LISREL: The short course

LISREL:The short course

Paul JoseNov. 8, 15, 22, 29

Victoria University

Okay, what are we going to do here today?

• Overview of SEM• Basic background on key statistical concepts (covariance)• Introduction to confirmatory factor analysis—how does CFA

fit into a systematic research plan?• Detailed example of a CFA-------------------------------------------------------------------------• Warning: I will at times be too technical, and at times I’ll be

too obvious and simple, but hopefully it will all work out.• Ask questions as I go. There are no stupid questions!• What do you want me to cover in the last session?• Homework? A prize for the best performance!

What is LISREL?• LISREL stands for “Linear structural relations”,

written by Karl Joreskog and Dag Sorbom. Now at version 8.51 (over 25 yrs.). Matrix-based.

• AMOS (Analysis of Moment Structures) is written by Arbuckle at Temple Univ., linked to SPSS. Diagrams.

• EQS (Equations) is written by Peter Bentler at UCLA. Equation-based.

• There are others: CALIS, RAMONA, LISCOMP, SEPATH.

• Which is the best? Tough question.

Okay, fine, but what do they do?

• They all can do SEM (structural equation modeling).

• That’s not all they can do, but that’s their main strength.

• What is SEM? There are a number of terms used somewhat interchangeably. They are:– Covariance structure analysis;– Causal modeling;– Analysis of covariance structures;– Model fitting

LISREL specifically can do for you . . .

• Confirmatory factor analysis• Observed variable path modeling• Latent variable path modeling• Longitudinal path modeling• Group comparisons on any parameter estimated in

any model (achieved through multi-group runs)• Whiter teeth, smarter kids, and the envy of your

neighbors

Confirmatory Factor Analysis• Why does one perform a CFA?• When does one perform a CFA?• How do I know if I have a good factor structure?• I hope that you didn’t answer “because they’re neat to run”;

“as often as possible”; and “if it looks good to me”; if you did, then you need to listen for the next hour or so.

• You should perform a CFA to make sure that you have a clear and reliable instrument.

• You should perform it before doing your main analyses.• There are a number of indicators from LISREL that

indicate that you have a “good-fitting model”

Suggested method for using a CFA

• Need to conduct a CFA after work has shown that a measure has a reliable factor structure.

• Do it first in measure development? I don’t recommend this.

• Two ways to do CFA:– Use author(s)’ factor structure from previous work;

and/or– Do the exploratory factor analysis yourself (if you have

sufficient sample size to divide into two equal sub-samples)

Overview of LISREL model • It’s all Greek to me!!!• Yes, it’s true, all parameters in the model are signified by

a particular Greek letter. • One does have to learn (re-learn) the names for each

peculiar squiggle because so much of the input and output of LISREL depends on knowing these associations.

• This model contains all possible parameters. Almost all models that you actually run are truncated versions of this one. (Observed variable models lack multiple indicators.)

Computations are performed on covariances

• What is a covariance? Definition please . . . .• If I told you that the covariance between stress and

social support coping in a sample of 1115 adolescents was –91.018, what would you think?

• If I told you that the correlation was -.33, what would you think?

• Covariancexy = (rxy) x (SDx) x (SDy)

• Correlationxy = (rxy) x (1) x (1)

Example of a covariance matrixCorrelations

1.000 -.333**. .000

385660.3 -101394

346.194 -91.0181115 1115-.333** 1.000.000 .

-101394 240697.8

-91.018 216.0661115 1115

Pearson CorrelationSig. (1-tailed)Sum of Squares andCross-productsCovarianceNPearson CorrelationSig. (1-tailed)Sum of Squares andCross-productsCovarianceN

EMUCH

SOCSS

EMUCH SOCSS

Correlation is significant at the 0.01 level(1-tailed).

**.

Descriptive Statistics

21.7822 18.6063 111583.9944 14.6992 1115

EMUCHSOCSS

Mean Std. Deviation N

Measurement model (CFA)

• Four key ingredients in a measurement model:– Number of latent variables (NK = number of ksi)– Pattern of factor loadings (PA LX gives the info of

whether a particular indicator loads on one ksi or another; stands for “pattern of lambda xs”

– Info about how latent variables relate to each other (PH matrix; phi matrix)

– Info about unique error in measured variables (TD or theta delta)

LISREL command language

• Many options:– Prelis: a preliminary data structuring program– Interactive mode (new, I’m not familiar with it)– Old style line commands (like old SPSS, etc.).

