sigtest: Test for changes in the level of statistical significance...
In influence.ME: Tools for Detecting Influential Data in Mixed Effects Models

Description Usage Arguments Details Value Author(s) Examples

Test for changes in the level of statistical significance resulting from the deletion of potentially influential observations

1	sigtest(estex, test = 1.96, parameters = 0, sort = FALSE, to.sort = NA)

`estex`	Object of class 'estex', as returned from the `influence` function.
`test`	Value of the test statistic against which statistical significance is to be evaluated
`parameters`	Vector specifying the parameter(s) of which the significance is to be evaluated. If left unspecified, all parameters of the model are evaluated
`sort`	Specify whether the output should be sorted on the (absolute) magnitude of the test statistic after deletion of potentially influential cases
`to.sort`	If `sort==true`, the variable on which to sort the output needs to be be specified

The "sigtest" function tests whether excluding the influence of a single case changes the statistical significance of any or more variables in the model. This test of significance is based on the test statistic provided by the lme4 package. The nature of this statistic varies between different distributional families in the generalized mixed effects models. For instance, the t-statistic is related to a normal distribution while the z-statistic is related to binomial distributions.

For each of the cases that are evaluated, the test statistic of each variable is compared to a test-value specified by the user. For the purpose of this test, the parameter is regarded to statistically significant if the test statistic of the model exceeds the specified value. The "sigtest" function reports for each variable the test statistic after deletion of each evaluated case, whether or not this updated test statistic results in statistical significance based on the user-specified value, and whether or not this new statistical significance differs from the significance in the original model. So, in other words, if a parameter was statistically significant in the original model, but is not longer significant after the deletion of a specific case from the model, this is indicated by the output of the "sigtest" function. It is also indicated when an estimate was not significant originally, but reached statistical significance after deletion of a specific case.

Returns a list. For each variable in the original model that was evaluated, this list contains a matrix showing the test statistic from the original model (column 1), the test statistic after a potentially influential case was excluded from the model (column 2) and the result (TRUE / FALSE) of the test whether statistical significance changed as a result from deletion of (potentially) influential cases.

Rense Nieuwenhuis, Manfred te Grotenhuis, Ben Pelzer

## Not run: 
data(school23)
m23 <- lmer(math ~ homework + structure 
   + (1 | school.ID), 
   data=school23)

estex.m23  <- influence(m23, group="school.ID")
   
sigtest(estex.m23, test=-1.96)$structure

## End(Not run)

Loading required package: lme4
Loading required package: Matrix

Attaching package: 'influence.ME'

The following object is masked from 'package:stats':

    influence

      Altered.Teststat Altered.Sig Changed.Sig
6053        -1.2991445       FALSE       FALSE
6327        -1.6403859       FALSE       FALSE
6467        -1.5623107       FALSE       FALSE
7194        -1.5159431       FALSE       FALSE
7472        -2.6299167        TRUE        TRUE
7474        -2.0072703        TRUE        TRUE
7801        -1.5219275       FALSE       FALSE
7829        -0.9758367       FALSE       FALSE
7930        -1.5280837       FALSE       FALSE
24371       -1.5172395       FALSE       FALSE
24725       -1.6177512       FALSE       FALSE
25456       -1.5499640       FALSE       FALSE
25642       -1.5337357       FALSE       FALSE
26537       -1.3716896       FALSE       FALSE
46417       -1.5976418       FALSE       FALSE
47583       -1.5128142       FALSE       FALSE
54344       -1.1132383       FALSE       FALSE
62821       -1.0657896       FALSE       FALSE
68448       -1.7024754       FALSE       FALSE
68493       -1.5309190       FALSE       FALSE
72080       -1.5268782       FALSE       FALSE
72292       -1.5465888       FALSE       FALSE
72991       -1.5788992       FALSE       FALSE