TITLE: RELIABILITY ESTIMATION AFTER REVISION (COMPARE WITH APPENDIX 3)
(MODIFY THIS COMMAND FILE IF MORE THAN 1 COMPONENT IS TO BE DELETED/ADDED TO A TENTATIVE SCALE VERSION. BELOW, S < R IS ASSUMED, SPECIFICALLY S = R-1). THIS CODE ALSO PROVIDES 95%- AND 99%-CI FOR RELIABILTY CHANGE DUE TO REVISION (IN CI FOR THE D).
DATA: FILE = ;
VARIABLE: NAMES = U1-UR;
MODEL: F BY U1*(B_1)
U2-UR (B_2-B_R);
U1-UR (THETA_1-THETA_R);
F@1;
MODEL CONSTRAINT:
NEW(R_UA, R_UB, D); ! PLACE-HOLDERS FOR RELIABILITY OF U_A, UB, D.
R_UA =(B_1+B_2+
+B_S)**2/
((B_1+B_2+
+B_S)**2+THETA_1+THETA_2+
+THETA_S); ! WRITE FULLY OUT
R_UB =(B_1+B_2+
+B_R)**2/
((B_1+B_2+
+B_R)**2+THETA_1+THETA_2+
+THETA_R); ! WRITE FULLY OUT
D = R_UA R_UB; ! RELIABILITY CHANGE DUE TO REVISION.
OUTPUT: CINTERVAL; ! REQUESTING CI OF D.
Note. With deviations from normality (not resulting from ceiling/floor effects, clustering effects, or highly discrete components), add the line ANALYSIS: ESTIMATOR = MLR; in order to invoke the robust ML method of estimation. (See Note to Mplus command file in Appendix 3 for variable names and evaluation of reliability before revision.) To obtain a CI for scale reliability after revision, call the R-function ci.rel in Appendix 3, using as its arguments the pertinent scale reliability estimate (before and after revision) and its standard error obtained with this Mplus command file. Check output section on confidence intervals, for the one of the change D in reliability due to revision, at confidence levels 95% and 99%. (If a different confidence level is to be used, compute the CI for D by adding and subtracting its large-sample standard error produced by Mplus via the delta-method, multiplied by the pertinent quantile of the standard normal distribution.)