Constraining effects to be equal PreviousNext
Mplus Discussion > Structural Equation Modeling >
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 koen ponnet posted on Wednesday, June 08, 2011 - 6:33 am
Dear,

I am analysing couple data, in which fathers as well as mothers rated their depression (depfath and depmoth) and responsive parenting style (respfath and respmoth).
Iím interested in the influence of depression on parenting style, and whether the strength of the pathways is similar for both mothers and fathers.

After an initial model without equality constraints (in mplus):
Respfath on depfath;
Respmoth on depmoth;
The model showed a significant negative effect between mothersí depression and parenting (beta = -.20, p < .05), and a positive effect between fathersí depression and parenting (beta = .08, ns).

To test for gender differences, I constrained the effects to be equal.
Respfath on depfath (1);
Respmoth on depmoth (1);

The chisquare difference test revealed no significant difference. In other words, the strength of the effects of depression on parenting are similar for mothers and fathers, with b = -.07, ns.

My questions are:
(a)is it allowed to constrain the effects to be equal in case that the first path is positive and the other path is negative, (in other words: does it make sense?)
(b)if so, is it still opportune to report the non-significant b=-.07 (after constraining the paths)?

Can someone help me and/or refer to a manuscript?

Thanks in advance,
Koen
 Bengt O. Muthen posted on Wednesday, June 08, 2011 - 8:17 am
I think your analyses are fine and it is informative to report your analysis sequence as you described it: In an unrestricted analysis the mother's effect is significant negative, but it is not significanty different from the father's effect.
 koen ponnet posted on Tuesday, June 14, 2011 - 3:19 am
Dear dr. Muthen,

Thank you very much for the answer.
I still have a little question. Is it allowed to use a chi-square difference test in case of a small sample size (n=224), and/or what is the drawback of small sample size when using equality constraints (with ML)?

Best regards,
koen
 Linda K. Muthen posted on Tuesday, June 14, 2011 - 2:30 pm
I would say the lack of power is a big issue with small samples.
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