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i want to see if different dummy variables are capturing significanly different effects from one another so i am running LR tests in which two (of the 4) dummies independent variables are merged in the restricted model.

the unrestricted model is something like: y= d1+d2+d3+d4+ othercontrols

i then command: gen d12= (d1+d2)

and then have the restricted model of: y= d12+d3+d4+ othercontrols

My question is, does this count as nesting even though i have not technically removed any variable from the regression (only merged them)? if so and my LR test is fine, how would i then interpret reusults?

Thank you!

Tom Witten
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1 Answers1

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Yes, these are nested models: Nested models occur when one model is a special case of the other, under particular restrictions on the model parameters of the more general model. Focusing on just the part you are changing, you have:

$$\begin{matrix} \text{General Model} & & & y_i = \beta_1 d_1 + \beta_2 d_2 + \cdots \\[6pt] \text{Restricted Model} & & & y_i = \beta_* (d_1 + d_2) + \cdots \\[6pt] \end{matrix}$$

The restricted model is a special case of the general model, where we have effectively imposed the parameter restriction $\beta_1=\beta_2$ (and we have denoted this common parameter as $\beta_*$).

Ben
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