually, I would like to express my deepest gratitude to Eva Tomeov

for her unlimited support and patience.

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CONTENTS

ACKNOWLEDGEMENTS.............................................................................................

LIST OF TABLES...........................................................................................................

LIST OF FIGURES .........................................................................................................

ABSTRACT.....................................................................................................................

STRUCTURE OF MOTOR SYMPTOMS OF PARKINSON'S DISEASE .....................

ON MEASUREMENT OF THEORETICAL CONCEPTS ..................................

PARKINSON'S DISEASE ...................................................................................

What Is Parkinson's Disease ......................................................................

Etiology of Parkinson's Disease..................................................................

Clinical Symptoms of Parkinson's Disease.................................................

Terms Used to Describe Motor Symptoms of Parkinson's Disease.......... 1

Parkinson's Disease Progression and Medication..................................... 1

Unified Parkinson's Disease Rating Scale ................................................ 1

Motor Section of UPDRS (MS UPDRS) and Its Dimensionality............. 1

RESEARCH QUESTION.....................................................................................

HYPOTHESES.....................................................................................................

METHODS ...........................................................................................................

Structural Equation Modeling (SEM)...................................................................

Introduction...............................................................................................

Types of SEM Models .............................................................................. 2

Statistical Assumptions of SEM ............................................................... 2

Types of Parameters Used in SEM Models .............................................. 3

Methods for Parameters Estimation.......................................................... 3

Note on Using Ordinal Variables in SEM ................................................ 3

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Identification Problem in SEM................................................................. 3

Model Testing and Fit Evaluation............................................................. 3

Chi-square statistic.................................................................................... 3

Alternative Fit Indices............................................................................... 3

Conventional Practice and Recommendations for Model Evaluation...... 4

Mokken's Scale Analysis ......................................................................................

Introduction...............................................................................................

IRT Versus Nonparametric IRT (NIRT)................................................... 4

Assumptions Underlying NIRT Models ................................................... 4

Extension of NIRT to Polytomous Items.................................................. 5

Mokken's Monotone Homogeneity Model for Polytomous Items............ 5

Mokken's Double Monotonicity Model for Polytomous Items ................ 5

Scaling Procedure .....................................................................................

Limitations and Issues of Mokken's Scale Analysis................................. 5

EMPIRICAL RESEARCH...................................................................................

Introduction...........................................................................................................

Sample Description...............................................................................................

Results...................................................................................................................

Initial Computations.................................................................................. 6

Exploratory Mokken's Scale Analysis of MS UPDRS............................. 6

Confirmatory Mokken's Scale Analysis of MS UPDRS .......................... 6

Summary of Results of Mokken's Scale Analyses.................................... 7

Building Structural Equation Models of Parts of MS UPDRS................. 7

Building Structural Equation Model of Entire MS UPDRS..................... 9

Differences Between Models for Patients in on and off States ....... 10

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Summary of Results of Structural Equation Modeling........................... 10

Discussion ........................................................................................................... 1

CONCLUSION...............................................................................................................

REFERENCES ...............................................................................................................

APPENDICES ................................................................................................................

Motor Section of Unified Parkinson's Disease Rating Scale.............................. 1

MS UPDRS Data Sheet ...................................................................................... 1

Exploratory Mokken's Scale Analysis for Non-trichotomized Data and Cutoff Criterion of H i >0.3............................................................................................. 12

Exploratory Mokken's Scale Analysis for Non-trichotomized Data and Cutoff Criterion of H i >0.4............................................................................................. 12

Parameter Estimates, Standard Errors and T-values of Selected Models........... 12

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LIST OF TABLES

1. Basic statistical properties of the data..........................................................................

2. Exploratory results for cutoff criterion of H i>0.3......................................................... 65

3. Exploratory results for cutoff criterion of H i>0.4......................................................... 67

4. Values of H i coefficients of confirmatory Mokken's scale analysis ............................. 6



7. Matrix of polychoric correlations of items related to tremor........................................

8. Fitted residuals ............................................................................................................9. Fitted residuals ............................................................................................................

10. Fitted residuals ...........................................................................................................


12. Matrix of polychoric correlations of items related to rigidity and bradykinesia ........





17. Matrix of polychoric correlations of items related to axial/gait bradykinesia............


19. Matrix of polychoric correlations of MS UPDRS ......................................................

20. Fitted residuals ..........................................................................................................

21. Differences between models for patients in on and off states ........................... 1

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LIST OF FIGURES

1. Latent variable modeling of theoretical concepts ........................................................

2. Example of path analytic model ..................................................................................

3. Logistic function ..........................................................................................................

4. IRFs of various difficulty parameters ..........................................................................

5. IRFs of various difficulty and discrimination parameters ............................................

6. Logistic IRF (solid curve), Nonparametric IRF (dashed curve); and ordered latent

class model IRF (step function) ................................................................................

7. Path diagram of one-factor model of tremor................................................................8. Path diagram of two-factor model of tremor ...............................................................

9. Path diagram of two-factor model of tremor ...............................................................

10. Path diagram of hierarchical model of tremor ...........................................................

11. Path diagram of two-factor model of rigidity and bradykinesia .................................

12. Path diagram of hierarchical model of rigidity and bradykinesia...............................

13. Path diagram of three-factor model of rigidity and bradykinesia ...............................

14. Path diagram of four-factor model of rigidity and bradykinesia ................................

15. Path diagram of one-factor model of axial/gait bradyknesia ......................................

16. Path diagram of three-factor model of the MS UPDRS ............................................

17. Path diagram of five-factor model of the MS UPDRS...............................................

18. Path diagram of hierarchical model of the MS UPDRS .............................................

19. Path diagram of seven-factor model of the MS UPDRS ...........................................

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ABSTRACT

The aim of this study is to investigate the number and the structure of the moto

symptoms of Parkinson's disease measured by Motor Section of the Unified Parkinso

Disease Rating Scale (UPDRS). This is inferred through statistical analysis of the Mo

Section of the UPDRS. First, the etiology and the clinical symptoms of Parkinson

disease are outlined. Then, the UPDRS is introduced with focus on the statistical featur

of the Motor Section of this scale. The next two chapters deal with Mokken's sca

analysis and structural equation modeling. Finally, dimensionality and reliability of th

Motor Section of the UPDRS are studied with nonparametric Mokken's scale analyand structural equation modeling.

The UPDRS measures were obtained from 405 patients with PD (237 men (3

off; 170 on; 28 unknown), 168 women (21 off; 140 on; 7 unknown)). Th

analysis showed high skewness of the data in most of the items substantiating the use o

nonparametric scaling method. Mokken's scale analysis allowed for separating the Mo

Section of the UPDRS into five dimensions. The first dimension consisted of axial/g

bradykinesia and left-sided items of rigidity and bradykinesia of the extremit

suggesting their co-occurrence. Right-sided items of rigidity and bradykinesia of t

extremities generated the second dimension. There was a high internal consistence

these two dimensions assessed by Cronbach's alpha (0.92 and 0.87, respectively). T

third and the fourth dimension consisted of tremor-right and tremor-left items (bo

resting and postural), respectively. Cronbach's alpha, however, was less satisfactory f

these dimensions (0.62 and 0.65). Items Speech and Facial expression generat

stand-alone, but statistically limited dimension (alpha = 0.76). Structural equatio

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modeling showed that the Motor Section of the UPDRS incorporates seven factor

rigidity, tremor, bradykinesia of the extremities, axial/gait bradykinesia

speech/hypomimia, and two additional factors for laterality. Finally, the structure o

motor symptoms of Parkinson's disease seems to be stable across on and off states.

Keywords: Kinanthropology, Mokken's scale analysis, structural equation

modeling, dimensionality, reliability, Motor Section of the UPDRS

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STRUCTURE OF MOTOR SYMPTOMS OF PARKINSON'S DISEASE

ON MEASUREMENT OF THEORETICAL CONCEPTS

In contrast with physical measurement such as time, length, and weight, etc., i psychology, sociology and other sciences some variables cannot be measured directSelf concept, IQ, attitudes, and motor abilities (e.g. motor coordination or motoendurance) are examples of such variables. They are called latent traits or theoreticconcepts or especially in psychology hypothetical constructs. They characterize tgeneral features of behavior and serve as a theoretical explanations of performanreferring to the abstract and generic attributes of human activity.

