topicVar: topic variance

Description

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

Usage

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.

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.

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 $$q_k = \frac{exp[e_k]}{1 + \sum exp[e_j]}.$$ Refer to Taddy (2011) for details.

References