Compute the DFBETAS measure of influential data

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Description

DFBETAS (standardized difference of the beta) is a measure that standardizes the absolute difference in parameter estimates between a (mixed effects) regression model based on a full set of data, and a model from which a (potentially influential) subset of data is removed. A value for DFBETAS is calculated for each parameter in the model separately. This function computes the DFBETAS based on the information returned by the influence() function.

Usage

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## S3 method for class 'estex'
dfbetas(model, parameters = 0, sort=FALSE, to.sort=NA, abs=FALSE, ...)

Arguments

model

An object as returned by the influence() function, containing the altered estimates of a mixed effects regression model

parameters

Used to define a selection of parameters. If parameters=0 (default), DFBETAS is calculated for all parameters in the model

sort

If sort=TRUE the values of DFBETAS are ordered based on magnitude. If sort=FALSE (default) no sorting takes place.

to.sort

Specify on which variable the DFBETAS must be sorted. If only one variable present (either in the model, or due to the selection specified in parameters), this parameter can be omitted. If DFBETAS is calculated for multiple variables, and sort=TRUE, specification of to.sort is required, or an error is returned.

abs

If abs=TRUE, the absolute values of DFBETAS are returned, while if abs=FALSE (default), both positive and negative values are possible. If both abs=TRUE and sort=TRUE, the abs parameters precedes the sort parameter, and thus the absolute values of DFBETAS are sorted.

...

Currently not used

Value

A matrix is returned, containing DFBETAS-values for each (selected) fixed parameter of the model, and separately for each evaluated set of influential data.

Author(s)

Rense Nieuwenhuis, Ben Pelzer, Manfred te Grotenhuis

References

Nieuwenhuis, R., Te Grotenhuis, M., & Pelzer, B. (2012). Influence.ME: tools for detecting influential data in mixed effects models. R Journal, 4(2), 38???47.

Belsley, D.A., Kuh, E. & Welsch, R.E. (1980). Regression Diagnostics. Identifying Influential Data and Source of Collinearity. Wiley.

Snijders, T.A. & Bosker, R.J. (1999). Multilevel Analysis, an introduction to basic and advanced multilevel modeling. Sage.

Van der Meer, T., Te Grotenhuis, M., & Pelzer, B. (2010). Influential Cases in Multilevel Modeling: A Methodological Comment. American Sociological Review, 75(1), 173-178.

See Also

influence.mer, cooks.distance.estex

Examples

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 data(school23)
 model <- lmer(math ~ structure + SES  + (1 | school.ID), data=school23)

 alt.est <- influence(model, group="school.ID")
 dfbetas(alt.est)