Question on linear regression coefficient interpretation

[Asli Mert]

Hello,

I have a question on interpreting the coefficients of multiple regressions. Can the coefficient of an independent variable in a multiple regression model be greater than the dependent variable units? E.g. if my dep. var. is categorical (10 scale), does it make sense if one of the coefficients in the model is 12.35 (statistically significant), and if so, how? Because how could a one unit increase in a predictor variable could increase the outcome var. by 12 points if there are 10 points in total? To make my question more clear, I’m trying to predict how research productivity (dep. var.) is affected by various predictor variables including having children. 1 is productivity least affected and 10 is most affected. The coefficient for having children (rather than not having any) is 12.35, which means that having children increases the reported negative impact on research productivity by 12.35 points, keeping other variables constant. What I’m wondering is, how could productivity be increased by 12 points if the maximum no. of units in the dep. var. is 10?

Thank you!

[Carlo Lazzaro]

Asli:
I'm a bit queasy about the appropriateness of OLS for a multilevel categorical regressand like the one you describe. I'd give -mlogit-a shot.
In addition, as per FAQ, please post what you typed and what Stata gave you back (via CODE delimiters, please). Thanks.
This approach is much more helpful than tons of words.

[George Ford]

As Carlo says, the categorical outcome does not suit OLS assumptions.

Also, the coef in linear regression depends on the scale of the x variable.

[Clyde Schechter]

Use of a simple linear model when the outcome has a limited range can be problematic. For example, although some linear probability models work very well, others end up predicting probabilities outside the 0 to 1 range when given realistic values of the predictor variables. In your case, you have a linear model where a dichotomous 0/1 variable is said to be associated with a 12.35 point increase in the outcome when it goes from 0 to 1, when the complete range of the outcome variable is 0 to 10. That is clearly not a good model.

While this model might possibly be saved by adding additional variables, or perhaps by removing some of the other variables already there, you are probably better off abandoning it. I would try an ordinal logistic regression (-ologit-) for this one. The logit link inherently squashes down extreme effects. While these -ologit- models are less intuitive than the linear model you used, I think you have demonstrated that this particular outcome variable simply does not lend itself to face-valid modeling by a simple linear predictor.

[Asli Mert]

Thank you very much for all your help and comments. After reading your replies and working further on the model, I decided not to proceed with OLS as I noticed further issues as well. Many thanks again!