# sampleUnivTMoE: Draw a sample from a univariate t mixture of experts (TMoE). In meteorits: Mixture-of-Experts Modeling for Complex Non-Normal Distributions

## Description

Draw a sample from a univariate t mixture of experts (TMoE).

## Usage

 `1` ```sampleUnivTMoE(alphak, betak, sigmak, nuk, x) ```

## Arguments

 `alphak` The parameters of the gating network. `alphak` is a matrix of size (q + 1, K - 1), with K - 1, the number of regressors (experts) and q the order of the logistic regression `betak` Matrix of size (p + 1, K) representing the regression coefficients of the experts network. `sigmak` Vector of length K giving the standard deviations of the experts network. `nuk` Vector of length K giving the degrees of freedom of the experts network t densities. `x` A vector of length n representing the inputs (predictors).

## Value

A list with the output variable `y` and statistics.

• `y` Vector of length n giving the output variable.

• `zi` A vector of size n giving the hidden label of the expert component generating the i-th observation. Its elements are zi[i] = k, if the i-th observation has been generated by the k-th expert.

• `z` A matrix of size (n, K) giving the values of the binary latent component indicators Zik such that Zik = 1 iff Zi = k.

• `stats` A list whose elements are:

• `Ey_k` Matrix of size (n, K) giving the conditional expectation of Yi the output variable given the value of the hidden label of the expert component generating the ith observation zi = k, and the value of predictor X = xi.

• `Ey` Vector of length n giving the conditional expectation of Yi given the value of predictor X = xi.

• `Vary_k` Vector of length k representing the conditional variance of Yi given zi = k, and X = xi.

• `Vary` Vector of length n giving the conditional expectation of Yi given X = xi.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```n <- 500 # Size of the sample alphak <- matrix(c(0, 8), ncol = 1) # Parameters of the gating network betak <- matrix(c(0, -2.5, 0, 2.5), ncol = 2) # Regression coefficients of the experts sigmak <- c(0.5, 0.5) # Standard deviations of the experts nuk <- c(5, 7) # Degrees of freedom of the experts network t densities x <- seq.int(from = -1, to = 1, length.out = n) # Inputs (predictors) # Generate sample of size n sample <- sampleUnivTMoE(alphak = alphak, betak = betak, sigmak = sigmak, nuk = nuk, x = x) # Plot points and estimated means plot(x, sample\$y, pch = 4) lines(x, sample\$stats\$Ey_k[, 1], col = "blue", lty = "dotted", lwd = 1.5) lines(x, sample\$stats\$Ey_k[, 2], col = "blue", lty = "dotted", lwd = 1.5) lines(x, sample\$stats\$Ey, col = "red", lwd = 1.5) ```

meteorits documentation built on Jan. 11, 2020, 9:13 a.m.