# QGmean: Compute the phenotypic mean on the observed scale In QGglmm: Estimate Quantitative Genetics Parameters from Generalised Linear Mixed Models

## Description

This function calculates the phenotypic mean on the observed scale from the latent mean and variance.

## Usage

 `1` ```QGmean(mu = NULL, var, link.inv, predict = NULL, width = 10) ```

## Arguments

 `mu` Latent intercept estimated from a GLMM (ignored if predict is not `NULL`). (numeric of length 1) `var` Latent total variance estimated from a GLMM. Usually, the sum of the estimated variances of the random effects, plus the "residual" variance. (numeric of length 1) `link.inv` Inverse function of the link function. (function) `predict` Optional vector of predicted values on the latent scale (i.e. matrix product Xb). The latent predicted values must be computed while only accounting for the fixed effects (marginal to the random effects). (numeric) `width` Parameter for the integral computation. The integral is evaluated from `mu` - `width * sqrt(var)` to `mu` + `width * sqrt(var)`. The default value is 10, which should be sensible for most models. (numeric)

## Details

This function needs the latent population mean (`mu`) or the marginal predicted values (`predict`) and the total latent variance (i.e. total latent variance `var`) to compute the observed phenotypic mean. To do so, it also requires the inverse function of the link function.

For example, if the link function is the natural logarithm, the inverse-link function will be the exponential. The inverse-link functions for many models are yielded by the `QGlink.funcs` function.

Contrary to `QGparams`, `QGmean.obs` never uses the closed form solutions, but always compute the integrals.

## Value

This function yields the phenotypic mean on the observed scale. (numeric)

## Author(s)

Pierre de Villemereuil & Michael B. Morrissey

`QGmvmean`, `QGparams`, `QGpred`, `QGlink.funcs`, `QGvar.dist`, `QGvar.exp`, `QGpsi`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```## Computing the observed mean for a probit link QGmean(mu = 0.3, var = 1, link.inv = pnorm) # The theoretical expectation is 1 - pnorm(0, 0.3, sqrt(1 + 1)) # Or, using the QGlink.funcs function QGmean(mu = 0.3, var = 1, link.inv = QGlink.funcs(name = "binom1.probit")\$inv.link) ## Computing the observed mean for a logarithm link QGmean(mu = 1, var = 1, link.inv = exp) # The theoretical expectation is exp(1 + 0.5 * 1) # This computation is automatically performed by QGparams # but directly using the closed form solution when available QGparams(mu = 1, var.p = 1, var.a = 0.5, model = "Poisson.log") ```