The problem is how the theoretical concepts can be introduced by the test battesince they are not observable by nature and can be measured only indirectly and by tewhich are (usually) scaled on the basis of physical variables like time, length, etMoreover, the items in the test battery have (usually) different empirical contents, ascored by different experimental operations, and their score values are possibrepresented in different measurement units. It deals with the mutual relationship of tempirical and theoretical levels of scientific knowledge. This issue can be solved throu

the so-called rules of correspondence (Blahu, 1996a). These rules enable the processinduction in which the more general and generic theoretical concepts (e.g. abilities) ainductively constructed from the empirical attributes (e.g. tests) that work as the partial and more specific empirical indicators. In other words, since theoretical conceare not measured directly, the researcher must operationally define the latent variable interest in terms of the behavior 1 believed to represent it. Assessment of the behavior,then, constitutes the weak associative measurement of an underlying concept (Byrn

2001). These measured scores (measurements) are termedobserved or manifest variables;they serve asindicatorsof the underlying theoretical concept that they are presumed to

1 The term behaviour is used here in the broadest sense to include, for instance in vivoobservation of some physical task or activity, coded response to interview questions, self-reportresponse to an attitudinal scale, etc.


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represent. Latent variablesare mathematically constructed variables supposed to modeltheoretical concepts (Raykov & Marcoulides, 2000).

Latent variables can be further divided into the so-calledexplanatory (or

exogenous) latent variablesand response(or endogenous) latent variables. Explanatorylatent variables are synonymous with independent variables (although the termindependent variable is mostly meant in the sense of multiple regression); they causfluctuations in the values of other latent variables in the model. Changes in the values explanatory variables are not explained by the model, rather they are considered to influenced by other factors external to the model (e.g. age or gender). Response latevariables are synonymous with dependent variables and, as such, are influenced by texplanatory variables in the model, either directly or indirectly. Fluctuations in the valuof response variables in the model are said to be explained by the model since all latevariables that influence them are included in the model specification.

Fig. 1. Latent variable modeling of theoretical concepts (Blahu, 1996a)

Models with latent variables can be defined as a class of statistical models thdescribe observable reality through its relationship with unobservable mathematicalconstructed characteristic (Blahu, 1980). They are helpful in offering the tools fsolving the problem of correspondence by representations of the semantic level in termof the syntactic or model level as shown in Figure 1. Moreover, such modeling isrelatively universal approach and therefore can be used in many branches.


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There are two basic conditions enabling the use of latent variable models in throle of formalized corresponding rules. They were introduced by McDonald (1979), bmore precisely described by Blahu (1991):

1) Concept formation by the weak associative measurement: This is represente by set of model equations, typically regression functions. Then, the associatimeasurement in Physics can be understood as a special case of this weak one.

2) Requirement of the completeness of explanation that the concept yield. In thsimplest case, this it the axiom of local independence (will be introduced later).

If these two principles are fulfilled then the concept formation can be understooas a weaker case of associative measurement carried out through statistical modeling wlatent variables.

Since the purpose of the models with latent variables is to specify and confirmregularities, these methods contribute to the two basic tasks of science - explanation a prediction (Blahu, 1996b). From a practical point of view they can be used for (Blah1985):

a) Estimation of the level of latent variable in Anthropomotoricity for examplestimation of the individual level of motor abilities

b) optimal test reduction usually exclusion of items with low validity or reliability

c) classification of variables especially developing new and more general term(e.g. terms static strength, dynamic strength and explosive strength can bcovered by the term strength)

d) development or confirmation of the structural hypothesese) transformating of variables into variables with better predictive properties

epika (2003) divides models with latent variables into three groups of modelsLinear factor analysis, nonlinear factor analysis, latent structure models. Rabe-Heske

and Skrondal (2005) propose another classification: generalized linear mixed (multilevel) models, measurement models (factor, item response, or latent class), astructural equation models. For the purpose of this study we suggest the followinclassification: Item response theory (IRT)models, which include 1- or 2- or 3-parameter logistic

models and various Nonparametric IRT models including Mokken's models. IR


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is focused on evaluation of the degree of precision and breadth of scales that aused to measure theoretical concepts, or (in IRT terms) underlying latent traitIRT consists of a class of statistical procedures that are used to model th

association between an individual's responses to survey questions/items (i probabilistic terms) and an underlying latent trait that is measured by the items.

Structural equation modeling (SEM). It is a method for determining the extent towhich data on a set of variables are consistent with hypotheses about associatioamong the variables. Usually, it is based on analysis of covariance or correlatiomatrix of observed variables. SEM includes factor analysis, multiple indicatomultiple cause (MIMIC), non-recursive (reciprocal effects) path models, growcurve models, ANOVA, ANCOVA, MANOVA, etc.

Latent class analysis(LCA). It is a statistical method for finding subtypes of related cases (latent classes) from multivariate categorical data. It is usually baseon analysis of frequency table of observed response patterns. For example, it ca be used to find distinct diagnostic categories given the presence/absence several symptoms or types of attitude structures from survey responses. Thresults of LCA can also be used to classify cases to their most likely latent clas Latent profile analysisis a variant on LCA for continuous variables.A detailed overview of special cases of the general model with latent variables

presented in Blahu (1985).In sport sciences, the first application of latent variable modeling can be found

the work of Burt (1925). Nowadays it is still widely used even though some new typesmodeling like multilevel modeling or the so-called Social Networks are being developeFrom the perspective of the czech kinanthropology, factor analysis was applied in mastudies (e.g. Blahu,elikovsk, & Kov , 1973). The more recent applications of IRT or

factor analysis can be found inepika (2000), tochl (2002), Tomeov (2003), etc.The problem of motor diagnostic methods (motor testing) in Kinanthropology

essentially related to standardization of these methods (Mkota & Blahu, 1983). As pointed out by Blahu (2004) the main and the minimum standardization requirements diagnostic quality contain:


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construct validitytowards the theoretical concepts that are covering thediagnosed domain as assessed through content validity by experts, the validitusually being modeled by correlations with the latent variable

verifieddimensionalityof the diagnosed domain so that the whole extent of thediagnosed domain and its structure are appropriately covered

reliabilityof the diagnostic methods, preferably verified by two or more ways, foexample by the stability over replications as well as by their internal consistency

practical validityto an external criterion, for example to other diagnosticmethods, sometimes also in the form of predictive validityThe assessment of the standardization criteria above necessarily include

application of statistical models with latent variables (

epika, R

i

ka, tochl, &

Blahu, 2003).Scientific diagnostics in general, not only in terms of testing, has to be clearl

distinguished from the clinical diagnostics methods (Blahu, 2004). This does not methat diagnostic methods that are routinely used in educational or even medical practiwould not be truly scientific. On the contrary, it is highly desirable that diagnostimethods are standardized on the same level of rigor as the scientific ones (Dvo kov,2002; tochl, 2002). Quite often, however, the clinical diagnostic methods of humamovements are not evaluated objectively from the above mentioned points of view; bthey are built on a rather intuitive background.

Neurological syndromes such as the combination of hypokinesia, rigidity, restintremor and postural abnormalities in Parkinson's disease (PD) represent such theoreticalconcepts which individual features can be statistically modeled as latent variables. Tidentification of the dimensionality of such syndromes is important because knowledabout the co-occurrence of symptoms may help to define disease phenotypes and provi

clues for differential diagnosis.This study discusses the dimensionality, the structure of latent variables, th

validity and the reliability assessment of the Motor Section of the Unified ParkinsonDisease Rating Scale (MS UPDRS) within the framework of two statistical approachmentioned above - nonparametric item response theory and structural equation modelin


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One is encouraged to recognize this study in the framework of Kinanthropologand its synonym Kinesiology since Kinanthropology is to be understood as comprehensive term for a scientific field dealing with the basic and applied research, w

potential practical applications in monitoring various quantitative as well as qualitatiindicators of human motor activities (Blahu et al., 1993). In addition, the content Kinanthropology was formed from Anthropomotoricity and therefore it focuses on motabilities and skills with the accent on the diagnostic quality of motor tests validitreliability, etc.


