# Adding 2nd level variable into Multi-level Modelling in R

I have a dataset (data.mrsa) about the MRSA prevalence of elderly in long term care facilities (LTCF) with the following information:

• mrsa_result: MRSA result of recruited elderly (positive VS negative)
• age: residents' age
• ltcf: UID for each LTCF (we sampled 30 out of 1000 LTCFs)
• ltcf_type: type of LTCF (private VS non-private)

I have a multi-level logistic regression model like the one below:

fit2 <- glmer(mrsa_result ~ age + (1|ltcf), family=binomial("logit"),data=data.mrsa)


I know I am trying to find out the effect of age on the log-odds of mrsa_result, having the ltcf on the 2nd level gives me a wider CI on the lod-odds.

Now I want to add the ltcf_type into the model, I think this should be a fixed effect, as there can only be private and non-private, but itcf_type should be considered as 2nd level data, right? As this describe the type of LTCF, not the type of elderly.

I am puzzled on where should I put the term ltcf_type into my model, I wonder which of the following lines is correct:

fit2a <- glmer(mrsa_result ~ age + ltcf_type + (1|ltcf), family=binomial("logit"),data=data.mrsa)
fit2b <- glmer(mrsa_result ~ age + (1|ltcf + ltcf_type), family=binomial("logit"),data=data.mrsa)


Thanks.

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## 1 Answer

fit2a <- glmer(mrsa_result ~ age + ltcf_type + (1|ltcf), family=binomial("logit"),data=data.mrsa)

The first line is correct. Each unit on L2 is represented in multiple data rows, and lme4 recognizes that ltcf_type is constant for each entry within a L2 unit. So it is treated automatically as a fixed effect on L2.

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