Dear all, 

I hope this is the right place to ask this question.

I am reviewing a research where the analyst(s) are using a linear regression model. The dependent variable (DV) is a continuous measure. The independent variables (IVs) are a mixture of linear and categorical variables.

The author investigates whether performance (DV - continuous linear) is a function of age (continuous IV1 - measured in years), previous performance (continuous IV2), country (categorical IV3 - six countries), the percentage of PhD graduates in each country (continuous IV4 - country level data - apparently only six different percentages since we have only six countries) and population of country (continuous IV5 - country level data - again only six numbers here, one for each country population).

My own opinion is that the lm function cannot be used with country level data as IVs (for example IV4 and IV5 cannot be entered into the model because they are country level data). If IV4 and IV5 are included in the model, it is possible that the model will not be able to be defined because we only have six countries and it is very likely that the levels of counties (IV3) may be confounding with IV4 and IV5. This also calls for multicollinearity issues, right? I would like to suggest to the analyst to use lmer using the IV3 as a random variable and  IV4 and IV5 as IV at the second level of the two-level model. 


The questions are: (a) Is it true that IV4 and IV5 cannot be entered in a one-level regression if we also have IV3?, (b) can I use an lm function to check for multicollinearity between IV3, IV4 and IV5?  and (c) If we use a two-level regression model, does lmer cope well with only six coutnries as a random effect?

Thank you for your help

Jason
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