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PARKINSON'S DISEASE

What Is Parkinson's Disease

Parkinson's disease is a progressive neurodegenerative disease based on extinctio(dysfunction and death) of neurons pars compacta substantiae nigrae which lead decrease of dopamine content of the striatum (Nevmalov, R ika, & Tich, 2002).

Parkinson's disease (PD) was first described in 1817 by James Parkinson (2002In the early 1900's, pathologists in Europe and the United States recognized a specifabnormality in the brains of individuals who in life had Parkinson's disease. In a regionthe brain called the midbrain, there are certain neurons that contain a dark pigmeknown as melanin and this cluster of neurons is known as the "substantia nigra", meani black substance. These pigmented neurons in the substantia nigra produce dopamiDopamine is a chemical messenger (neurotransmitter) responsible for transmitting sign between the substantia nigra and several clusters of neurons that together comprise "basal ganglia" and is vital for normal movement. There is an abundant reservoir dopamine in this region, but when the level drops below 20%, symptoms of Parkinsondisease begin to emerge. Thus, the loss of dopamine causes the nerve cells of the bas

ganglia to fire out of control, leaving patients unable to direct or control their movemein a normal manner.

Etiology of Parkinson's Disease

There are currently four theories on the cause of Parkinson's disease (Ebbit2005) and many scientists believe that it is probably a combination of one or more of t

following factors.In the field of genetics, some researchers believe that Parkinson's disease has

genetic cause and is therefore hereditary (Foltynie, Sawcer, Brayne, & Barker, 200Gasser, 1998). In many families, Parkinson's has occurred in many generations. Groupvictims tends to follow one side, either the mother or the father. Studies show that fir


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degree relatives of Parkinson's victims are two times more likely to develop the diseathan relatives in families in which there is no history of Parkinson's (Rybicki, JohnsoPeterson, Kortsha, & Gorell, 1999). By studying families in which Parkinson's has pass

through generations, researchers have identified an abnormal gene that as the cause some cases of Parkinson's disease. However, in other Parkinson's patients there is ngenetic link and the illness does not run in the family. For this reason, genetic studies Parkinson's remain controversial (The Parkinsons web, 2005).

Most scientists believe Parkinson's is caused by a combination of environmentand genetic influences. Parkinson's may be the result of environmental factors such drinking well water (Gorell, Johnson, Rybicki, Peterson, & Richardson, 1998), living the rural communities (Ferraz, Andrade, Tumas, Calia, & Borges, 1996), and exposureheavy metals. Carbon monoxide poisoning, carbon disulphide, potassium cyanide, amethyl alcohol may also contribute to an environmental cause of Parkinson's. Somscientists have implicated manganese ore dust as a possible cause as well (Olano2004). Through recent research, and testing it has been determined that no onenvironmental agent could be the only cause of Parkinson's disease ( Parkinson's disease:etiology and genetics, 2005).

The MPTP (by product in the process of heroin production) has been known

destroy substantia nigra (Muramatsu et al., 2003). This often results in many of thsymptoms of Parkinson's disease.

Infectious disease has been suggested as a possible cause of Parkinson's as we(Kristensson, 1992). In the early 1900's, there was an epidemic of an illness that caus people to fall into a stupor or suffer severe insomnia. This disease was called sleepisickness or encephalitis lethargic. Many of the victims of this disease developed a certaform of Parkinson's disease.

Still other scientists believe that Parkinson's disease may be a direct result of th process of accelerated aging. This process occurs for currently unknown reasoThrough this aging, some of the brain's ability to produce dopamine decreases. Thresults in many of the symptoms of Parkinson's disease.

The single factor that has been most consistently associated with a reduced risk PD is cigarette smoking, which has been demonstrated in numerous studies (e.g. Alla


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Del Castillo, & Navajas, 2002; Hernan et al., 2001). Caffeine consumption is alsassociated with a reduced incidence of PD (Deleu, 2001; James, 2003).

Clinical Symptoms of Parkinson's Disease

Parkinson's disease causes motor (movement) and nonmotor symptoms. Prior the diagnosis of PD, a person may begin to feel a drop in energy or a loss of coordinati(Okun, McDonald, & DeLong, 2002). Several symptoms such as impaired handwritinreduced arm swing, a "limp" or tremor may begin to emerge on one side of the bo(Poewe & Wenning, 1998). Other early symptoms may include internal shakines

difficulty in getting out of a chair, a soft voice and/or depression. These symptoms evolgradually and may even be imperceptible to the patient or family members until physically or emotionally stressful event occurs, triggering an exacerbation of thesymptoms ( Parkinsons disease, 2005).

When the disease is fully expressed, the major clinical features includ bradykinesia (slow movement), tremor (typically at rest and extinguished wmovement), rigidity (a clinical finding of resistance to movement, often associated with jerky sensation called cogwheeling) and impaired postural reflexes (poor balan(Worldwide education and awareness for movement disorders, 2005).

Many patients also suffer from secondary symptoms. These include depressionsleep disturbances, dementia, forced eyelid closure, speech problems, drooling, difficuin swallowing, weight loss, constipation, breathing problems, difficulty in voidindizziness stooped posture, swelling of the feet, and sexual problems (The Parkinsonsweb, 2005).

A variety of other symptoms can be associated with Parkinson's disease includin

fatigue, weakness, joint pain, internal tremor, anxiety, impaired recent memory, oily faor scalp, constipation, bladder urgency, soft hoarse speech, sleep disturbances, restlelegs, etc.

The average Parkinson's disease patient experiences 2 - 3 hours of off state eaday. Generally, off state is reffered to as state of impaired motoricity (Roth, Sekyrov


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& R ika, 1999). Patients in off state experience handwriting problems, overaslowness, loss of olfaction, loss of energy, stiffness of muscles, walking problems, sledisturbances, balance difficulties, challenges getting up from a chair, and many oth

motor and non-motor symptoms. For the use of clinical diagnostics, on state and ofstate are defined more rigorously (Langston et al., 1992): Defined on state: state after dosage standard dues of medication (L-DOPA or agonist of dopamine) Defined off state: state patient with PN after 12-hourly omission anti-Parkinson's medication (it is 12 clock around of last dues of treatment), least 1 o'cloafter awakening, to do away possible "sleep benefit").

Terms Used to Describe Motor Symptoms of Parkinson's Disease

Bradykinesia: literally slowed movement. Dystonia: involuntary contraction of a muscle or a group of muscles. Dyskinesias: abnormal involuntary movements that can be characterized aswrithing movements and can include dystonic movements. These movements can be se

in a variety of disorders such as Huntington's Chorea, the dystonias and Touretsyndrome. These movements are commonly caused by levodopa and otheantiparkinsonian medication and are often seen as a delayed reaction to antipsychomedication. Rigidity: stiffness, increased resistance to passive movement. It is present whenlimbs are still, but increases as they move. It is related to over elasticity of specific nercells in the spinal cord that control muscle tone. Tremor : 5-6 Hz alternating activity og antagonist muscles controlling a jointleading to alternating joint movements (Latash, 1998). Tremors are often worse on oside of the body than on the other. Resting tremor : a tremor of a limb that increases when the limb is at rest. Action/postural tremor : a tremor that increases when the hand/muscle is movingvoluntarily.


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Parkinson's Disease Progression and Medication

The progression of Parkinson's disease is highly variable, although th progression may be relatively slower in patients whose initial symptoms include trem(Jankovic & Tolosa, 2002). The likelihood of developing PD increases with age. Ptypically begins in a person's 50s or 60s, and slowly progresses with increasing age. Taverage age of onset is 62.4 years. Onset before age 30 is rare, but up to 10% of ca begin by age 40 (Worldwide education and awareness for movement disorders, 2005).

