I have a generic question about whether it might sometimes make sense to fix specific regression coefficients to predetermined values. And if this makes sense in particular cases, how do you best go about it?
In my case, I have about 1,600 observations but I am interested chiefly in a variable for which about 600 observations are missing. If I run a normal regression (OLS,GLS,CLM) all the variables that have missing values are dropped, and I am wondering whether it is possible to "save" all the observations to determine the coefficients for the variables for which I have full information, and then run a separate regression to determine the coefficients of the variables with all the missing values.
In simple formulas it looks about like this:
x1,x2,x3,x4 I have 1,600 observations
glm.core <- glm(y ~ x1 + x2 + x3 + x4) # determine the coefficients in the regression beta <- glm.core$coef
z2 I only have a 1,000 observations
glm.main <- glm(y ~ beta*x1 + beta*x2 + beta*x3 + beta*x4 + z1 + z2)
So I want to predetermine the betas for which I have full information and then fix their values in the main regression. (Maybe this is a completely pointless idea and if so please tell me)
I know something like that can be achieved with
offset BUT this does not work for factor variables and
x3 are factors (
x2 has values 'university', 'firm', 'government', and
x3 has values 'known' , 'unknown', 'not relevant').
Is an alternative to solving this problem to reduce the response variable
ywith the fitted values of the
glm.coremodel and run the regression like that?
If this is a sensible option
- What happens to the errors?
- How to calculate degrees of freedom?
- Would this work as well with ordered logit (CLM) models where the fitted values are percentages?
Are there better ways of dealing with this problem?
PS: I am using R software, forgot to mention this initially...