TY - JOUR
T1 - A Bayesian Significance Test for the Difference and Linear Combination of Factor Means between Groups
AU - Hoshino, Takahiro
AU - Hashimoto, Takamitsu
AU - Shigemasu, Kazuo
PY - 2001
Y1 - 2001
N2 - The present article proposes Bayesian inference for multiple group factor analysis, via a Gibbs sampling algorithm. When this method is used, a significance test for the difference of factor means between groups and a test for linear contrast can be done to determine whether a point hypothesis is in the Bayesian canfidemce interval of the posterior distribution. Baysian inference is not used in research in educational psychology because of its arbitrariness in the selection of the prior distribution. However, all the methods described in the present article can be done with a noninformative prior distribution, thus excluding subjectivity. As a result, researchers will be able to use Bayesian inference easily and objectively. In order to compare the proposed method with a x2 asymptotic likelihood test in terms of their respective power, 1400 simulation data sets for N = 160 and N = 80 were generated. The proposed method has some advantages over the x2 test in that control of Type-1 errors is complete with small-sized samples, and also in that the Haywood case problem does not occur. The proposed method was used to analyze the relationship of age and intelligence as measured by the WAIS-R, and a composite hypothesis was evaluated.
AB - The present article proposes Bayesian inference for multiple group factor analysis, via a Gibbs sampling algorithm. When this method is used, a significance test for the difference of factor means between groups and a test for linear contrast can be done to determine whether a point hypothesis is in the Bayesian canfidemce interval of the posterior distribution. Baysian inference is not used in research in educational psychology because of its arbitrariness in the selection of the prior distribution. However, all the methods described in the present article can be done with a noninformative prior distribution, thus excluding subjectivity. As a result, researchers will be able to use Bayesian inference easily and objectively. In order to compare the proposed method with a x2 asymptotic likelihood test in terms of their respective power, 1400 simulation data sets for N = 160 and N = 80 were generated. The proposed method has some advantages over the x2 test in that control of Type-1 errors is complete with small-sized samples, and also in that the Haywood case problem does not occur. The proposed method was used to analyze the relationship of age and intelligence as measured by the WAIS-R, and a composite hypothesis was evaluated.
KW - Bayesian inference
KW - Difference between groups
KW - Multiple groups
KW - Significance test
KW - Structural equation modeling
UR - http://www.scopus.com/inward/record.url?scp=0035632401&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0035632401&partnerID=8YFLogxK
U2 - 10.5926/jjep1953.49.1_31
DO - 10.5926/jjep1953.49.1_31
M3 - Article
AN - SCOPUS:0035632401
VL - 49
SP - 31
EP - 40
JO - Japanese Journal of Educational Psychology
JF - Japanese Journal of Educational Psychology
SN - 0021-5015
IS - 1
ER -