A principal aim of PD therapy is to replace the brain's supply of dopamine witthe drug levodopa, which the brain converts into dopamine. Levodopa was introduceda PD therapy in the 1960s, and remains the most effective therapy for motor symptom

(Hoehn, 1992). It lessens and helps to control all the major motor symptoms of PDincluding bradykinesia.

Nausea and vomiting are the most common side effects, and are due accumulation of dopamine in the bloodstream (Hunter, Shaw, Laurence, & Stern, 197Markham, Diamond, & Treciokas, 1974). Orthostatic hypotension (low blood pressuupon standing) also occurs (Lang, 2001). The risk of hallucinations and paranoincreases over time (Klawans, 1988). Compulsive behavior, including gambling anhypersexuality, is another risk (Proctor & McGinness, 1970).

Drowsiness is a common adverse effect of levodopa and other dopaminergitherapies, and sudden sleep onset is possible (Tracik & Ebersbach, 2001). Patients mnot experience any warning signs of sudden sleep onset.

The most troubling adverse effect from long-term levodopa use is dyskinesia(Friedman, 1985). Dyskinesias result from the combination of long-term levodopa uand continued neurodegeneration. They typically begin to develop in milder forms afteto 5 years of treatment, but are more severe after 5 to 10 years of treatment.

Unified Parkinson's Disease Rating Scale

The Unified Parkinson's Disease Rating Scale (UPDRS) is one of the most wideused rating scales for assessing patients with Parkinson's disease (PD). The UPDRS w


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designed to provide a measure of signs and symptoms of Parkinson's disease in clinic practice and research. It is a scale that was developed in an effort to incorporate elemefrom existing scales, and to provide a comprehensive but efficient and flexible way

monitor PD-related disability and impairment. Prior to its development, multiple scalincluding the Webster, Columbia, King's College, Northwestern University Disabilit New York University Parkinson's Disease Scale, and UCLA Rating Scales, were useddifferent centers, making comparative assessments difficult. The development of tUPDRS involved multiple trial versions, and the final published scale is officially knowas UPDRS version 3.0.1.

The scale itself has four components - Part I, Mentation, Behavior and Mood; PaII, Activities of Daily Living; Part III, Motor Section; Part IV, Complications of Therap

The original concept of the scale was to provide a core assessment tool that cou be accompanied by additional measures to focus on global impairment. For exampwhereas the UPDRS is often accompanied by and reported with such scales as thSchwab and England and Hoehn and Yahr scales. Of all available clinical scales for tassessment of Parkinsonian motor impairment and disability, the UPDRS is currently tmost commonly used. Sixty-nine percent of 19941998 articles using a PD-rating scarelied on the UPDRS as the standard tool (Goetz, 2003). This trend is an international o

and the UPDRS predominates as the primary scale in published studies from both US aother geographical regions.

Utilization of UPDRS

One of the core advantages of the UPDRS is that it was developed as a compounscale to capture multiple aspects of PD (Goetz, 2003). It assesses both motor disabili(Part II: Activities of Daily Living; contains 13 items) and motor impairment (Part I

Motor Section; contains 27 items). In addition, Part I (4 items) addresses mentdysfunction and mood, and Part IV (11 items) assesses treatment related motor and nomotor complications.

Another unique feature of the UPDRS is the availability of a teaching-videotapstandardizing the practical application of the scale and thereby serving as an importa


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asset to enhance inter-rater reliability (Goetz, Stebbins, & Chmura, 1995). This feature particularly relevant to the training of new raters and to the conduct of multicentherapeutic trials in PD. Despite its multidimensional approach with four different par

the UPDRS has proven an easy-to-use instrument in clinical practice with an averatime requirement for administration of the full scale between 10 and 20 minutes. Thtime can be further shortened by self-administration of the Mentation and ADL parts patients in the waiting room.

The UPDRS is increasingly used as a gold standard reference scale. The UPDRis also the common reference scale in studies of instrument development for ratinspecific aspects of PD (Martinez-Martin et al., 1997). The UPDRS has also been useddefine the placebo response in PD (Goetz, Leurgans, & Raman, 2002). Almost all recetrials of surgical interventions for PD, both related to intracerebral transplantation adeep brain surgery, have employed the UPDRS. It is a key component of the CoAssessment Programs for Intracerebral Transplantation and Surgical InterventionTherapies for PD (CAPIT/CAPSIT) (Goetz, LeWitt, & Weidenman, 2003). Althougspecifically developed to assess PD, the UPDRS has also been utilized to raParkinsonian features of other conditions, including normal aging, progressivsupranuclear palsy, and Lewy body dementia.

The UPDRS has been used in studies of early, mild PD, moderate but stable PDand severe disease and motor fluctuations. Prior studies have demonstrated that the scfavors the assessment of moderate and severe impairments, and may not be idealconfigured to assess very mild disease-related signs and symptoms (Vieregge, StolzKlein, & Heberlein, 1997). Several longitudinal studies of PD have demonstrated that tUPDRS score increases over time and scores are higher at key clinical decision-maki points like the need to introduce symptomatic therapy (Poewe & Wenning, 199

Numerous studies indicate that the UPDRS is responsive to therapeutic interventioPublished reports using the UPDRS, however, have focused almost exclusively oCaucasians (white men), and the UPDRS characteristics have not been extensiveinvestigated in different racial or ethnic minorities (Tanner, 1999). Insufficieninformation is available on the ability of the UPDRS to discriminate between diseacategories of clinical pertinence. To date, operative definitions of minimal, mild


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moderate and severe stages of PD have not been explicitly defined (Goetz, 200UPDRS scores, however, correlate with the Hoehn and Yahr scale and with the Schwand England scale (Martinez-Martin et al., 1994). Furthermore, within the UPDRS, t

objective, physician-derived Motor Section (Part III) correlates well with the subjectiv patient-derived Activities of Daily Living section (Part II).

Clinimetric Issues

Of all available PD rating scales, the UPDRS has the additional advantage that is the most thoroughly tested instrument from a clinimetric point of view. Almost onthird of all studies assessing clinimetric properties of impairment and disability scales f

PD identified in a recent systematic review were targeted on the UPDRS (RamakeMarinus, Stiggelbout, & Van Hilten, 2002). Clinimetric scale evaluation usually assessa scale's reliability and validity. The UPDRS has shown excellent internal consistencacross multiple studies (Martinez-Martin et al., 1994). This high degree of internconsistency may be artificially inflated due to redundancy in the large number of itemsParts II and III of the UPDRS. Assessments of rater consistency included both inter-rareliability and intra-rater reliability. Inter-rater reliability appears adequate for the totUPDRS (Martinez-Martin et al., 1994) as well as the Activities of Daily Living and tMotor Section. Several studies reports on the unacceptably low inter-rater reliability fselected items assessing speech and facial expression on the Motor Section of thUPDRS (Camicioli, Grossmann, Hudnell, & Anger, 2001). Other studies, howevereported acceptable inter-rater reliability estimates for these items (Martinez-Martin et a1994). There are also some published reports examining intra-rater reliability (Camiciet al., 2001). This latter study shows low to medium intra-rater reliability. Among 40early-stage PD subjects, examined on two occasions, separated by approximately

weeks, the intraclass correlation coefficients were very high: total score, 0.92; Mentatio0.74; Activities of Daily Living, 0.85; Motor Section, 0.90 (Siderowf et al., 2002).

The UPDRS has adequate face validity and samples important and typicadomains associated with PD. In addition, its construction was guided by experts in tfield and based on previous scales. Criterion validity has not been established becau


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there is no absolute gold standard that can be used for this assessment. The majorityvalidation studies have assessed the construct validity of the UPDRS. These studies hagenerally found satisfactory results regarding convergent validity with other instrumen

assessing PD, such as the Hoehn and Yahr or Schwab and England scales or timed mottests (Stebbins & Goetz, 1998; Stebbins, Goetz, Lang, & Cubo, 1999). Divergent validior the degree to which the scale does not measure domains unrelated to PD, has not bewell established.

Multiple studies have examined construct validity of the UPDRS through factoanalysis. These studies have found between three and six factors that account forsignificant proportion of the total scale variance (Martinez-Martin et al., 1994; Stebbi& Goetz, 1998; Stebbins et al., 1999).

