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Fit any model to plausible-value outcomes with replicate-weight inference

Source: R/lsa_model.R
lsa_model.Rd

A general estimation engine: fit an arbitrary model (linear, generalised linear, multilevel, ...) to a plausible-value outcome on each plausible value and each replicate weight, and pool the coefficients with Rubin's rules and replicate-weight variance. This lifts the package beyond the built-in estimators – and beyond the OLS-only support of intsvy and similar – to any model whose fitter accepts formula, data and weights.

Usage

lsa_model(
  data,
  formula,
  achievement,
  fitter = stats::lm,
  coefs = stats::coef,
  weight = NULL,
  repweights = NULL,
  rep_method = c("BRR", "JK2", "JK1"),
  fay = 0.5,
  design = NULL,
  level = 0.95,
  ...
)

Arguments

data

A data frame of student-level records.

formula

A one-sided formula of the predictor/structure, e.g. ~ ESCS + IMMIG or, for a multilevel model, ~ ESCS + (1 | school_id). The outcome is filled in from achievement for each plausible value.

achievement

Character vector of achievement plausible-value columns (the outcome set). A single column is allowed.

fitter

The model-fitting function (default stats::lm); e.g. stats::glm, lme4::lmer. Must accept formula, data and weights.

coefs

A function extracting a named numeric vector of the parameters to pool from a fitted model (default stats::coef; use lme4::fixef for lme4::lmer).

weight, repweights, rep_method, fay, design

Weighting/replication specification, exactly as in the other estimators (see social_gradient() and lsa_design()).

level

Confidence level for the stored interval (default 0.95).

...

Further arguments passed to fitter (e.g. family = binomial() for a logistic model).

Value

An object of class "lsa_model" / "lsastrat_estimate" with one row per model coefficient (see lsastrat_estimate for methods).

Details

Standard errors are design-based: each coefficient's sampling variance comes from refitting on the replicate weights, and the spread across plausible values adds the imputation component (Rubin's rules). With multilevel fitters this means many model fits (replicates x plausible values); use a modest number of replicates while prototyping. For weighted logistic models prefer family = quasibinomial() over binomial() to avoid the "non-integer #successes" warning that survey weights trigger.

Examples

data(pisa_mini)
des <- lsa_design(weight = "W_FSTUWT", repweights = paste0("W_FSTURWT", 1:64))
# a multiple regression on a PV outcome
lsa_model(pisa_mini, ~ ESCS + IMMIG, achievement = paste0("PV", 1:10, "MATH"),
          design = des)
#> Model: stats::lm(<PV> ~ ESCS + IMMIG)
#>   10 plausible value(s)  |  n = 2048
#>   Variance: BRR, 64 replicate weights (+ PV imputation); t reference
#> 
#> 
#>                 Estimate Std.Error      t     df       p
#> (Intercept)      496.490     2.220 223.66 4968.3 0.0e+00
#> ESCS              40.679     1.871  21.74  382.1 8.5e-69
#> IMMIGsecond_gen   -9.843     4.308  -2.28  231.0 2.3e-02
#> IMMIGfirst_gen    -4.038     9.319  -0.43  469.4 6.6e-01
#> 
#> fitter = stats::lm