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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