The resultant factors form rational groupings of the items, and suggest that thscale has a valid multidimensional assessment format. So far, one factor structurcomposed of six factors (axial/gait bradykinesia, right bradykinesia, left bradykinesrigidity, rest tremor, and action/postural tremor) has been shown to be stable across and off states (Stebbins & Goetz, 1998; Stebbins et al., 1999).

Additional validity studies have been conducted to assess the ability of thUPDRS to detect changes in function in either untreated or treated states. In gener

these studies have demonstrated that the UPDRS is sensitive to changes in clinical statu

Ambiguities of UPDRS

Despite the marked strengths and wide usage of the UPDRS, a number olimitations nonetheless exist.

First, as a composite scale, the UPDRS is uneven in the type of information gathers. For example, Part I is conceptually different from Part II and Part III, and a

screening assessment for the presence of depression, dementia or psychosis, it cannot used as an adequate severity measure of any of these behaviors (Goetz, 2003). Part IVconstructed differently than the rest of the UPDRS with a mixture of 5-point categoriand dichotomous (yes/no) ratings that are difficult to analyze together.


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Some items of the Motor Section have relatively poor inter-rater reliabilityincluding Speech, Facial expression, Posture, Body bradykinesia, and all itemof action/postural tremor and rigidity (Martinez-Martin et al., 1994). A specific examp

of a key testing problem is the assessment of postural stability in Part III. Because tresponse of the patient and the assigned rating depend directly on the force of the postuthreat, standardized instructions and application of the test are essential for consisteratings. These instructions are not part of the UPDRS.

Additionally, there is some redundancy of items in both the ADL and MotoSection. While duplication of material enhances the internal consistency of the scalsome critics consider such enhancement a spurious inflation (Martinez-Martin et a1994). Redundancy also increases the time required to administer the scale. Efforts reduce redundancy have led to the Short Parkinson's Evaluation Scale (SPES), basdirectly on the UPDRS, but with fewer items and reduced rating categories of 0(Goetz, 2003). The SPES is a disease-specific scale, omitting the UPDRS items that aconsidered as redundant or of minor clinical significance. It contains four parts: menstate (3 items), ADL (8 items), motor examination (8 items), and complications therapy (5 items). Furthermore, the HY and a scoring of motor fluctuations are includThe SPES adopts a four-point ordinal scale for each item (Martignoni, Franchigno

Pasetti, Ferriero, & Picco, 2003).The allocation of items to specific parts of the UPDRS is not altogethe

consistent, leading to potential ambiguities of interpretation. Part II, titled Activities Daily Living, includes a mixture of items which are directly related to daily activiti(e.g. dressing, eating), but also examine patient perceptions of primary diseasmanifestations (e.g. tremor, salivation). Items that overlap these two categories incluthe gait items that assess primary Parkinsonian features (freezing, falls), and impact

walking as an activity of daily living.The UPDRS Part II is culturally biased, and the anchoring descriptions for som

item ratings are not applicable to all ethnic environments. For example, Dressing (It10) describes difficulty with buttons, even though many traditional cultures do not uthem; Cutting food/handling utensils (Item 9) presumes that food is regularly cut feating and that utensils are used, although some cultures serve food in bite-size portio


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and some do not use eating utensils. Although the scale was considered applicable most international urban settings, the UPDRS may be limited by ambiguities wheapplied in epidemiological research efforts that involve field work to rural an

geographically isolated cultures (Goetz, 2003).

Comorbidities and the UPDRS

PD is more prevalent in subjects over 50 years of age, therefore the co-existenof other diseases like diabetes, stroke, and arthritis can confound the evaluation of Prelated impairment and disability. Furthermore, common co-existent disorders likdepression can potentially affect the speed of a patient's movement, alter motivation, a

enhance perceptions of disability even when PD itself is stable (Goetz, 2003).

Important Elements Not Covered

Several key elements of PD are not covered by the UPDRS. When the scale waformulated in the mid-1980s, the developers were well aware of this limitation, but thmade choices to delete questions on some Parkinsonian impairments, mainly to createscale that was reasonably simple and short. Several areas of concern exist (Goetz, 2003

Items not covered by the Unified Parkinson's Disease Rating Scale includeanhedonia, bradyphrenia, anxiety, hypersexuality, sleep disorders (insomnia, excessidaytime sleepiness), fatigue, dysautonomia (urinary dysfunction, constipation, impotensweating), dysregulation, and health-related quality of life.

Motor Section of UPDRS and Its Dimensionality

As mentioned earlier, the UPDRS has several parts: Part I. (Mentation, Behaviand Mood); Part II. (Activities of Daily Living (ADL)); Part III. (Motor Section); Part I(Complications of Therapy).

This study focuses on the Motor Section of the UPDRS (MS UPDRS) whicconsists of the following 27 items:


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1. Speech2. Facial expression3 -7. Tremor at rest (Face/lips/chin (FLC); Right upper extremity (RUE); Left upper

extremity (LUE); Right lower extremity (RLE); Left lower extremity (LLE))8 -9. Action/postural tremor of hands (Right; Left)10 -14. Rigidity (Head/neck (H/N); RUE; LUE; RLE; LLE)15 -16. Finger taps (Right; Left)17 -18. Hand movements (Right; Left)19 -20. Rapid alternating movements of hands (Right; left)21 -22. Leg agility (Right; Left)23. Arising from chair 24. Posture25. Gait26. Postural stability27. Body bradykinesia and hypokinesia

Each item of the Motor Section is scored in one of five response categories. Thewording of the response categories is formulated differently for each item; however,

ordering of categories is invariant across the items. Categories (scores) are numberfrom zero to four and they are ordered increasingly. This means that the higher thecategory, the higher the value on the corresponding latent trait. In this context the terlatent trait expresses the hidden quality of symptoms such as rigidity, bradykinesitremor, et cetera, which are, in principle, measurable for any person: the level of alatent trait equals zero in case of absence of the corresponding symptom.

Within the MS UPDRS, main motor symptoms of PD (tremor, rigidity and

bradykinesia) and axial symptoms, such as speech, posture, postural stability and gadefine symptom groups as being evaluated according to their respective severity. Thesymptom groups are typically derived by using (statistical) scaling techniques. Previoresearch assessing the dimensionality of the MS UPDRS (Cubo et al., 2000; MartineMartin et al., 1994; Stebbins & Goetz, 1998; Stebbins et al., 1999) found between thrand six factors accounted for a proportion ranging from 59% to 78% of the total sca


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variance. However, all these studies used exploratory factor analysis (EFA), a scali procedure, which is explorative and relies on either strong assumptions concerning distribution of single variables or the number of observations or the level of statistic

measurement (Dunteman, 1989; Eliason, 1993). As will be discussed later, howevegiven the statistical properties of the indicators in the MS UPDRS, neither EFA nor somof the confirmatory factor analysis (CFA) estimators are the most appropriate scalitechniques, because the assumptions of the underlying statistical model may easily violated.

Instead of EFA, we used methods conforming to nonparametric item responsetheory (NIRT) and structural equation modeling (SEM). NIRT represent a family of statistical measurement models based on a minimal set of assumptions necessary toobtain useful measurements with the aim to order items or persons with respect to their latent trait value (Sijtsma & Molenaar, 2002). NIRT does not parametrically define thefunction describing the relation between the probability of a response in an item responcategory and the value on the latent trait. Since NIRT models are designed for ordinalmeasurement they are well suited for the purposes of the MS UPDRS. Comparing to NIRT, the extra feature of SEM is that it provides evaluation of structure of thesymptoms underlying Motor Section and therefore the conclusions about the co-

occurrence of the symptoms can be inferred.


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RESEARCH QUESTION

While previous studies assessed the dimensionality of the Motor Section of thUnified Parkinson's Disease Rating Scale (MS UPDRS) using inappropriate statisticmethods, the results of the number of concepts underlying the MS UPDRS cannot trustworthy. Further there is a necessity to determine the diagnostic quality of motor te(in the sense of validity and reliability) employed for clinical praxis of diagnosinParkinson's disease. In addition, the investigation of the relationships among the motsymptoms of Parkinson's disease is essential. Therefore the following scientific questiis addressed:

What kind of theoretical concepts and relationships among these conceptunderlie clinical motor tests diagnosing Parkinson's disease?

