Cumulative-logit ordered categorical missing-predictor family

cumulative_logit() declares the predictor-model family for an ordered categorical missing predictor used inside mi() with impute_model(family = cumulative_logit()). The missing ordered predictor is marginalised EXACTLY by a finite-state cumulative-logit sum over its K categories (K >= 3); there is no latent variable. The predictor link is cumulative logit, with K - 1 free cutpoints c_1 < ... < c_{K-1} and a cell probability Pr(x = k | z) = F(c_k - eta_x) - F(c_{k-1} - eta_x), where eta_x = X_x beta_x (no separate predictor intercept; the cutpoints carry the location). The missing predictor must be an ordered factor (or integer category scores) with at least three levels; a two-level predictor uses binomial() (the binary route).

Usage

cumulative_logit()

Value

A gllvmTMB_impute_family object for the family argument of impute_model().

Details

This is a predictor-model family tag consumed by impute_model(family = ), NOT a response family for gllvmTMB(). The predictor cumulative-logit link is DISTINCT from the ordinal_probit() RESPONSE family (a probit threshold model) AND from ordinal_logit() (the cumulative-logit RESPONSE family, fitted on the multivariate response via gllvmTMB(family = ordinal_logit())). cumulative_logit() and ordinal_logit() share no code path: one declares a missing covariate's marginal distribution inside mi(), the other is a family = argument for the observed response.

See also

impute_model(), binomial() for a binary missing predictor, ordinal_probit() and ordinal_logit() for the ordinal RESPONSE families (UNRELATED to this predictor-model family despite the similar name).

Examples

impute_model(score ~ z, family = cumulative_logit())
#> $formula
#> score ~ z
#> <environment: 0x558dad2b4270>
#> 
#> $family
#> $name
#> [1] "cumulative_logit"
#> 
#> $family
#> [1] "cumulative_logit"
#> 
#> $link
#> [1] "cumulative_logit"
#> 
#> attr(,"class")
#> [1] "gllvmTMB_impute_family"
#> 
#> $family_type
#> [1] "ordinal"
#> 
#> attr(,"class")
#> [1] "gllvmTMB_impute_model"