Fit of Responses to the Model II—Analysis of Residuals and General Principles

Abstract

The residual is the difference between a person’s response to an item and the response that is expected according to the model. When it is referenced to its standard deviation, it is a standardized residual. The residual distributions produced in RUMM2030 can be helpful in interpreting residuals. Correlations between item residuals can be helpful in determining whether pairs of items have more in common than they have in common with other items. A Principal Component Analysis (PCA) of residuals examines patterns in the residuals to show which subsets of items have something more in common than is accounted for by the single variable. A person or item fit-residual statistic can be calculated from the standardized residuals to assess the person or item fit, respectively. The Bonferroni correction is an adjustment to the significance level (of a fit statistic) to reduce the risk of a type I error. It is necessary to have a range of person locations in order for there to be some power in the test of fit.

Exercises

• Exercise 2: Basic analysis of dichotomous andpolytomousresponses in Appendix C.

• Exercise 3: Advanced analysis of dichotomous responses Part A in Appendix C.

• Exercise 6: Analysis of data with dependence in Appendix C.