HYPOTHESES

H1: While the motor impairment of the Parkinson's syndrome is a complex systeof difficulties, it is assumed that the Motor Section of the Unified ParkinsonDisease Rating Scale will be multidimensional.

H2: It is assumed that the generic reliabilities of all dimensions of the MotoSection of the Unified Parkinson's Disease Rating Scale will be lower than thstandard requirements for such type of the motor tests, i.e. lower than 0.9.

H3: No difference of items' factor loadings for patients in on and off states assumed.


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METHODS

Structural Equation Modeling

Introduction

Structural equation modeling (SEM) is a statistical methodology that takes confirmatory (i.e. hypothesis-testing) approach to the analysis of a structural theo bearing on some phenomenon (Byrne, 2001). Kaplan (2000) defines SEM as a classmethodologies that seeks to represent hypotheses about the means, variances, ancovariances of observed data in terms of a smaller number of structural paramete

defined by a hypothesized underlying model. SEM is a parametric statisticamethodology and its the goal is to draw inferences to a large, but (usually) finit population based on estimates from a sample obtained from that population. SEM widely used by biologists, economist, educational researchers, marketing researchemedical researchers and a variety of social and behavioral scientists. It providresearchers with a comprehensive method for the quantification and testing of theoriOther major characteristic of SEM is that it explicitly takes into account the measuremeerror that is ubiquitous in most disciplines and that it can deal with latent variables.

The term structural equation modeling conveys two important aspects (Byrne,2001):

a) the processes under study are presented by a series of structural (i.e. regressioequations

b) these structural relations can be visualized graphically to enable a cleareconceptualization of the theory under study.The hypothesized model can be tested statistically in a simultaneous analysis o

the entire system of equations to determine the extent to which it is consistent with tdata. If the so-called goodness of fit is adequate, the plausibility of postulated relatioamong variables is enhanced; if it is inadequate, the tenability of such relations is rejec(Byrne, 2001).

Boomsma (2004) enumerates what SEM can and cannot provide:1) Allow multiple indicators of the same concept


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2) Estimate the nature of measurement error in observed variables3) Estimate relationships between concepts corrected for measurement error 4) Allow for correlated disturbances or measurement errors

5) Test the ability of an hypothesized model to account for the variances andcovariances among the observed variables

6) Compare the fit of different hypothesized models to the data7) Cannot prove causation8) Cannot establish that a model is true

Byrne (2001) formulated several aspects of SEM set it apart from the oldegeneration of multivariate procedures. First, it takes a confirmatory rather than aexploratory approach to the data analysis. Furthermore, by demanding that the pattern intervariable relations is specified a priori, SEM lends itself well to the analysis of dafor inferential purposes. By contrast, most other multivariate procedures are essentiadescriptive by nature (e.g. exploratory factor analysis), so that testing of hypothesesdifficult, if not impossible. Second, although traditional multivariate procedures aincapable of either assessing or correcting for measurement error, SEM provides expliestimates of these error variance parameters. Indeed, alternative methods (e.g. Gene

Linear Model) assume that error(s) in the explanatory (independent) variables vanishThus, applying those methods when there is error in the explanatory variables tantamount to ignoring error, which may lead to serious inaccuracies especially whthe errors are sizeable. Third, although data analyses using the former methods are bason observed measurements only, those using SEM procedures can incorporate bounobserved (i.e. latent) and observed variables. Finally, there are no widely and easapplied alternative methods for modeling multivariate relations, or for estimating poi

and/or interval indirect effects.From the historical point of view, SEM represents the hybrid of two separat

statistical traditions. The first tradition is factor analysis developed in the disciplines psychology and psychometrics. The origins of factor analysis can be traced to the workGalton and Pearson on the problem of inheritance of genetic traits. It is the work Spearman (1904), however, on the underlying structure of mental abilities that can


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credited with the development of the common factor model. Spearman's theoretic position was that the intercorrelations among tests of mental ability could be accountfor by a general ability factor common to all of the tests and specific ability facto

associated with each of the separate tests.In the 1930's attention shifted to the work of Thurstone and his colleagues at th

University of Chicago. According to Kaplan (2000), Thurstone argued that there did nexist one underlying general factor of ability accompanied by specific ability factors postulated by Spearman, but rather that there existed major group factors referred to primary mental abilities(Thurstone, 1935).

By the 1950s and 1960s factor analysis gained tremendous popularity, owinmuch to the development and refinement of statistical computing capacity. IndeeMulaik (1972) characterized this era as a time of agnostic and blind factor analysisHowever, during this era, developments in statistical factor analysis were also occurrinSpecifically, work by Jreskog (1967) and Lawley (1940) led to the development ofmaximum likelihood based approach to factor analysis. A generalized least squarapproach was developed later by Jreskog and Goldberger (1972). Developments researchers like Anderson and Rubin (1956) led to the methodology of confirmatofactor analysis that allowed for testing hypotheses regarding the number of factors a

the pattern of loadings.The second tradition is simultaneous equation modeling developed mainly i

econometrics, but having an early history in the field of genetics. The genetic origin SEM had its beginnings with the biometric work of Sewell Wright (1918; 1921). Wrighmajor contribution was in showing how the correlations among variables could be relatto the parameters of a model as represented by a path diagram a pictorial device thWright was credited with inventing. A second line of development occurred in the fie

of econometrics. The form of econometric modeling of relevance to SEM should credited to the work of Haavelmo (1943), who was interested in modeling thinterdependence among economic variables. This approach is known as simultaneoequation modeling.


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The combination of these two types of methodologies into the coherent analytiframework was based on the work of Jreskog (1970), Keesling (1972) and Wiley (197which, besides others, led to developing of LISREL model used in this study.

Types of SEM Models

Structural equation modeling (SEM), sometimes also labeled as Causal modelinLatent variable modeling, Covariance structure analysis, LISREL models, et(Boomsma, 2004), can be considered as an umbrella term of other more specifstatistical methods including Simultaneous equations (path analysis), Multivaria

regression, confirmatory factor analysis (CFA), etc.A number of members of the SEM family, however, may vary from study t

study. In accordance with Kelloway (1998), Raykov and Marcoulides (2000) as well with Kaplan (2000), the following classification is recommended:

Observed variable path analysis (or simply path analysis) Factor analysis (in SEM terminology measurement model) General structural equation models

Path Analysis Model

These models are usually conceived only in terms of observed variables. For threason, some researchers do not consider path analysis models to be typical SEM mode Nonetheless, path analysis is the important part of the historical development of SEM auses the same underlying idea of model fitting and testing and therefore should bincluded into the family of SEM. An example of a path analysis model is presented Figure 2.

Path analysis was derived to partition direct and indirect relationships amonvariables. It deals with dependency relationships among variables and uses multipregression as a method for estimating model parameters. Path models are presumed


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represent causal hypotheses. However, a significant path model does not imply causal(rather one can use the model to test for causality using experimental data).

Let p be the number of response variables andq the number of explanatory

variables. The system of structural equations representing the model in Figure 2 can written as

y = + y + x + ,

where is a p x 1 vector of observed response variables, is aq x 1 vector of observed

explanatory variables, is p x 1 vector of structural intercepts, is a p x p coefficient

matrix that relates response variables to each other, is a p x q coefficient matrix thatrelates response to explanatory variables, and is a p x 1 vector of disturbance terms

wherecov( ) = is the p x p covariance matrix of the disturbance terms. Finally let

cov( ) = be theq x q covariance matrix of the explanatory variables.

y x

x

Fig. 2. Example of path analytic model

Two general path analytic models can be distinguished: a) recursive, and bnonrecursive ones. A characteristic feature of recursive systems is that elements of acontained in the lower triangular part of . In addition, for recursive models, isdiagonal matrix whose elements are the variances of the disturbances. In nonrecursimodels a feedback loop between two response variables is specified. In other words, not lower triangular. Furthermore, it is typically the case that a covariance term

X2

X1

Y2

X3

e2 1

Y1 e1 1

Y3 1 e3


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specified between the disturbances among response variables in the feedback loop. Thmeans that is specified to be a symmetric matrix with nonzero off-diagonal elemen Nonrecursive models are referred to in the field of econometrics as simultaneous equati

models and have been widely used in economics to study problems such as supply ademand for certain commodities. The presence of feedback loops also implies aunderlying dynamic specification to the structural model insofar as some period of timerequired for the feedback to take place (Kaplan, 2000).

