Tidy a MAIHDA summary, model, or analysis

tidy methods that return the MAIHDA estimates as a tidy tibble, ready for downstream tables (gt, flextable) and ggplot2. They read the slots that summary.maihda_model already computes and add no new statistics.

Usage

# S3 method for class 'maihda_summary'
tidy(x, component = c("strata", "variance", "fixed"), ...)

# S3 method for class 'maihda_model'
tidy(x, component = c("strata", "variance", "fixed"), ...)

# S3 method for class 'maihda_analysis'
tidy(
  x,
  component = c("strata", "variance", "fixed"),
  which = c("null", "adjusted"),
  ...
)

Arguments

x

A maihda_summary (from summary), a maihda_model (from fit_maihda), or a maihda_analysis (from maihda).

component

Which estimates to return:

"strata"

(default) the stratum (intersection) random-effect estimates – one row per stratum, with estimate, std.error and conf.low/conf.high, plus the human-readable intersectional label when available.

"variance"

the variance-components table (between-stratum, any other random effects, residual, and total) with each component's variance, SD and proportion.

"fixed"

the fixed-effect estimates in broom's term/estimate/std.error/statistic/ p.value/conf.low/conf.high shape.

...

Unused, for S3 consistency.

which

For a maihda_analysis, whether to tidy the "null" (default) or "adjusted" model's summary.

Value

A tibble. For component = "strata": columns stratum, label, estimate, std.error, conf.low, conf.high. For "variance": component, variance, sd, proportion. For "fixed": term, estimate, std.error, statistic, p.value, conf.low, conf.high.

Fixed-effect statistics

For the lme4, WeMix and ordinal engines statistic is the Wald \(z\) (estimate / std.error), p.value its two-sided normal-approximation p-value, and conf.low/conf.high the matching Wald interval at the conf_level the summary was computed at (95% by default). No denominator degrees of freedom are estimated, so these are z-based rather than Satterthwaite or Kenward-Roger.

Which terms that approximation is safe for depends on how they vary. A covariate that varies within a stratum has an effective sample size of the number of observations, and z is essentially exact for it. The intercept and the dimension main effects of an adjusted MAIHDA model are constant within a stratum by construction, so their effective sample size is the number of strata, however large \(n\) is: with few strata their intervals are too narrow and their p-values anticonservative. As a rough guide, a Kenward-Roger check gives those terms about 5% wider intervals at 50 strata but roughly 40% wider at 10. When that matters, apply lmerTest or pbkrtest to the underlying fit (x$model, an lmerMod), or use the brms engine.

For brms the estimate is the posterior mean with its Est.Error and credible interval, and statistic/p.value are NA. Standard errors are NA where they are undefined (a boundary fit).

See also

glance.maihda_analysis for the one-row model summary.

Examples

data("maihda_health_data")
m <- fit_maihda(BMI ~ Age + (1 | Gender:Race:Education), data = maihda_health_data)
tidy(m)                       # stratum estimates
#> # A tibble: 50 × 6
#>    stratum label                           estimate std.error conf.low conf.high
#>    <chr>   <chr>                              <dbl>     <dbl>    <dbl>     <dbl>
#>  1 1       male × Hispanic × Some College  -0.245       1.04   -2.29      1.80  
#>  2 2       male × Black × College Grad      0.772       1.11   -1.41      2.96  
#>  3 3       female × White × College Grad   -1.82        0.352  -2.51     -1.13  
#>  4 4       male × Hispanic × 8th Grade      0.921       1.32   -1.66      3.51  
#>  5 5       female × Mexican × 8th Grade     1.82        0.951  -0.0409    3.69  
#>  6 6       male × White × College Grad     -0.743       0.357  -1.44     -0.0431
#>  7 7       female × White × High School     0.00494     0.419  -0.816     0.826 
#>  8 8       male × White × Some College      1.02        0.356   0.326     1.72  
#>  9 9       female × White × 9 - 11th Grade  0.685       0.604  -0.498     1.87  
#> 10 10      female × Hispanic × High School  0.287       1.07   -1.81      2.38  
#> # ℹ 40 more rows
tidy(m, component = "variance")
#> # A tibble: 3 × 4
#>   component                 variance    sd proportion
#>   <chr>                        <dbl> <dbl>      <dbl>
#> 1 Between-stratum (random)      2.90  1.70     0.0627
#> 2 Within-stratum (residual)    43.4   6.59     0.937 
#> 3 Total                        46.3   6.80     1     
tidy(m, component = "fixed")
#> # A tibble: 2 × 7
#>   term        estimate std.error statistic p.value  conf.low conf.high
#>   <chr>          <dbl>     <dbl>     <dbl>   <dbl>     <dbl>     <dbl>
#> 1 (Intercept)  28.2      0.453       62.3   0      27.3        29.1   
#> 2 Age           0.0150   0.00736      2.04  0.0410  0.000616    0.0295