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Bootstrapping

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.

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Bootstrapping

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  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 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)

  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.

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

  7. 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

  8. Bootstrap Estimates of Standard Errors

  9. Maximum Likelihood and Bootstrap Estimates of Standard Errors

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