[疑难杂症]Multilevel Logistic Models in R

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Problem: I need to estimate a set of multinomial logistic multilevel models and can’t find an appropriate R package. What is the best R package to estimate such models? STATA 13 recently added this feature to their multilevel mixed-effects models – so the technology to estimate such models seems to be available.

Details: A number of research questions require the estimation of multinomial logistic regression models in which the outcome variable is categorical. For example, biologists might be interested to investigate which type of trees (e.g., pine trees, maple trees, oak trees) are most impacted by acid rain. Market researchers might be interested whether there is a relationship between the age of customers and the frequency of shopping at Target, Safeway, or Walmart. These cases have in common that the outcome variable is categorical (unordered) and multinomial logistic regressions are the preferred method of estimation. In my case, I am investigating differences in types of human migration, with the outcome variable (mig) coded 0=not migrated, 1=internal migration, 2=international migration. Here is a simplified version of my data set:

migDat=data.frame(hhID=1:21,mig=rep(0:2,times=7),age=ceiling(runif(21,15,90)),stateID=rep(letters[1:3],each=7),pollution=rep(c("high","low","moderate"),each=7),stringsAsFactors=F)

   hhID mig age stateID pollution

1     1   0  47       a      high

2     2   1  53       a      high

3     3   2  17       a      high

4     4   0  73       a      high

5     5   1  24       a      high

6     6   2  80       a      high

7     7   0  18       a      high

8     8   1  33       b       low

9     9   2  90       b       low

10   10   0  49       b       low

11   11   1  42       b       low

12   12   2  44       b       low

13   13   0  82       b       low

14   14   1  70       b       low

15   15   2  71       c  moderate

16   16   0  18       c  moderate

17   17   1  18       c  moderate

18   18   2  39       c  moderate

19   19   0  35       c  moderate

20   20   1  74       c  moderate

21   21   2  86       c  moderate

My goal is to estimate the impact of age (independent variable) on the odds of (1) migrating internally vs. not migrating, (2) migrating internationally vs. not migrating, (3) migrating internally vs. migrating internationally. An additional complication is that my data operate at different aggregation levels (e.g., pollution operates at the state-level) and I am also interested in predicting the impact of air pollution (pollution) on the odds of embarking on a particular type of movement.

Clunky solutions: One could estimate a set of separate logistic regression models by reducing the data set for each model to only two migration types (e.g., Model 1: only cases coded mig=0 and mig=1; Model 2: only cases coded mig=0 and mig=2; Model 3: only cases coded mig=1 and mig=2). Such a simple multilevel logistic regression model could be estimated with lme4 but this approach is less ideal because it does not appropriately account for the impact of the omitted cases. A second solution would be to run multinomial logistic multilevel models in MLWiN through R using the R2MLwiN package. But since MLWiN is not open source and the generated object difficult to use, I would prefer to avoid this option. Based on a comprehensive internet search there seem to be some demand for such models but I am not aware of a good R package. So it would be great if some experts who have run such models could provide a recommendation and if there are more than one package maybe indicate some advantages/disadvantages. I am sure that such information would be a very helpful resource for multiple R users. Thanks!!

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关键词：Multilevel logistic ogistic logisti models understand individual prediction variation question