multilogistic.sql_in File Reference

SQL functions for multinomial logistic regression. More...

Functions
float8[]	__mlogregr_irls_step_transition (float8[] state, integer y, integer num_categories, integer ref_category, float8[] x, float8[] prev_state)
float8[]	__mlogregr_irls_step_merge_states (float8[] state1, float8[] state2)
float8[]	__mlogregr_irls_step_final (float8[] state)
aggregate float8[]	__mlogregr_irls_step (integer y, integer numcategories, integer ref_category, float8[] x, float8[] previous_state)
float8	__internal_mlogregr_irls_step_distance (float8[] state1, float8[] state2)
mlogregr_result	__internal_mlogregr_irls_result (float8[] state)
integer	__compute_mlogregr (varchar source, varchar depvar, varchar indepvar, integer num_categories, integer max_num_iterations, varchar optimizer, float8 precision, integer ref_category)
mlogregr_result	mlogregr (varchar source, varchar depvar, varchar indepvar, integer max_num_iterations=20, varchar optimizer="irls", float8 precision=0.0001, integer ref_category)
	Compute logistic-regression coefficients and diagnostic statistics. More...
mlogregr_result	mlogregr (varchar source, varchar depvar, varchar indepvar)
mlogregr_result	mlogregr (varchar source, varchar depvar, varchar indepvar, integer max_num_iterations)
mlogregr_result	mlogregr (varchar source, varchar depvar, varchar indepvar, integer max_num_iterations, varchar optimizer)

Detailed Description

Date

July 2012

See Also

For a brief introduction to multinomial logistic regression, see the module description Multinomial Logistic Regression.

Function Documentation

integer __compute_mlogregr	(	varchar	source,
		varchar	depvar,
		varchar	indepvar,
		integer	num_categories,
		integer	max_num_iterations,
		varchar	optimizer,
		float8	precision,
		integer	ref_category
	)

mlogregr_result __internal_mlogregr_irls_result

(

float8[]

state)

float8 __internal_mlogregr_irls_step_distance	(	float8[]	state1,
		float8[]	state2
	)

aggregate float8 [] __mlogregr_irls_step	(	integer	y,
		integer	numcategories,
		integer	ref_category,
		float8[]	x,
		float8[]	previous_state
	)

float8 [] __mlogregr_irls_step_final

(

float8[]

state)

float8 [] __mlogregr_irls_step_merge_states	(	float8[]	state1,
		float8[]	state2
	)

float8 [] __mlogregr_irls_step_transition	(	float8[]	state,
		integer	y,
		integer	num_categories,
		integer	ref_category,
		float8[]	x,
		float8[]	prev_state
	)

mlogregr_result mlogregr	(	varchar	source,
		varchar	depvar,
		varchar	indepvar,
		integer	max_num_iterations = 20,
		varchar	optimizer = "irls",
		float8	precision = 0.0001,
		integer	ref_category
	)

To include an intercept in the model, set one coordinate in the independentVariables array to 1.

Parameters

source	Name of the source relation containing the training data
depvar	Name of the dependent column (of type INTEGER < numcategories)
indepvar	Name of the independent column (of type DOUBLE PRECISION[])
max_num_iterations	The maximum number of iterations
optimizer	The optimizer to use ( 'irls'/'newton' for iteratively reweighted least squares)
precision	The difference between log-likelihood values in successive iterations that should indicate convergence. Note that a non-positive value here disables the convergence criterion, and execution will only stop after \ max_num_iterations iterations.
ref_category	The reference category specified by the user

Returns

A composite value:

• ref_category INTEGER - Reference category
• coef FLOAT8[] - Array of coefficients, \( \boldsymbol c \)
• log_likelihood FLOAT8 - Log-likelihood \( l(\boldsymbol c) \)
• std_err FLOAT8[] - Array of standard errors, \( \mathit{se}(c_1), \dots, \mathit{se}(c_k) \)
• z_stats FLOAT8[] - Array of Wald z-statistics, \( \boldsymbol z \)
• p_values FLOAT8[] - Array of Wald p-values, \( \boldsymbol p \)
• odds_ratios FLOAT8[]: Array of odds ratios, \( \mathit{odds}(c_1), \dots, \mathit{odds}(c_k) \)
• condition_no FLOAT8 - The condition number of matrix \( X^T A X \) during the iteration immediately preceding convergence (i.e., \( A \) is computed using the coefficients of the previous iteration)
• num_iterations INTEGER - The number of iterations before the algorithm terminated

Usage

• Get vector of coefficients \( \boldsymbol c \) and all diagnostic statistics:
  

  SELECT * FROM mlogregr('sourceName', 'dependentVariable',
     'numCategories', 'independentVariables');

• Get vector of coefficients \( \boldsymbol c \):
  

  SELECT (mlogregr('sourceName', 'dependentVariable',
     'numCategories', 'independentVariables')).coef;

• Get a subset of the output columns, e.g., only the array of coefficients \( \boldsymbol c \), the log-likelihood of determination \( l(\boldsymbol c) \), and the array of p-values \( \boldsymbol p \):

  SELECT coef, log_likelihood, p_values
     FROM mlogregr('sourceName', 'dependentVariable',
    'numCategories', 'independentVariables');

Note

This function starts an iterative algorithm. It is not an aggregate function. Source and column names have to be passed as strings (due to limitations of the SQL syntax).

mlogregr_result mlogregr	(	varchar	source,
		varchar	depvar,
		varchar	indepvar
	)

mlogregr_result mlogregr	(	varchar	source,
		varchar	depvar,
		varchar	indepvar,
		integer	max_num_iterations
	)

mlogregr_result mlogregr	(	varchar	source,
		varchar	depvar,
		varchar	indepvar,
		integer	max_num_iterations,
		varchar	optimizer
	)