Premium
Detecting patterns of bivariate mean vectors using model‐selection criteria
Author(s) -
Huang ChuenChuen Joyce,
Dayton C. Mitchell
Publication year - 1995
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1995.tb01054.x
Subject(s) - akaike information criterion , bivariate analysis , mathematics , kurtosis , statistics , skewness , homogeneous , normality , model selection , selection (genetic algorithm) , econometrics , computer science , artificial intelligence , combinatorics
Three model‐selection criteria, (1) AIC (Akaike, 1973), (2) SIC (Schwarz, 1978), and (3) CAIC (Bozdogan, 1987), were evaluated for detecting patterns of differences among mean vectors with bivariate data. This simulation study involved three and five group cases with equal‐sized samples of 10, 20 and 50. Ten different distributions, including situations with extreme skewness and kurtosis, were generated to assess the robustness of the criteria with respect to non‐normality. Both homogeneous and heterogeneous covariances cases were examined. The three model‐selection criteria were compared in terms of correct decision rates based on 500 replications for each condition studied. Results indicate that all three criteria are relatively robust with respect to non‐normality. SIC and CAIC performed especially well for large sample sizes when the true model contained only one or two clusters of homogeneous mean vectors. Overall, AIC tended to be superior to SIC and CAIC for homogeneous cases when the null case was excluded and, in general, for heterogeneous cases.