# covratio: Influence on precision of fixed effects in HLMs In HLMdiag: Diagnostic Tools for Hierarchical (Multilevel) Linear Models

## Description

These functions calculate measures of the change in the covariance matrices for the fixed effects based on the deletion of an observation, or group of observations, for a hierarchical linear model fit using `lmer`.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23``` ```## Default S3 method: covratio(object, ...) ## Default S3 method: covtrace(object, ...) ## S3 method for class 'mer' covratio(object, level = 1, delete = NULL, ...) ## S3 method for class 'lmerMod' covratio(object, level = 1, delete = NULL, ...) ## S3 method for class 'lme' covratio(object, level = 1, delete = NULL, ...) ## S3 method for class 'mer' covtrace(object, level = 1, delete = NULL, ...) ## S3 method for class 'lmerMod' covtrace(object, level = 1, delete = NULL, ...) ## S3 method for class 'lme' covtrace(object, level = 1, delete = NULL, ...) ```

## Arguments

 `object` fitted object of class `mer` or `lmerMod` `...` do not use `level` variable used to define the group for which cases will be deleted. If `level = 1` (default), then individual cases will be deleted. `delete` index of individual cases to be deleted. To delete specific observations the row number must be specified. To delete higher level units the group ID and `group` parameter must be specified. If `delete = NULL` then all cases are iteratively deleted.

## Details

Both the covariance ratio (`covratio`) and the covariance trace (`covtrace`) measure the change in the covariance matrix of the fixed effects based on the deletion of a subset of observations. The key difference is how the variance covariance matrices are compared: `covratio` compares the ratio of the determinants while `covtrace` compares the trace of the ratio.

## Value

If `delete = NULL` then a vector corresponding to each deleted observation/group is returned.

If `delete` is specified then a single value is returned corresponding to the deleted subset specified.

## References

Christensen, R., Pearson, L., & Johnson, W. (1992) Case-deletion diagnostics for mixed models. Technometrics, 34(1), 38–45.

Schabenberger, O. (2004) Mixed Model Influence Diagnostics, in Proceedings of the Twenty-Ninth SAS Users Group International Conference, SAS Users Group International.

`leverage.mer`, `cooks.distance.mer` `mdffits.mer`, `rvc.mer`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37``` ```data(sleepstudy, package = 'lme4') ss <- lme4::lmer(Reaction ~ Days + (Days | Subject), data = sleepstudy) # covratio for individual observations ss.cr1 <- covratio(ss) # covratio for subject-level deletion ss.cr2 <- covratio(ss, level = "Subject") ## Not run: ## A larger example data(Exam, package = 'mlmRev') fm <- lme4::lmer(normexam ~ standLRT * schavg + (standLRT | school), data = Exam) # covratio for individual observations cr1 <- covratio(fm) # covratio for school-level deletion cr2 <- covratio(fm, level = "school") ## End(Not run) # covtrace for individual observations ss.ct1 <- covtrace(ss) # covtrace for subject-level deletion ss.ct2 <- covtrace(ss, level = "Subject") ## Not run: ## Returning to the larger example # covtrace for individual observations ct1 <- covtrace(fm) # covtrace for school-level deletion ct2 <- covtrace(fm, level = "school") ## End(Not run) ```