% -*- texinfo -*- % @deftypefn {Function File} {[@var{theta}, @var{beta}, @var{dev}, @var{dl}, @var{d2l}, @var{p}] =} logistic_regression (@var{y}, @var{x}, @var{print}, @var{theta}, @var{beta}) % Perform ordinal logistic regression. % % Suppose @var{y} takes values in @var{k} ordered categories, and let % @code{gamma_i (@var{x})} be the cumulative probability that @var{y} % falls in one of the first @var{i} categories given the covariate % @var{x}. Then % % @example % [theta, beta] = logistic_regression (y, x) % @end example % % @noindent % fits the model % % @example % logit (gamma_i (x)) = theta_i - beta' * x, i = 1 @dots{} k-1 % @end example % % The number of ordinal categories, @var{k}, is taken to be the number % of distinct values of @code{round (@var{y})}. If @var{k} equals 2, % @var{y} is binary and the model is ordinary logistic regression. The % matrix @var{x} is assumed to have full column rank. % % Given @var{y} only, @code{theta = logistic_regression (y)} % fits the model with baseline logit odds only. % % The full form is % % @example % @group % [theta, beta, dev, dl, d2l, gamma] % = logistic_regression (y, x, print, theta, beta) % @end group % @end example % % @noindent % in which all output arguments and all input arguments except @var{y} % are optional. % % Setting @var{print} to 1 requests summary information about the fitted % model to be displayed. Setting @var{print} to 2 requests information % about convergence at each iteration. Other values request no % information to be displayed. The input arguments @var{theta} and % @var{beta} give initial estimates for @var{theta} and @var{beta}. % % The returned value @var{dev} holds minus twice the log-likelihood. % % The returned values @var{dl} and @var{d2l} are the vector of first % and the matrix of second derivatives of the log-likelihood with % respect to @var{theta} and @var{beta}. % % @var{p} holds estimates for the conditional distribution of @var{y} % given @var{x}. % @end deftypefn

- logistic_regression_derivatives % Called by logistic_regression. Calculates derivates of the
- logistic_regression_likelihood % Calculates likelihood for the ordinal logistic regression model.

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