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Split repeated-measures variance into within- and between-person parts

Source: R/stats_within_between.R
variance_components.Rd

The first question to ask of any repeated-measures variable: is the variation mostly between people (some people simply score higher) or within people (everyone moves around a lot over time)? The answer decides whether person-specific modelling can pay off at all.

Usage

variance_components(x, ...)

# S3 method for class 'data.frame'
variance_components(x, vars = NULL, id, method = c("anova", "reml"), ...)

# S3 method for class 'idiostats_wb'
variance_components(x, ...)

Arguments

x

A data frame of repeated measures, or a fit_within_between() result.

...

Ignored.

vars

Columns to decompose (any fit_lm() selector). Defaults to every numeric column other than id.

id

Person/unit ID column.

method

"anova" (base R, the default) or "reml" (needs lme4).

Value

A data.frame with class idiographic_variance. For a data frame: one row per variable, with variable, n, people, var_within, var_between, var_total, icc, reliability. For a fitted model: one row per grouping level, with level, variance, sd, icc.

Details

Called on a data frame, the default estimator is the one-way random-effects ANOVA, which handles unbalanced panels through the usual n0 correction rather than assuming equal numbers of occasions per person:

$$\sigma^2_{between} = (MS_{between} - MS_{within}) / n_0, \qquad \sigma^2_{within} = MS_{within}$$

method = "reml" fits v ~ 1 + (1 | id) with lme4 instead. The two agree closely on balanced data; REML is preferable when the panel is badly unbalanced.

icc is the share of variance that lies between people. A high icc means people differ mostly in level, and a pooled model that ignores the person will be badly confounded. A low icc means most of the action is within-person, which is what idiographic modelling is for.

reliability is a different question – how precisely each person's mean is measured, given how many occasions they contributed. A variable can have a low icc (little between-person variance) and still have high reliability (that little variance is measured well).

Called on a fit_within_between() result fitted with estimator = "reml" or "ml", it returns the model's variance components instead: one row per grouping level plus the residual, which is what a null multilevel model is usually run to obtain.

Examples

variance_components(srl, vars = "efficacy:organizing", id = "name")
#> VARIANCE COMPONENTS
#>   Grouping   name
#>   Method     anova
#> 
#>                  Within    Between     ICC   Reliability
#> --------------------------------------------------------
#>   efficacy     472.5379   249.7267   0.346         0.988
#>   value        502.4351   208.0738   0.293         0.985
#>   planning     498.5651   217.8932   0.304         0.986
#>   monitoring   467.1183   437.6607   0.484         0.993
#>   effort       522.5017   207.7688   0.285         0.984
#>   control      552.2896   337.4665   0.379         0.990
#>   help         440.6868   327.0538   0.426         0.991
#>   social       469.0540   443.5421   0.486         0.993
#>   organizing   519.6494   251.0974   0.326         0.987
#> 
#>   ICC         share of variance lying BETWEEN groups
#>   Reliability precision of each group's own mean