Validating Wykoff's Model, Take 2: Equivalence tests and spatial analysis in a design-unbiased analytical framework Robert Froese, Ph.D., R.P.F. School of Forest Resources and Environmental Science Michigan Technological University, Houghton MI 49931 http://www.teresco.org/pics/signs/20010627/forest.jpg
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Robert Froese, Ph.D., R.P.F. School of Forest Resources and Environmental Science
Validating Wykoff's Model, Take 2: Equivalence tests and spatial analysis in a design-unbiased analytical framework. Robert Froese, Ph.D., R.P.F. School of Forest Resources and Environmental Science Michigan Technological University, Houghton MI 49931. - PowerPoint PPT Presentation
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Validating Wykoff's Model, Take 2:Equivalence tests and spatial analysis in a design-unbiased analytical framework
Robert Froese, Ph.D., R.P.F.School of Forest Resources and Environmental ScienceMichigan Technological University, Houghton MI 49931
• The model and the objectives• The region, the data and the approach• How well does Wykoff’s model predict?• Does Wykoff’s model pass a validation
test?• How does accuracy relate to model and
data structures• What does it mean for model users and
future revisions
This presentation has six parts
Introduction
Methods
Equivalence
Trends
Relevance
Performance
• The model and the objectives• The region, the data and the approach• How well does Wykoff’s model predict?• Does Wykoff’s model pass a validation
test?• How does accuracy relate to model and
data structures• What does it mean for model users and
future revisions
This presentation has six parts
Introduction
Methods
Equivalence
Trends
Relevance
Performance
• The model and the objectives• The region, the data and the approach• How well does Wykoff’s model predict?• Does Wykoff’s model pass a validation
test?• How does accuracy relate to model and
data structures• What does it mean for model users and
future revisions
This presentation has six parts
Introduction
Methods
Equivalence
Trends
Relevance
Performance
• The model and the objectives• The region, the data and the approach• How well does Wykoff’s model predict?• Does Wykoff’s model pass a validation
test?• How does accuracy relate to model and
data structures• What does it mean for model users and
future revisions
This presentation has six parts
Introduction
Methods
Equivalence
Trends
Relevance
Performance
• The model and the objectives• The region, the data and the approach• How well does Wykoff’s model predict?• Does Wykoff’s model pass a validation
test?• How does accuracy relate to model and
data structures?• What does it mean for model users and
future revisions
This presentation has six parts
Introduction
Methods
Equivalence
Trends
Relevance
Performance
• The model and the objectives• The region, the data and the approach• How well does Wykoff’s model predict?• Does Wykoff’s model pass a validation
test?• How does accuracy relate to model and
data structures• What does this mean for model users and
for future revisions?
Wykoff’s model predicts basal area increment but is used to project diameter
Introduction
Methods
Equivalence
Trends
Relevance
Performance
DDS = DBH2t+10 - DBH2
t
BAG = (π/4)·(DBH2t -
DBH2t-10)
DG = (DBH2 + DDS)0.5 - DBH
ln(DDS) = f(SIZE +SITE +COMP)
Wykoff’s model is a multiple linear regression on the logarithmic scale
( ) ( )( ) ( )
( ) 1001ln
sincos
lnln
12112
109
287
26543
2210
CCFbDBHBALbCRbCRb
ELbELbSLbSLbSLASPbSLASPb
DBHbDBHbbDDS
⋅++⋅+⋅+⋅+
⋅+⋅+⋅+⋅+⋅+⋅⋅+
⋅+⋅+=
• bi – coefficients estimated by ordinary least squares, of which:– b0 depends on habitat type and nearest National Forest
– b2 depends on nearest National Forest
– b12 depends on habitat type
This validation is focused on two notions
• Caswell (1976) introduces two ideas:– does a model user care if the internal structures are truthful, as long
as the model makes accurate predictions?– does the scientist care if the model makes accurate predictions, as
long as the model is useful for testing hypotheses about the underlying system?
• Robinson and Froese (2004) question how statistical tests are used for model validation– The usual null hypothesis is of no difference, or that a model is
valid, which seems unscientific– Arbitrarily small differences are detectable– A failure to reject may simply imply low power
This study had four objectivesand two perspectives
The objectives were:• to estimate model bias by species across the range of application;• to demonstrate a specific validation of Wykoff’s model for diameter
increment prediction through a test of equivalence;• to identify significant trends between bias and predictor variables,
and;• to evaluate spatial trends in bias across the geographic area to which
Prognosis is usually applied.
Two perspectives were taken regarding Wykoff’s model:• as a diameter increment model, and;• as it contributes to predictions of per hectare volume increment,
which is more intuitive or of more interest to many forest managers.
Forests that are equivalent have an obvious matrix of public and private land across elevation and geography
Wykoff’s model for prediction
• Equivalence tests provide an objective methodology for assessing model validity– There is added subjectivity in the selection of I
• For diameter, a large I would be necessary to validate Wykoff’s model– For most species I = 25% would have to be used– largely because of bias not two-one-sided CI
• For volume, the model is largely validated– But trends show bias is close to zero for average
conditions• Overprediction of > 3 mil m3•dec-1 is not insubstantial• Species results differ, and may imply invalid stand
dynamics
Introduction
Methods
Equivalence
Trends
Relevance
Performance
Wykoff’s model as a theory
• Wykoff’s model is surprisingly robust– These tests involve substantial extrapolation in time and
space
• Model improvements should focus on the way climate is represented– LOC as a proxy for regional climate– EL as a global parabolic function– Interactions with other predictors, like DBH2
– Static proxies or process variables?
• Other issues remain– Small trees
Summary
Wykoff’s model modestly over predicts diameter increment, but the effect on volume is smaller
Equivalence tests fail to validate the model for diameter increment, but less often for volume
As a theory, the model is surprisingly robust
The way climate is represented in the model needs to be addressed