# posterior.comparison.freqMAP: Compare Two Frequency Moving Average Plot (MAP) Objects In freqMAP: Frequency Moving Average Plots (MAP) of Multinomial Data by a Continuous Covariate

## Description

This function compares the posterior distributions on two frequency MAPs from two unmatched populations. Posterior summaries are calculated of the population frequency differences and log odds ratios.

## Usage

 `1` ```posterior.comparison.freqMAP(group1, group2) ```

## Arguments

 `group1` A `freqMAP` object `group2` A `freqMAP` object

## Details

Posterior summaries are calculated by simply comparing the posterior samples inside the two `freqMAP` objects. The probability that group1 frequency is greater than group2 frequency is calculated, the log odds ratio mean and 95% central posterior interval (CPI) is also calculated for each pair of categories.

For any given category, the posterior distributions on the frequencies in the two populations are assumed independent. Namely the category data in the two populations is assumed to be unmatched.

The two frequency MAPs `group1` and `group2` must have the same values in their elements `[["cat.names"]]`,`[["hw"]]`, and `[["x.label"]]`. Further, the values of the continuous covariate in `...\$cat.ma[,...\$x.label]` must be the same in both groups.

## Value

Dataframe with the following columns:

 ` x ` The values of the continuous covariate. ` n1 ` The number of observations in group 1 falling into the bucket centered at `x[i]`. ` n2 ` The number of observations in group 2 falling into the bucket centered at `x[i]`. ` *.gr1.gt.gr2 ` (One column for each category) The posterior probability that group 1 frequency for this category is greater than the frequency in group 2. ` *.*.lor.mean ` (One column for each possible pair of categories) The posterior mean on the log odds ratio for each pair of categories. ` *.*.lor.lpi & *.*.lor.cpi ` (One column for each possible pair of categories) The posterior lower (lpi) and upper bounds (upi) on the CPI on the log odds ratio for each pair of categories.

## Author(s)

Colin McCulloch <colin.mcculloch@themccullochgroup.com>

`freqMAP`, `plot.freqMAP`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23``` ``` #Make two sets of 2-category frequency data, y1 & y2, which both vary as #a function of a continuous variable x x <- runif(2000,min=-2,max=2) y1 <- c("a","b")[1+rbinom(n=length(x),size=rep(1,length(x)),prob=pnorm(x/2))] y2 <- c("a","b")[1+rbinom(n=length(x),size=rep(1,length(x)),prob=pnorm(x/5))] #Create the frequency MAP objects for y1 and y2 fp1 <- freqMAP(data.frame(x=x,y=y1,stringsAsFactors=FALSE), x=seq(-2,2,by=.2),x.label="x",hw=.2) fp2 <- freqMAP(data.frame(x=x,y=y2,stringsAsFactors=FALSE), x=seq(-2,2,by=.2),x.label="x",hw=.2) #Examine the frequency MAP objects summary(fp1) print(fp2) #Compare the posterior distributions on the two frequency MAPs pc <- posterior.comparison.freqMAP(group1=fp1,group2=fp2) #Three example plots plot(fp1,ylim=matrix(c(0,1),nrow=length(fp1\$cat.names),ncol=2,byrow=TRUE)) plot(fp1,fp2,type="freq",legend=c("y1","y2"),show.p.value.legend=TRUE) plot(fp1,fp2,type="or") ```