Interaction detection for generalized linear models

Abstract

Provided are techniques for interaction detection for generalized linear models. Basic statistics are calculated for a pair of categorical predictor variables and a target variable from a dataset during a single pass over the dataset. It is determined whether there is a significant interaction effect for the pair of categorical predictor variables on the target variable by: calculating a log-likelihood value for a full generalized linear model without estimating model parameters; calculating the model parameters for a reduced generalized linear model with a recursive marginal mean accumulation technique using the basic statistics; calculating a log-likelihood value for the reduced generalized linear model; calculating a likelihood ratio test statistic using the log-likelihood value for the full generalized linear model and the log-likelihood value for the reduced generalized linear model; calculating a p-value of the likelihood ratio test statistic; and comparing the p-value to a significance level.

1 . A method, comprising:
 calculating, using a computer, basic statistics for a pair of categorical predictor variables and a target variable from a dataset during a single pass over the dataset; and   determining, using the computer, whether there is a significant interaction effect for the pair of categorical predictor variables on the target variable by:
 calculating, using the computer, a log-likelihood value for a full generalized linear model without estimating model parameters; 
 calculating, using the computer, the model parameters for a reduced generalized linear model with a recursive marginal mean accumulation technique using the basic statistics; 
 calculating, using the computer, a log-likelihood value for the reduced generalized linear model; 
 calculating, using the computer, a likelihood ratio test statistic using the log-likelihood value for the full generalized linear model and the log-likelihood value for the reduced generalized linear model; 
 calculating, using the computer, a p-value of the likelihood ratio test statistic; and 
 comparing, using the computer, the p-value to a significance level. 
   
     
     
         2 . The method of  claim 1 , wherein the full generalized linear model is of the form g(μ)=Xiβi+Xjβj+(Xi×Xj)βij, wherein g(μ) is a link function of μ and μ is an expected value vector of the target variable Y, wherein Xi and Xj are the categorical predictor variables, and wherein βi, βj, and βij are the model parameters. 
     
     
         3 . The method of  claim 1 , wherein the reduced generalized linear model is of the form g(μ)=Xiβi+Xjβj, wherein g(μ) is a link function of μ and μ is an expected value vector of the target variable Y, wherein Xi and Xj are the categorical predictor variables, and wherein βi and βj are the model parameters. 
     
     
         4 . The method of  claim 1 , wherein the recursive marginal mean accumulation technique calculates search directions for the model parameters calculation by an iterative process based on accumulating weighted marginal means. 
     
     
         5 . The method of  claim 1 , further comprising:
 performing, using the computer, m-way interaction detection among m categorical predicator variables, where m>2.   
     
     
         6 . The method of  claim 1 , further comprising:
 performing, using the computer, m-way interaction detection among multiple possible combinations of m categorical predictor variables, where m>1, wherein the dataset contains predictor variables, and the basic statistics for each of the possible combinations are calculated during a single pass over the dataset.   
     
     
         7 . The method of  claim 1 , wherein a Software as a Service (SaaS) is provided to perform the method. 
     
     
         8 - 21 . (canceled)