Class sizes and item-response probabilities of the measurement model

class_sizes() returns the estimated class proportions and item_probs() the class-conditional item-response probabilities of the Step-1 measurement model underlying any fitted tseLCA object.

Usage

class_sizes(object, ...)

# S3 method for class 'tseLCA'
class_sizes(object, se = FALSE, ...)

item_probs(object, ...)

# S3 method for class 'tseLCA'
item_probs(object, se = FALSE, ...)

Arguments

object: A fitted tseLCA object.
...: Further arguments (currently unused).
se: Logical. If TRUE, also return standard errors.

Value

class_sizes(): a named numeric vector of length T summing to one. item_probs(): a matrix with one row per item (binary items: \(P(Y = 1 \mid X = t)\)) or per item category (polytomous items: \(P(Y = k \mid X = t)\)) and one column per class. With se = TRUE, a list with elements estimate and se of that form.

Details

With se = TRUE, their standard errors are returned as well. They are obtained by the delta method from the variance of the measurement model's log-ratio parameters (vcov() of the measurement model): class sizes are the softmax of \(\log(\pi_t / \pi_1)\), and the response probabilities of an item in class \(t\) the softmax of \(\log(P(Y = k \mid X = t) / P(Y = 0 \mid X = t))\). Parameters on the boundary of the parameter space are treated as fixed and get a standard error of zero.

Examples

d <- generate_data(200, "high", "covariate", seed = 1)
m <- tse_lca(cbind(Y1, Y2, Y3, Y4, Y5, Y6) ~ 1, data = d, nclass = 3)
class_sizes(m)
#>        C1        C2        C3 
#> 0.3495138 0.2915216 0.3589645 
item_probs(m)
#>                C1         C2         C3
#> P(Y1|C) 0.8702096 0.79456644 0.12317767
#> P(Y2|C) 0.9016604 0.88525528 0.10247858
#> P(Y3|C) 0.8743309 0.87570434 0.06720021
#> P(Y4|C) 0.8565891 0.09127798 0.06686104
#> P(Y5|C) 0.8909744 0.09780804 0.02807791
#> P(Y6|C) 0.8206322 0.13853263 0.09135284
item_probs(m, se = TRUE)$se
#>                 C1         C2         C3
#> P(Y1|C) 0.04554151 0.06597822 0.04799340
#> P(Y2|C) 0.03714323 0.05935448 0.04764421
#> P(Y3|C) 0.04439277 0.06221734 0.04390390
#> P(Y4|C) 0.05534999 0.05443704 0.03138966
#> P(Y5|C) 0.05008769 0.05959757 0.02279529
#> P(Y6|C) 0.05707720 0.05842492 0.03747299