Robust score (Rao) tests for multinomial regression.

Usage

multinom_test(
  X = NULL,
  Y,
  formula = NULL,
  data = NULL,
  strong = FALSE,
  j = NULL,
  all_score = FALSE,
  penalty = FALSE,
  pseudo_inv = FALSE
)

Arguments

X: A \(n x p\) design matrix of covariates.
Y: A \(n x J\) data matrix of outcomes.
formula: a one-sided formula specifying the form of the mean model to be fit (use with data argument if X is not included)
data: a dataframe with \(n\) rows containing variables given in formula (use with formula argument if X is not included)
strong: If FALSE, this function will compute the robust score statistic to test the weak null that for one specific \(j\), \(\beta_j = 0\) for the length \(p\) vector \(\beta_j\). If TRUE, this function instead computes the robust score statistic to test the strong null that \(\beta_1 = \beta_2 = \dots = \beta_{J-1} = 0\) for all length \(p\) vectors \(\beta_j\), \(j\in\{1,\ldots,J-1\}\). Default is FALSE.
j: If strong is FALSE, this argument must be supplied. This gives the category \(j\) in the weak null hypothesis that \(\beta_j = 0\).
all_score: If TRUE, score tests for each individual covariate and category pair (i.e. null that \(\beta_{jk} = 0\) for each category \(j = 1, \dots, J-1\) and each covariate \(k = 1, \dots, p\) pair) will be run and reported in output coefficient table. Default is FALSE.
penalty: If TRUE will apply a Firth penalty to estimation under the alternative and under the null. Defaults to FALSE (ask Amy her preference)
pseudo_inv: Use pseudo inverse for inverted portion of the robust score test to avoid issues with nearly singular matrices.

Value

The robust score test statistic for the specified hypothesis test. A list including the test statistic, p-value, estimated parameters under the null hypothesis, and estimated parameters under the alternative hypothesis.

Author

Shirley Mathur