# Estimates the heritability of a binomial trait Estimates the narrow-sense heritability of a binomial trait and calculates a p value by randomization. ```r h2Estimate(data,nreps=1000) ``` ## Arguments - `data`: a (non-empty) numeric matrix with three columns. The first two should contain the trait data (number of occurances of each outcome type) and the third should contain the group ids. - `nreps`: a (non-empty) numeric value indicating the number of resamples to perform when calculating the emperical p value. ## Details Estimates the narrow-sense heritability of a binomial trait. This function works by fitting two models, one with and one without a random-effect of sire. These models are compared by randomizing the sire ids nreps times and re-fitting the model. For each of the nreps model pairs, a deviance is calculated and a "p value" estimated by comparing that distribution of deviance to the observed. The heritability is approximatly tau2/(tau2+(pi/sqrt(3))^2), where tau2 is the random-effect variance due to sire. ## Returns Returns a list. The list contains: - **h2**: The estimated narrow-sense heritability. The narrow-sense heritability is approximatly tau2/(tau2+(pi/sqrt(3))^2), where tau2 is the random-effect variance due to sire. - **pval**: The probability that the best-fit model includes an extra variance term for sire (random effect of dad). The value is calculated by comparing the deviances from nreps number of randomized model comparisions. - **deviance**: The deviance between a null model without a random effect of dad and a model with. - **sim**: The simulated deviances used in calculating the p value in pval. - **obsMod**: The glmer model object resulting from the observed data. ## Examples ```r #non-zero heritability ndads <- 18 mm <- 4 vv <- 6 tau2 <- 2.5 nbins <- 3 mylogit <- function(x) log(x/{1-x}) ilogit <- function(x) 1/{1+exp(-x)} swimprob <- ilogit(rnorm(ndads, 0, sqrt(tau2))) mytable <- NULL for(i in 1:ndads) { bincounts <- pmax(1,rnbinom(nbins, mu = mm, size = mm^2/{vv-mm})) swim <- rbinom(3, bincounts,swimprob[i]) set <- bincounts - swim theserows <- data.frame(set=set,swim=swim, Dad = i, Bin = 1:nbins) mytable <- rbind(mytable, theserows) } est <- h2Estimate(mytable,nreps=10) print(est$h2) #zero heritability ndads <- 18 mm <- 4 vv <- 6 tau2 <- 0 nbins <- 3 mylogit <- function(x) log(x/{1-x}) ilogit <- function(x) 1/{1+exp(-x)} swimprob <- ilogit(rnorm(ndads, 0, sqrt(tau2))) mytable0 <- NULL for(i in 1:ndads) { bincounts <- pmax(1,rnbinom(nbins, mu = mm, size = mm^2/{vv-mm})) swim <- rbinom(3, bincounts,swimprob[i]) set <- bincounts - swim theserows <- data.frame(set=set,swim=swim, Dad = i, Bin = 1:nbins) mytable0 <- rbind(mytable0, theserows) } est0 <- h2Estimate(mytable0,nreps=10) print(est0$h2) ```

h2Estimate function