deff {quest}

Design Effect from Multilevel Numeric Vector

Description

deff computes the design effect for a multilevel numeric vector. Design effects summarize how much larger sampling variances (i.e., squared standard errors) are due to the multilevel structure of the data. By taking the square root, the value summarizes how much larger standard errors are due to the multilevel structure of the data.

Usage

deff(x, grp, how = "lme", REML = TRUE)

Arguments

x

numeric vector.

grp

atomic vector the same length as x providing the grouping variable.

how

character vector of length 1 specifying how the ICC(1,1) should be calculated. There are four options: 1) "lme" uses a linear mixed effects model with the function lme from the package nlme, 2) "lmer" uses a linear mixed effects modeling with the function lmer from the package lme4, 3) "aov" uses a one-way analysis of variance with the function aov, and 4) "raw" uses the observed variances, which provides a biased estimate of the ICC(1,1) and is not recommended (It is only included for teaching purposes).

REML

logical vector of length 1 specifying whether restricted maximum likelihood estimation (TRUE) should be used rather than traditional maximum likelihood estimation (FALSE). Only used for linear mixed effects models if how = "lme" or how = "lmer".

Details

Design effects are a function of both the intraclass correlation (ICC) and the average group size. Design effects can be large due to large ICCs and small group sizes or small ICCs and large group sizes. For example, with an ICC = .01 and average group size of 100, the design effect would be 2.0, whose square root is 1.41. For more information, see myths 1 and 2 in Huang (2018).

Value

double vector of lenght 1 providing the design effect.

References

Huang, F. L. (2018). Multilevel modeling myths School Psychology Quarterly, 33(3), 492-499.

See Also

icc_11 deffs

Examples

icc_11(x = airquality$"Ozone", grp = airquality$"Month")
length_by(x = airquality$"Ozone", grp = airquality$"Month", na.rm = TRUE)
deff(x = airquality$"Ozone", grp = airquality$"Month")
sqrt(deff(x = airquality$"Ozone", grp = airquality$"Month")) # how much SE inflated