<2014.2.10>

AC's attempts at learning to do this in R.

Added package lme4 to R. http://cran.r-project.org/web/packages/lme4/lme4.pdf

Also added plyr package, because it has a rename() function for renaming columns in a data frame: (http://www.cookbook-r.com/Manipulating_data/Renaming_columns_in_a_data_frame/)

However, I found it easier to do this:

colnames(x) <- c("name1","name2"...)

based on guidance from:

https://stat.ethz.ch/R-manual/R-devel/library/base/html/colnames.html

and from

http://cran.r-project.org/doc/manuals/r-devel/R-data.html

Column names can be given explicitly via the col.names; explicit names override the header line (if present).

Added arm package: http://cran.r-project.org/web/packages/arm/index.html

arm: Data Analysis Using Regression and Multilevel/Hierarchical Models R functions for processing lm, glm, svy.glm, merMod and polr outputs.

arm package provides the coefplot() function for plotting the regression coefficient values and std. errors.

Need to specify that subjects is a nominal variable, using the factor command:

http://www.statmethods.net/input/datatypes.html

Tell R that a variable is nominal by making it a factor. The factor stores the nominal values as a vector of integers in the range [ 1… k ] (where k is the number of unique values in the nominal variable), and an internal vector of character strings (the original values) mapped to these integers.

A nice description from:

https://stat.ethz.ch/pipermail/r-sig-mixed-models/2011q1/015590.html

In this case the coefficient corresponds to one of the terms in the model and I would advocate performing a likelihood ratio test comparing the two models

fm <- glmer(SameSite~BreedSuc1+Sex+(1|Bird), family="binomial")
fm0 <- glmer(SameSite~Sex+(1|Bird), family="binomial")  # the null
hypothesis model
anova(fm0, fm)

Even though the function is called anova it will, in this case, perform a likelihood ratio test (LRT). It also prints the values of AIC and BIC if you prefer to compare models according to one of those criteria but I prefer using the likelihood ratio for nested models.

However, before doing that comparison you should ask yourself whether you want to compare models that have the, apparently unnecessary term for Sex in them. The way I would approach the model building is first to reduce the model to

fm1 <- lmer(SameSite~BreedSuc1+(1|Bird), family="binomial")

You could then compare

anova(fm1, fm)

which I presume will give a large p-value for the LRT, so we prefer the simpler model, fm1. After that, I would compare

fm2 <- lmer(SameSite ~ 1 + (1|Bird), family="binomial")