Compares a quantity (a gradient slope, a mean, a segregation index, ...) across two or more assessment cycles and reports the change from the baseline cycle, propagating the linking (equating) error into the standard error of each change. Comparing scores across PISA/TIMSS cycles carries an extra uncertainty from re-equating the scale; the variance of a cross-cycle difference is $$\mathrm{Var}(\Delta) = SE_1^2 + SE_2^2 + \mathrm{linkerror}^2.$$
Arguments
- cycles
A named list of fitted estimate objects (class
"lsastrat_estimate"), one per cycle, in chronological order; the names are the cycle labels (e.g."2012","2018","2022"). The first cycle is the baseline.- term
Which term (coefficient row) to track; defaults to the first.
- link_error
The linking error to add to each change's standard error: a single value applied to every cycle-vs-baseline comparison, or a vector of length
length(cycles) - 1. Defaults to0(no link error).- level
Confidence level for the change intervals (default
0.95).
Value
An object of class "lsa_trend": a list with a coefficients data
frame (one row per cycle: estimate, se, and – for non-baseline cycles
– change, change_se, statistic, p, ci_lo, ci_hi of the change
from baseline) plus metadata. Cross-cycle change tests use a normal
reference.
Details
The link error applies only to quantities expressed on the achievement
scale (means, score-point gradient slopes). For scale-free quantities
(correlations, the gradient strength / \(R^2\), segregation indices,
inequality-of-opportunity shares) set link_error = 0.
Examples
data(pisa_mini)
des <- lsa_design(weight = "W_FSTUWT", repweights = paste0("W_FSTURWT", 1:64))
math <- paste0("PV", 1:10, "MATH")
# two illustrative "cycles" (here, two halves of the simulated data)
h <- nrow(pisa_mini) %/% 2
c1 <- social_gradient(pisa_mini[1:h, ], math, "ESCS", design = des)
c2 <- social_gradient(pisa_mini[-(1:h), ], math, "ESCS", design = des)
lsa_trend(list("2018" = c1, "2022" = c2), term = "slope", link_error = 3.5)
#> Trend in `slope` (social_gradient) across 2 cycles; baseline = 2018
#> linking error: 3.5 (added to each change SE)
#>
#> cycle estimate se change change.se z p
#> 2018 41.308 2.874 0.000 NA NA NA
#> 2022 41.454 2.426 0.146 5.137 0.03 0.98
#>
#> change = estimate - baseline; SE includes the linking error