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Socio-economic achievement gradient

Source: R/social_gradient.R
social_gradient.Rd

Computes the socio-economic gradient of achievement from large-scale assessment data, following the OECD PISA definition: the slope is the score-point change in achievement per one-unit change in the socio-economic index (e.g. ESCS), and the strength is the percentage of achievement variance explained by socio-economic status (\(R^2 \times 100\)). Optionally the quadratic curvature term is also reported.

Usage

social_gradient(
  data,
  achievement,
  escs = "ESCS",
  weight = NULL,
  repweights = NULL,
  rep_method = c("BRR", "JK2", "JK1"),
  fay = 0.5,
  design = NULL,
  curvature = TRUE,
  level = 0.95
)

Arguments

data

A data frame of student-level records.

achievement

Character vector of column names holding the achievement plausible values (e.g. paste0("PV", 1:10, "MATH")). A single column is allowed but then no imputation variance is estimated.

escs

Name of the socio-economic index column (default "ESCS").

weight

Name of the final student weight column. If NULL, all cases are weighted equally (with a message).

repweights

Optional character vector of replicate-weight column names. When supplied, standard errors are design-based; when NULL, a model-based (independence) standard error is returned with a warning.

rep_method

Replication design: "BRR" (PISA default), "JK2" (TIMSS/PIRLS) or "JK1". Used only when repweights is supplied.

fay

Fay adjustment for BRR (PISA uses 0.5); see rep_factor().

design

Optional lsa_design() bundling weight, repweights, rep_method and fay; when supplied it overrides those arguments.

curvature

Logical; if TRUE (default) also fit a quadratic model and report the curvature (ESCS-squared) coefficient.

level

Confidence level for the stored interval (default 0.95).

Value

An object of class "social_gradient" / "lsastrat_estimate" (see lsastrat_estimate for methods): a list with a coefficients data frame (rows slope, strength, and optionally curvature) plus metadata.

Details

Achievement is supplied as a set of plausible values (PVs); estimates are pooled across PVs with Rubin's rules, and the sampling variance is obtained from replicate weights when supplied (see pool_pv() and rep_factor()). Inference uses a \(t\) reference (see pool_pv() for the degrees of freedom).

References

OECD (2023). PISA 2022 Results (Volume I), Annex A3 (socio-economic gradient: slope and strength = \(R^2 \times 100\)).

Examples

data(pisa_mini)
social_gradient(
  pisa_mini,
  achievement = paste0("PV", 1:10, "MATH"),
  escs = "ESCS",
  weight = "W_FSTUWT",
  repweights = paste0("W_FSTURWT", 1:64)
)
#> Socio-economic achievement gradient
#>   SES index: ESCS   |   10 plausible value(s)   |   n = 2048
#>   Variance:  BRR, 64 replicate weights (+ PV imputation); t reference
#> 
#> 
#>           Estimate Std.Error     t    df       p
#> slope       41.357     1.831 22.59 399.4 2.1e-73
#> strength    20.189     1.799 11.22 389.1 1.7e-25
#> curvature    1.025     1.597  0.64 406.7 5.2e-01
#> 
#> slope = score points per 1 unit of ESCS; strength = % variance explained (R^2 x 100)