1. Bootstrapping James G. Anderson, Ph.D. Purdue University

2. 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.

3. Introduction Bootstrapping provides additional standard errors for R 2 s, 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)

4. 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.

5. 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.

7. Procedures Click on Analysis Properties Go to the Bootstrap tab Check the box for Perform Bootstrap Enter 500 in the Number of Bootstrap Samples

8. 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

9. Bootstrap Estimates of Standard Errors Regression. Weights SE Bootstrap SE/SEMeanBiasSE Bias Visperc – Spatial 0.000 1.0000.000 Cubes – Spatial 0.1400.0040.609-0.0010.006 Lozenges- Spatial 0.3730.0121.2160.0180.017 Paragraph -- Verbal 0.000 1.0000.000 Sentence – Verbal 0.1760.0061.3450.0110.008 Wordmean – Verbal 0.2540.0082.2460.011

10. Maximum Likelihood and Bootstrap Estimates of Standard Errors Regression. Weights SE/MLSE/Bootstrap Estimate Parameter/ ML Estimate Parameter/ Bootstrap Estimate Visperc -- Spatial0.000 1.000 Cubes – Spatial 0.1430.1400.6100.609 Lozenges- Spatial 0.2720.3731.1981.216 Paragraph -- Verbal 0.000 1.000 Sentence – Verbal 0.1600.1761.3341.345 Wordmean – Verbal 0.2630.2542.2342.246