Bootstrapping
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.
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.
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.
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
spatial
Example 19: Bootstrapping
Procedures
• Click on Analysis Properties
• Go to the Bootstrap tab
• Check the box for Perform Bootstrap
• Enter 500 in the Number of Bootstrap
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
Bootstrap Estimates of Standard Errors
Regression.
Weights SE Bootstrap SE/SE Mean Bias SEBias
Visperc – Spatial
0.000 0.000 1.000 0.000 0.000
Cubes – Spatial
0.140 0.004 0.609 -0.001 0.006
Lozenges-Spatial
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 – Verbal
Maximum Likelihood and Bootstrap
Estimates of Standard Errors
Regression.
Weights SE/ML SE/BootstrapEstimate 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
Lozenges-Spatial
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 – Verbal
