generate_multinom_probs {sim2Dpredictr}

Generate Probabilities for Multinomial Draws

Description

Obtain probabilities for each category of a multinomial distribution based on covariate and parameter values based on the logit models for the multinomial distribution.

Usage

generate_multinom_probs(V = NULL, B = NULL, X = NULL, X.incl.X0 = FALSE)

Arguments

V

A numeric value stating the number of categories desired.

B

A list, each element of which contains a parameter vector. The list should have length V - 1, i.e., should contain parameter values associated with all categories except the reference category, following Agresti (2007). Alternatively, B may be a list of length V if one desires to specify parameters for every category, i.e., the over-parameterized model used in Friedman (2010).

X

A matrix, each row of which contains subject covariate/predictor values.

X.incl.X0

Logical. When TRUE, X should contain column of 1's for the intercept. Otherwise, a column of 1's is generated internally. Default is FALSE.

Value

A matrix containing subject-specific probabilities for each category of the multinomial distribution. The number of rows equals nrow(X) and the number of columns equals V.

References

Agresti A (2007). An Introduction to Categorical Analysis, 2nd edition. John Wiley & Sons, Hoboken, New Jersey.

Friedman J, Hastie T, Tibshirani R (2010). “Regularization paths for generalized linear models via coordinate descent.” Journal of Statistical Software, 33, 1-22. doi:10.18637/jss.v033.i01.

Examples

## number of categories
vt <- 3

## covariate values
xt <- matrix(rnorm(10 * 2), ncol = 2, nrow = 10)

## list of parameter vectors
bt <- list(b1 = c(1, 0.25, -0.25),
           b2 = c(-0.5, 0.15, 0.15))
           
## list of parameter vectors (over-parameterized model)
bu <- list(b1 = c(1, 0.25, -0.25),
           b2 = c(-0.5, 0.15, 0.15),
           b3 = c(-1, 0.1, -0.20))

## subject specific probabilities for each category
generate_multinom_probs(V = vt, X = xt, B = bt)

## subject specific probabilities for each category 
## (over-parameterized model)
generate_multinom_probs(V = vt, X = xt, B = bu)