Assumptions of path analysis models are as follows ( Path analysis and structured linear equations, 2004):

Linear and additive relationships. In other words, path analysis excludecurvilinear and multiplicative models

Error terms are supposed to be uncorrelated with one another (except fononrecursive models)

Recursive models only one way causal flows Observed variables are measured without error

Confirmatory Factor Analysis (CFA) Model

The model used to relate observed measures to factors is thelinear factor analysismodel which can be written as

xx = + ,

where is q x 1 vector of observed responses onq questions that are assumed tomeasure respective latent variable, isq x k matrix of factor regression weights(usually called loadings),

x

x

is a k x 1 vector k latent variables and isq x 1 vector of

unique variables that contain both measurement error and specific error to be describ below.

It is convenient to evoke the assumptions that


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E () = 0 ,

E () = 0 ,

and

cov(, ) = 0 .

Under these assumptions, the covariance matrix of the observed data can bwritten in the form of the fundamental factor analytic equation,

cov E E = = +x x x x (xx ) ( ) ( ) = + ,

where is aq x q population covariance matrix, is a k x k matrix of factor variancesand covariances, and is aq x q diagonal matrix of unique variances.

Because the CFA model focuses solely on the link between factors and theimeasured variables, within the framework of SEM, it represents what has been termedmeasurement model (Byrne, 2001).

Structural Equation Models and LISREL Definition

There are several general structural equation models, for exampleCovarianceStructure Analysis(COSAN) developed by McDonald (1978; 1980), Reticular ActionModel (RAM) credited to McArdle (1980) and McArdle and McDonald (1984), Linear Equations(LINEQS) developed by Bentler and Weeks (1980); and Linear Structural Relationships(LISREL) first published by Jreskog (1973) but additionally credited tWiley (1973). All of them are very general and following this generality, McDona(1991) showed that RAM is the special case of COSAN and COSAN can be consideras a special case of RAM as well. Finally COSAN is a special case of LISREL. ThLISREL approach, which is used in this study, defines the structural equation model as

= + + ,


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The effects of non-normality on parameter estimates, standard errors, and tests model fit are well known. In general, simulation studies (e.g. Kline, 1998) suggest thunder conditions of severe non-normality of data, SEM parameter estimates are still fai

accurate but corresponding significance coefficients are too high. In contrast, standaerrors appear to be underestimated relative to the empirical standard deviation of testimates. Lack of multivariate normality usually inflates the value of the chi-squastatistic such that the overall chi-square fit statistic for the model as a whole substantially overestimated, and this overestimation appears to be related to the numbof degrees of freedom of the model (Boomsma, 1983).

The Satorra-Bentler adjusted chi-square are used for inference of exact structurfit when there is reason to think there is lack of multivariate normality. There are alother estimation methods than ML such as Weighted Least Squares (WLS) or DiagonaWeighted Least Squares (DWLS) which do not require the assumption of multivarianormality (see Bollen, 1989).

b) Linearity

SEM assumes linear relationships between indicator and latent variables, an

between latent variables. However, as with regression, it is possible to add exponentilogarithmic, or other nonlinear transformations of the original variable to the modThese transforms are added alone to model power effects or along with the originvariable to model a quadratic effect, with an unanalyzed correlation (curved doublheaded arrow) connecting them in the diagrammatic model. It is also possible (althounot without difficulties) to model quadratic and nonlinear effects of latent variable(Kline, 1998).

c) Sufficient sample size

Sample size should not be small since SEM is an asymptotic theory which impliethat the behaviour of parameter estimates and test statistics are known only for larsample sizes.


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One rule of thumb, is to have at least 15 cases per measured variable or indicat(Loehlin, 1992). Another rule of thumb found in the literature is that sample size shou be at least 50 more than 8 times the number of variables in the model (Kaplan, 200

Bentler and Chou (1987) recommend at least 5 cases per parameter estimate (includierror terms as well as path coefficients). The researcher should go beyond these minimusample size recommendations principally when data are non-normal (skewed, kurtotic)incomplete.

d) Absence of multicollinearity

Complete multicollinearity is assumed to be absent, but correlation among th

independents may be modeled explicitly in SEM (Structural equation modeling , 2005).Complete multicollinearity will result in singular covariance matrices, which are ones onwhich one cannot perform certain calculations (e.g. matrix inversion) because division zero will occur. Also, when the correlation coefficient (r ) is high, say ,multicollinearity is considered high and empirical underidentification may be a proble(Rindskopf, 1984). Even when a solution is possible, high multicollinearity decreases treliability of SEM estimates.

.85r

High multicollinearity might be suggested by values of standardized regressioweights greater than +1 and or less than -1 (Jreskog, 1999). Likewise, when there atwo nearly identical latent variables, and these two are used as causes of a third latevariable, the difficulty in computing separate regression weights may well be reflectedmuch larger standard errors for these paths than for other paths in the model, reflectihigh multicollinearity of the two nearly identical variables (Structural equation modeling ,2005). The same difficulty in computing separate regression weights may well breflected in high covariances of the parameter estimates for these paths - estimates muhigher than the covariances of parameter estimates for other paths in the model. Anotheffect of the multicollinearity may be negative error variance estimates.

Strategies for dealing with covariance matrices which are not positive defini(Structural equation modeling , 2005): Allow the LISREL program (Jreskog & Srbom,2004a) to add automatically aridge constant , which is a weight added to the diagonal of


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the covariance matrix (the ridge). This strategy can result in markedly different chsquare fit indexes, however. Other strategies include removing one or more highcorrelated items to reduce multicollinearity; using different starting values; usin

different reference items for the metrics of latent variables; or replacing tetrachorcorrelations with Pearsonian correlations in the input correlation matrix.

Types of Parameters Used in SEM Models

There are three types of model parameters that are important in conducting SEManalyses: All parameters that are supposed to be estimated by the program are common

referred to as free parameters. Parameters whose values that are set to a given constantare called fixed parameterssince they do not change value when the model is fit to theobserved data. Fixing parameters (usually to zero) is the way how to postulate the modThe other types of parameters are calledconstrained parameters(also referred to asrestricted or restrained ). Nonlinear constraint can also be specified. Models that includeconstrained parameters have parameters that are postulated to be equal to one another, their value is not specified in advance as is that of fixed parameters. Constraine parameters are typically included in a model if their restriction is derived from texisting theory or represents a substantively interesting hypothesis tested in a proposmodel (Kaplan, 2000).

Methods for Parameters Estimation

Generally, the aim of SEM is to reach as close a fit of the estimated covariancmatrix with the observed covariance matrix as possible (Urbnek, 2000). Thus, tsubstantive hypothesis of SEM can be expressed as

S = () ,


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where is the observed covariance matrix and is the population covarianc

matrix. This equation, however, is valid only if the model is so-called just identified . For overidentified models(that are in the scope of SEM) the solution which minimizes the so-

called lost-function or discrepancy function

S ()

E = S - ()

is desired. There are several estimation methods and types of discrepancy functions thare used in SEM programs like AMOS (Arbuckle, 2003), COSAN (McDonald & Fras1990), EQS (Bentler, 1995a), etc. The application of each estimation method is based

the minimization of a corresponding discrepancy function. The current version of tmost popular LISREL program (Jreskog & Srbom, 2005) provides the followinestimation methods:

a) Unweighted Least Squares (ULS)The simplest of all commonly used discrepancy functions. It can be expressed as

( )( )2

ULS

1F 2tr = S - ()

b) Generalized Least Squares (GLS)This function is given by following expression

( )( )21GLS 1F 2 tr = I S () ,

where I is unit matrix.

c) Maximum Likelihood (ML)This function is well known as a part of method of confirmatory factor analys

(Urbnek, 2000).


