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Research with Diverse GroupsResearch Designs and Multivariate Latent Modeling for Equivalence$

Antoinette Y. Farmer and G. Lawrence Farmer

Print publication date: 2014

Print ISBN-13: 9780199914364

Published to Oxford Scholarship Online: June 2014

DOI: 10.1093/acprof:oso/9780199914364.001.0001

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(p.93) Appendix A Chi-Square Difference Testing Using the Satorra-Bentler Scaled Chi-Square: Hispanic and African American Males

(p.93) Appendix A Chi-Square Difference Testing Using the Satorra-Bentler Scaled Chi-Square: Hispanic and African American Males

Source:
Research with Diverse Groups
Publisher:
Oxford University Press

Dr. Scott Colwell from the University of Guelph has developed a web-based calculator that will perform these calculations (See http://www.uoguelph.ca/~scolwell/qmlinks2.html). The calculations and instructions presented are based on the information found on the Mplus website (http://statmodel.com/chidiff.shtml).

  1. 1. Difference in test scaling correction cd.

cd = ((d0 * c0) − (d1 * c1))/(d0 − d1); d0 = df in the nested model. c0 = scaling factor for the nested model. d1 = df in the comparisons model, and c1 = scaling correction for the comparison model.

cd = ((34 * 1.414) − (32 * 1.374))/(34 − 32) = 2.054 (p.94)

  1. 2. Compute the MLR scaled chi-square difference test.

  2. T0 = MLR chi-square values for the nested model. T1 = MLR chi-square values for the comparison model.

ΔMLR χ2(Δdf) = ((T0 * c0) – (T1 * c1))/cd

ΔMLR χ2(2) = ((82.30 * 1.414) − (56.44 * 1.374))/2.054

ΔMLR χ2(2) =18.90, p <.01

Establishing the Base CFA Model Hispanic and African American Females

  1. 1. Difference in test scaling correction cd.

cd = ((34 * 1.281) − (31 * 1.22))/(34 − 31) = 1.92

  1. 2. Compute the MLR scaled chi-square difference test.

  • T0 = MLR chi-square values for the nested model. T1 = MLR chi-square values for the comparison model.

ΔMLR χ2(ΔNewdf) = ((T0 * c0) − (T1 * c1))/cd

ΔMLR χ2(3) = ((91.98 * 1.281) − (42.68 * 1.22))/1.92

ΔMLR χ2(3) = 34.25, p <.01