# Wald test to compare equality of regression weights (MR) - correct for multiple testing?

Suppose I have a linear regression with 5 predictors (x1 to X5) and 1 outcome (y).

I want to see whether the effects of X1 to X5 on Y differ between boys and girls.

A possible answer may be: the effects of X1, X3 and X5 on Y are similar between boys and girls, but the effect of X2 on Y is stronger for girls, and the effect of X5 is nonsignificant for girls, and significant for boys.

Now first I tested whether the model with X1 to X5 constrained to be the same between boys and girls, differs from the model where X1 to X5 are freely estimated. The model with paths freely estimated are better than the model in which the paths are the same.

I know I can now use wald test to see if X1[boys] = X1[girls] etc. However, becuase I have 5 predictors, this results in at least 5 wald tests. Is there a correction for multiple testing, and if so, sould I apply it, and if so, how can I do that?

I normally do a single Wald test with 5 df, which is the omnibus test, if that is significant I then run five individual 1 df individual tests. That provides some protection against type I errors.

For the 5 df test, you would use:

Model test:
b1 = g1;
b2 = g2;
b3 = g3;
b4 = g4;
b5 = g5;


If that is significant, the look at the 5 individual tests.

Model test:
b1 = g1;

Model test:
b2 = g2;


Etc.

• Please excuse my ignorance, I am not very familar with these types of models, nor with Mplus. Am I correct to understand that the "omnibus test" may be similar to what I discribed (i.e., compare completely constrained to model with 5 effects free), but using Wald instead of log-likelihood difference (I use MLR so no chi square)? Second, what do you mean by "five individual 1 df tests"? Is this the same as doing [[Model test: b1 = g1]] then doing [[model test: b2 = g2]] ... [[Model test: b5 = g5]]? If not, could you point me in the right direction? – GerineL Dec 8 '14 at 22:00
• Yes, I misread your question, sorry. I think that gives you enough protection. – Jeremy Miles Dec 8 '14 at 22:41