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( ) ( )1MLF ln lntr p q= + () S () S +

S

d) Weighted Least Squares (WLS)In both continuous and categorical cases, the approach to estimation under non

normality utilizes a class of discrepancy functions referred generally asWeighted Least Squares(WLS). The WLS discrepancy function can be written as

WLS F = -1(s - )W (s - ) ,

where andvech( )=s [ ]vech= ( ) are vectorized elements of S and

respectively

()

1. The matrixW is a consistent estimate of the asymptotic covariance matrixof s and must be positive definite.

e) Diagonally Weighted Least Squares (DWLS)

Let be an estimate of the asymptotic variance of . These estimates may b

used with a discrepancy function of the form

ghw ghs

DWLS F = 2gh gh gh (1/ w ) (s - )

Recently, the opinion of leader authors on SEM has shifted toward using DWLinstead of WLS for ordinal or categorical data, since using WLS requires for huge samsize and often led to problems with parameter estimates (negative error variances, etc.)

Which method of estimation should a researcher use? Some clues are given bJreskog and Srbom (2004b).

1 The vech() operator takes the( 1) / 2k k + nonredundant elements of thek k matrix and syringe theminto a vector of dimension[ ]( 1) / 2k k + 1.


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1. If the data are continuous and approximately follow a multivariate normadistribution, then the method of Maximum Likelihood is recommended.

2. If the data are continuous and approximately do not follow a multivariatnormal distribution and the sample size is not large, then the Robust MaximumLikelihood method is recommended. For larger sample sizes, the method of WeightLeast Squares is recommended. Both these methods will require an estimate of thasymptotic covariance matrix of the sample variances and covariances.

3. If the data are ordinal, categorical or mixed, then the Diagonally WeighteLeast Squares (DWLS) method for polychoric correlation matrices is recommended. Tmethod will require an estimate of the asymptotic covariance matrix of the sampcorrelations.

Note on Using Ordinal Variables in SEM

Observations on an ordinal variable represent responses to a set of orderecategories. It is only assumed that a person who selected a specific category has morethe characteristic than if he/she had chosen a lower category, but it is unknown how mumore. Ordinal variables do not have origins or units of measurement. Means, variancand covariances have no meaning (Jreskog & Srbom, 2004a). That is why othtechniques are employed for using ordinal variables in structural equation modeling.

For ordinal variable z it is assumed that there is an underlying continuous variable

which represents the attitude underlying the ordered responses to z and it is assumed

to have range from to . This continuous variable can be used in SEM (insteaof observed z) since it assigns a metric to the ordinal variable z. Polychoric correlations

reflect the relationships among ordinal variables assuming existence of .

* z + * z

* zAdvocation for using the polychoric correlations for ordinal data is based on th

work of Jreskog and Srbom (1988). In this simulation study the Phi, Spearman ranand Kendall tau-b correlations performed poorly, whereas the polychoric correlatio


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with ordinal data produced robust parameter estimates and better fitting modelFurthermore, Ethington (1987) determined that the Pearson correlation coefficieunderestimates the factor loadings of the ordinal variables and overestimates the ch

square values.One problem associated with the use of polychoric correlations is that th

polychoric correlation matrices do not ensure positive definiteness . This could be caus by sampling, outliers, or variable collinearity. One approach to correcting this problemto smooth the matrix using ridge constant (Wothke, 1992), which is implemented in tLISREL program. Another problem is that the polychoric correlation matrices genera provide inflated chi-square values and underestimated standard errors of estimates duelarger variability (Schumacker & Beyerlein, 2000).

The WLS or DWLS estimators are recommended for parameter estimations models where ordinal data are used (compare Jreskog and Srbom (1993) and (2004b Numerous simulation studies focused on the robustness properties of the WLS estimatIt was that WLS produce biased estimates for sample sizes less than 400 (Hooglan1999). Further, Muthn and Kaplan (1992) found that the WLS chi-square was markedsensitive to sample size and this sensitivity increased as the size of the model increaseIn addition, standard errors produced by WLS were noticeably downward biase

becoming worse as the model size increased (Kaplan, 2000).

Identification Problem in SEM

The general problem of identification is whether unique estimates of th parameters of the full model can be determined from the elements of the covarianmatrix of the observable variables. In this sense, there are three types of SEM mode

underidentified, just-identified, and overidentified.There are several rules for the identification of structural models. Here, only thet

rule is introduced. Interested readers are referred to Bollen (1989).The t rule says that one cannot estimate more parameters than there are uniqu

elements in the covariance matrix. This means that given thek covariance matrix(wherek is the number of observed variables), more than

k

( 1) / 2k k + parameters cannot


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be computed. Computing exactly ( 1) / 2k k + parameters results in just-identified

model, sometimes also referred to as saturated model (Medsker, Williams, & Holahan,1994). Such a model always provides an unique solution that is able to perfect

reproduce the covariance matrix. Saturated models have no statistical character atherefore are out of interest of the SEM.

When the number of unknowns exceeds the number of equations, the model said to beunderidentified . This is a problem since the model parameters cannot beuniquely estimated; there is no unique solution. In fact there are an infinite number solutions.

Finally, and most importantly, when the number of equations exceeds the numbe

of unknowns, the model is referred asoveridentified . When models are overidentified,there are a number of solutions to obtain unique estimate, and the task in moapplications of structural equation modeling techniques is to find the solution th provides the best fit to the data. Thus, besides the empirical identification problems, tidentification of structural equation model is purely a matter of the number of estimat parameters (Bollen, 1989).

Thet rule is a necessary but not a sufficient condition for model identification.

Model Testing and Fit Evaluation

Structural equation models are used to test a theory about relationships betweetheoretical concepts. A major aspect of model-fit evaluation involves the issue of thsubstantive considerations of the model. Specifically, all models considered in researshould be conceptualized according to the latest knowledge about the phenomenon undstudy (Raykov & Marcoulides, 2000).

Whereas classical methodology is typically interested in rejecting null hypotheseSEM is most concerned with finding a model that does not contradict the data. In othwords, when using SEM methodology one is usually interested in not rejecting the nuhypothesis. However, not rejecting a null hypothesis does not mean that it is truSimilarly, because model testing in SEM involves testing the null hypothesis that thmodel is capable of perfectly reproducing the analyzed matrix of observed variables, n


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rejecting a fitted model does not imply that it is the true model. Not rejecting a fittmodel can be due to incorrect specification of the model or due to sampling error. addition, just because a model fits the data well does not mean that it is the only mod

that fits the data well. As noted by Raykov and Marcoulides (2000), there are usuallynumber of models that fit the data equally well as the model under consideration interpretation. Which one of these models is better and which one is wrong can only decided on the basis of a sound body of knowledge about the studied phenomenon. Ocan also evaluate the validity of a proposed model by conducting replication studies (icross-validation). The value of a proposed model is greatly enhanced if the same modcan be replicated in new samples from the same population (Raykov & Marcoulide2000).

Chi-square statisticModel discrepancy is often expressed as the asymptotic chi-square test statisti

The value of the chi-square statistic should not be significant if there is a good model since a significant chi-square indicates lack of satisfactory model fit. That is, the chsquare statistic is a "badness-of-fit" measure in that a finding of significance means t

given model's covariance structure is significantly different from the observed covarianmatrix. If the corresponding p value is less than .05, the researcher's model is rejected.

There are three ways, listed below, in which the value of the chi-square tesstatistic may be misleading:

a) The more complex the model, the more the chi-square test statistic tends tindicate a good fit and therefore can mislead a researcher. In other words, the chi-squtest statistic tests the difference between the researcher's model and a just-identifie

version of it, so the closer the researcher's model is to being just-identified, the molikely good fit will be found. In a just-identified model, there will be always a perfect regardless the quality of a model.

b) The larger the sample size, the more likely the rejection of the model and thmore likely a Type II error (rejecting true hypothesis). In very large samples, even ti

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