# topicVar: topic variance In TaddyLab/maptpx: MAP Estimation of Topic Models

## Description

Tools for looking at the variance of document-topic weights.

## Usage

 1 2 3 topicVar(counts, theta, omega) logit(prob) expit(eta) 

## Arguments

 counts A matrix of multinomial response counts, as inputed to the topics or predict.topics functions. theta A fitted topic matrix, as ouput from the topics or predict.topics functions. omega A fitted document topic-weight matrix, as ouput from the topics or predict.topics functions. prob A probability vector (positive and sums to one) or a matrix with probability vector rows. eta A vector of the natural exponential family parameterization for a probability vector (with first category taken as null) or a matrix with each row the NEF parameters for a single observation.

## Details

These function use the natural exponential family (NEF) parametrization of a probability vector q_0 ... q_{K-1} with the first element corresponding to a 'null' category; that is, with NEF(q) = e_1 ... e_{K-1} and setting e_0 = 0, the probabilities are

q_k = \frac{exp[e_k]}{1 + ∑ exp[e_j]}.

Refer to Taddy (2012) for details.

## Value

topicVar returns an array with dimensions (K-1,K-1,n), where K=ncol(omega)=ncol(theta) and n = nrow(counts) = nrow(omega), filled with the posterior covariance matrix for the NEF parametrization of each row of omega. Utility logit performs the NEF transformation and expit reverses it.