Specifying formula of lmer() function in R .

#1
Am I specifying my lmer model correctly ?

Say I have one independent variable (X) at individual level and one independent variable (Z) at group level. Both are continuous variable . If the model is

\(Y_{ij}=\gamma_{00}+\gamma_{10}X_{ij}+\gamma_{01}Z_{j}+\gamma_{11}X_{ij}Z_{j}+u_{1j}X_{ij}+u_{0j}+e_{ij}\)

where \(Y_{ij}\) is the score of individual \(i\) in group \(j\) on the dependent variable ;

\(X_{ij}\) is the score of individual \(i\) in group \(j\) on the independent variable on the individual level ;

\(Z_{j}\) is the score of group \(j\) on the independent variable on the group level ;

\(\gamma_{00}\) is the general intercept ;

\(\gamma_{10}\) is the regression coefficient of the direct effect of \(X_{ij}\) on \(Y_{ij}\) ;

\(\gamma_{01}\) is the regression coefficient of the effect of \(Z_{j}\) on \(Y_{ij}\) ;

\(\gamma_{11}\) is the regression coefficient of the effect of \(Z_{j}\) on the influence of \(X_{ij}\) on \(Y_{ij}\)

\(e_{ij}\) is the error term on the individual level ;

\(u_{0j}\) is the error term on the group level in the intercept ;

\(u_{1j}\) is the error term on the group level in the effect of \(Z_{j}\) on the influence of \(X_{ij}\) on \(Y_{ij}\) .


Then using "lmer" syntex will the model be
Code:
lmer(Y~X+Z+(1|group)+(0+X|Z) ,data=d)
where `group` is another variable in the data frame to indicate in which group the individual belongs to ?

or the model is
Code:
lmer(Y~X+Z+(1|group)+(0+X|group) ,data=d)
Thanks & Regards .
 
Last edited:

TheEcologist

Global Moderator
#2
Re: Am I specifying my lmer model correctly ?

or the model is
Code:
lmer(Y~X+Z+(1|group)+(0+X|group) ,data=d)

Thanks & Regards .
If group is your higher level grouping variable, then I would use this one. The former model - Using Z - may work, but only if all groups have unique values of Z- but even then it's never as clean as the latter model.

Cheers,

TE