11a_Bootstrapping.ppt 51KB Jan 10 2009 11:12:40 AM
Bootstrapping
James G. Anderson, Ph.D.
Purdue University
Introduction
• Bootstrapping is a statistical resampling
method.
• Bootstrapping can be used to obtain
empirical standard error estimates of
model parameters in addition to the
regular standard errors provided by the
AMOS output.
• Bootstrapping requires fairly large
samples.
Introduction
• Bootstrapping provides additional
standard errors for R2s, Indirect and Total
Effects, etc. not provided in the regular
AMOS output.
• Bootstrapping estimates are good even
when the assumptions of multivariate
normality are not met by the data.
• Bootstrapping can be used to compare
alternative models (see Example 20)
Types of Bootstrapping
• Nonparamertric – The sample of data is treated as a
psuedo-population. Cases from the original data file are
randomly selected with replacement to generate data
sets. When repeated many times (e.g., 500) this
procedure simulates the drawing of samples from a
population.
• Standard errors are estimated as the SD of the empirical
sampling distribution of the same estimator across all
generated samples.
• Nonparametric bootstrapping assumes only that the
sample distribution has the same basic shape as the
population distribution.
• A raw data file is necessary for nonparametric
bootstrapping.
Types of Bootstrapping
• Parametric Bootstrapping – The computer
draws random samples from a probability
density function with parameters specified
by the researcher.
• Similar to the Monte Carlo method used in
computer simulation studies of the
properties of particular estimators used in
SEM to measure the fit of the model.
1
spatial
visperc
cubes
lozenges
1
verbal
paragraph
sentence
wordmean
1
1
1
1
1
1
err_v
err_c
err_l
err_p
err_s
err_w
Example 19: Bootstrapping
Holzinger and Swineford (1939) Girls' sample
Model Specification
Procedures
•
•
•
•
Click on Analysis Properties
Go to the Bootstrap tab
Check the box for Perform Bootstrap
Enter 500 in the Number of Bootstrap
Samples
Results of the Analysis
• The unstandardized parameter estimates
for the model are the same as for Example
8.
• The model fit is the same as for Example
8.
– Chi Square = 7.853
– Degrees of Freedom = 8
– Probability Level = 0.448
Bootstrap Estimates of Standard Errors
Regression.
Weights
SE
Bootstrap
SE/SE
Mean
Bias
SE
Bias
Visperc –
Spatial
0.000
0.000
1.000
0.000
0.000
Cubes –
Spatial
0.140
0.004
0.609
-0.001
0.006
LozengesSpatial
0.373
0.012
1.216
0.018
0.017
Paragraph -Verbal
0.000
0.000
1.000
0.000
0.000
Sentence –
Verbal
0.176
0.006
1.345
0.011
0.008
Wordmean –
0.254
0.008
2.246
0.011
0.011
Verbal
Maximum Likelihood and Bootstrap
Estimates of Standard Errors
Regression.
Weights
SE/ML
SE/Bootstrap
Estimate
Parameter/
ML Estimate
Parameter/
Bootstrap
Estimate
Visperc -- Spatial
0.000
0.000
1.000
1.000
Cubes –
Spatial
0.143
0.140
0.610
0.609
LozengesSpatial
0.272
0.373
1.198
1.216
Paragraph -Verbal
0.000
0.000
1.000
1.000
Sentence –
Verbal
0.160
0.176
1.334
1.345
Wordmean –
0.263
0.254
2.234
2.246
Verbal
James G. Anderson, Ph.D.
Purdue University
Introduction
• Bootstrapping is a statistical resampling
method.
• Bootstrapping can be used to obtain
empirical standard error estimates of
model parameters in addition to the
regular standard errors provided by the
AMOS output.
• Bootstrapping requires fairly large
samples.
Introduction
• Bootstrapping provides additional
standard errors for R2s, Indirect and Total
Effects, etc. not provided in the regular
AMOS output.
• Bootstrapping estimates are good even
when the assumptions of multivariate
normality are not met by the data.
• Bootstrapping can be used to compare
alternative models (see Example 20)
Types of Bootstrapping
• Nonparamertric – The sample of data is treated as a
psuedo-population. Cases from the original data file are
randomly selected with replacement to generate data
sets. When repeated many times (e.g., 500) this
procedure simulates the drawing of samples from a
population.
• Standard errors are estimated as the SD of the empirical
sampling distribution of the same estimator across all
generated samples.
• Nonparametric bootstrapping assumes only that the
sample distribution has the same basic shape as the
population distribution.
• A raw data file is necessary for nonparametric
bootstrapping.
Types of Bootstrapping
• Parametric Bootstrapping – The computer
draws random samples from a probability
density function with parameters specified
by the researcher.
• Similar to the Monte Carlo method used in
computer simulation studies of the
properties of particular estimators used in
SEM to measure the fit of the model.
1
spatial
visperc
cubes
lozenges
1
verbal
paragraph
sentence
wordmean
1
1
1
1
1
1
err_v
err_c
err_l
err_p
err_s
err_w
Example 19: Bootstrapping
Holzinger and Swineford (1939) Girls' sample
Model Specification
Procedures
•
•
•
•
Click on Analysis Properties
Go to the Bootstrap tab
Check the box for Perform Bootstrap
Enter 500 in the Number of Bootstrap
Samples
Results of the Analysis
• The unstandardized parameter estimates
for the model are the same as for Example
8.
• The model fit is the same as for Example
8.
– Chi Square = 7.853
– Degrees of Freedom = 8
– Probability Level = 0.448
Bootstrap Estimates of Standard Errors
Regression.
Weights
SE
Bootstrap
SE/SE
Mean
Bias
SE
Bias
Visperc –
Spatial
0.000
0.000
1.000
0.000
0.000
Cubes –
Spatial
0.140
0.004
0.609
-0.001
0.006
LozengesSpatial
0.373
0.012
1.216
0.018
0.017
Paragraph -Verbal
0.000
0.000
1.000
0.000
0.000
Sentence –
Verbal
0.176
0.006
1.345
0.011
0.008
Wordmean –
0.254
0.008
2.246
0.011
0.011
Verbal
Maximum Likelihood and Bootstrap
Estimates of Standard Errors
Regression.
Weights
SE/ML
SE/Bootstrap
Estimate
Parameter/
ML Estimate
Parameter/
Bootstrap
Estimate
Visperc -- Spatial
0.000
0.000
1.000
1.000
Cubes –
Spatial
0.143
0.140
0.610
0.609
LozengesSpatial
0.272
0.373
1.198
1.216
Paragraph -Verbal
0.000
0.000
1.000
1.000
Sentence –
Verbal
0.160
0.176
1.334
1.345
Wordmean –
0.263
0.254
2.234
2.246
Verbal