Sorry, but that’s the one I will teach

CFA command language

• Title line: anything that doesn’t start with any of the main command language abbreviations: DA; RA; SE; LA; MO; etc.

• DA: data line, specifies number of groups-NG; number of indicators-NI; number of observations-NO; type of matrix analyzed-MA

• RA: raw data, gives address for data file• LA: labels of all inputted variables• SE: selects some of the inputted vars, be sure to

finish with a backslash

More LISREL commands• MO: model line, number of X indicators-NX; number of

ksi’s-NK; lambda X matrix-LX; phi matrix-PH; theta delta matrix-TD; and other matrices

• PA LX: pattern of LX loadings• LK: label of ksi’s• PD: path diagram• OU: output• SS: standardized solutions for ksi’s• SC: completely standardized• AD: number of iterations

Values for variables

• Three types of specification of variable values:– Free (FR): allows the program to estimate this value for

you;– Fixed (FI): given a specific value, usually 1.0– Contrained (CO): used in multi-group runs when want

to compare the size of parameters between two samples on a single model

– Equalized (EQ): used in multi-group runs to equalize parameters to test one that is not equalized

Two factor modelConfirmatory Factor Analysis of the Buss-Perry Aggression Questionnaire:

Two-factor model

DA NG=1 NI=13 NO=172 MA=CM

RA FI=c:\WPfiles\data\lisrelfiles\bussdemo\buss.dat

la

gender va1 ho1 pa1 ho2 ang1 va2 ang2 pa2 va3 ho3 pa3 ang3

SE

pa1 pa2 pa3 va1 va2 va3/

MO NX=6 NK=2 LX=FU,FR PH=ST TD=DI,FR

PA LX

1 0

1 0

1 0

0 1

0 1

0 1

LK

Physical Verbal

PD

OU SS SC AD=50

Model comparison• One may wish to compare the fit of two different models

on the same dataset, for example a one-factor and a two-factor solutions to the Buss-Perry Agg. Questionnaire.

• Does a single factor yield a better fit than two separate factors?

• Compare them by doing two separate analyses; one specifying one factor, and the other specifying two factors.

• Logic of the comparison is that the chi-square statistic gives one a good sense of how well the model fits.

Model comparison chi-square df

BaselineModel 119.95 9

Two-factorModel 18.71 8

Difference 101.24 1---------------------------------------------------------------Look up whether this chi-square value is significant or not for 1

df. It is!

Model fit

• There are many occasions where one just wants to know whether a given model fits well for a given sample.

• Chi-square is typically used. Which direction? Large chi-sq (small p value) is bad; small chi-sq (large p value) is good. Can’t use strict p < .05. Chi-sq is susceptible to distortion due to sample size also.

• So who are you going to call?

Absolute and relative fit• Want to avoid overparameterization (too many) and

underpara-meterization (too few) in model.• Want chi-sq to be as small as possible, but affected

by sample size.• Want perfect fit AND parsimony—hard to have both.• There is no one “magic” fit index, although GFI is

most often used.• Absolute fit: measures whether the links are strong;

Relative fit: compares model to saturated model (see handout for specific indices).

• Want GFI > .90, RMSEA < .10, Critical N > 200

Do two samples show the same factor structure?

• It may occur that you have a large sample that is composed of two or more sub-samples (e.g., boys and girls), and you’re curious whether the model fits both groups equally well.

• Why care? Because it’s in your job description! No, it’s because you care whether a given measure is psychometrically reliable for whatever group you use it for. For example, Buss-Perry for boys and girls: do the four factors (verbal agg; physical agg; hostility; and anger exist in the same relationships with each other for both groups?

Multi-group runs

• So, how does one compare two groups? Before, one would typically do exploratory (or CFAs, if sophisticated) on both samples and eyeball the data.

• LISREL can compare the factor structure at several different levels through the use of multi-group runs. In essence, running two model-fitting analyses back-to-back in a single run.

3 types of measurement model comparisons

• Congeneric measurement model: the two groups should yield the same number and type of ksi’s.

• Tau-equivalent: the loadings on the ksi’s are generally equivalent (same # of ksi’s).

• Parallel measures: error variances are similar (in addition to loadings and ksi’s).