Covariances Constrained to the Variance of the Intercept

[dessert_fox]

I estimated an OLS regression using this equation:

Y = Bo + B1PhaseSetting1 + B2PhaseSetting2 + ei

where Setting is dummy coded.

I ran a proc reg and requested for covariances of Bo, B1(Setting1's effect), and B2 (Setting2's effect), and I got weird results

where the covariances of Bo & B1, and Bo & B2, and B1 & B2 were all the same as the variance of Bo.

Does anyone know why is this happening?

Thanks,

Rommel

[1zmm]

If Setting is a dichotomous variable, and if PhaseSetting1 and PhaseSetting2 are the names of the two dummy-coded values of Setting, then a situation like what your are describing could happen:

       Setting                      PhaseSetting1       PhaseSetting2

            1                                   1                           0

            2                                   0                           1

Use either PhaseSetting1 or PhaseSetting2 but NOT both as independent variables in your regression.  Otherwise, PhaseSetting1 and PhaseSetting2 are collinear.

[dessert_fox]

I'm curious are you doing something related to multilevel meta-analysis with single-case experimental designs? I used dummy codes ( and did exactly what you suggested) and what happened is that when I included both PhaseSetting1 and PhaseSetting2 in the regression I had that problem I described. So are you saying I should run a simple regression one at a time?

Thanks,

Rommel

[1zmm]

Without seeing what your code was for your multilevel meta-analysis, I can't answer your question.  However, in ordinary least-squares regression, including both PhaseSetting1 and PhaseSetting2 as indicator ("dummy") variables coded from the original dichotomous variable, Setting, in the way I described could have caused the problem you originally described, "Covariances constrained to the variance of the intercept", because of collinearity.

In multi-level analysis, the models at each level are usually considered distinct, though they are combined to allow the program (for example, PROC MIXED or PROC GLIMMIX) to estimate the parameters for these models.  If an independent variable on one level were collinear with another independent variable on another level, I think that the collinearity would also show up; but, although plausible, I haven't checked whether this is true.

[dessert_fox]

Thank you so much for your helpful comment.

Rommel