# What does the residual higher level variance tell me?

I have a multilevel logistic regression model predicting the probability of item nonresponse, where the random intercept variance at country level takes on the following distribution for the different countries (unconditional model):

Given the country codes Belgium (BE), Bulgaria (BG), Croatia (HR), Cyprus (CY), Czech Republic (CZ), Denmark (DK), Estonia (EE), Finland (FI), France (FR), Germany (DE), Greece (GR), Hungary (HU), Ireland (IE), Israel (IL), Lithuania (LT), Netherlands (NL), Norway (NO), Poland (PL), Portugal (PT), Russian Federation (RU), Slovakia (SK), Slovenia (SI), Spain (ES), Sweden (SE), Switzerland (CH), United Kingdom (GB) and Ukraine (UA) it is clear there is a trend of the Western countries having a lower odds and the Eastern countries having a higher odds compared to the average, with Portugal defying this trend. I assume this variance is due to differences in composition of the population and specific country characteristics. Entering some demographic variables to predict the odds (age, gender, education) not much of the country variance in explained, except that Portugal now follows the trend West vs East better. Could this mean that for Portugal the higher odds were due to composition effects, but less for the other countries?

Then I also add a country variable: mode of administration (PAPI = paper and pencil interview and CAPI = computer assisted interview). This explains a lot of the variance in odds between the countries, and removes a bit the West-East trend:

However, I know most Western countries were CAPI countries and most Eastern countries were PAPI countries:

Is it possible that my predictor 'mode' is not related to the odds, but actually explains away the variability because it makes a clear distinction between the Eastern and Western countries?

It could be possible. If you code an east-west variable, a simple binary variable. Check it's correlation with your mode variable. If they are very highly correlated, then multicollinearity may be at play. i.e. your mode variable may in fact be explaining away the east west divide.

• I did what you proposed and there is indeed a Phi correlation of .779, which is extremely high. I shall leave it out of my model. Any opinion on my interpretation for the Portugal shift? May 17, 2013 at 12:19
• The interpretation of the Portugal shift is difficult to explain with the given data. There could be a factor at work you haven't touched upon. Since some of the shift was explained with the variables you entered, I think it is safe to say that your interpretation is reasonable. Although, bare in mind, the confidence interval for Portugal indicates that the true value of the odds of DK could be in line with the west. Not understanding Portugal's conditions with regards to the east vs. west, its difficult to state whether it is surprising or not that it follows an eastern trend more. May 17, 2013 at 12:51