# Specifying formula of lmer() function in R .

#### Cynderella

##### New Member
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
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