Composite regression estimator (CRE / regression composite estimation)

Final-weight step for rotating panels that exploits the sample overlap in the estimation, not only in the variance. It is the composite calibration of the Canadian LFS (Gambino, Kennedy and Singh 2001; Fuller and Rao 2001) and the composite calibration of the Uruguayan ECH (INE, methodology sec. 8.4): the same estimator. On top of the ordinary calibration to known population totals X, it adds a second set of constraints to control totals Zhat estimated from the previous wave (the composite auxiliaries: previous-month labour status, optionally crossed by domains). Because Zhat uses the previous wave's composite weights, the estimator is recursive.

Usage

step_cre(
  spec,
  previous = NULL,
  status,
  composite = list(NULL),
  id_unit,
  formula,
  totals = NULL,
  count = NULL,
  birth = NULL,
  alpha = 2/3,
  overlap = "auto",
  on_missing_prev = c("carry_backward", "zero"),
  cluster = NULL,
  equal_within_cluster = FALSE,
  calfun = c("linear", "logit", "raking"),
  bounds = NULL,
  rotation_group = NULL,
  status_ref = NULL,
  id = NULL
)

Arguments

spec: a weighting_spec (its recipe up to here yields the nonresponse-adjusted weights w_nr that this step starts from).
previous: the prepped previous-wave recipe (prep() output), which supplies the previous composite weights and the previous labour status for Zhat and the overlap imputation. NULL (default) is the seed wave: with no t-1 there is no composite block and the step reduces to an ordinary linear calibration to X – the start of the recursion.
status: bare or quoted name of the categorical labour-status column (e.g. employed / unemployed / inactive) in the current wave; must exist with the same name in previous. Its indicators are the composite auxiliaries.
composite: a list of domain crossings, each defining one block of composite control totals. NULL = country total; a string = status crossed by that domain (e.g. "sex"); a character vector = status crossed by the interaction (e.g. c("sex","age")). This mirrors the methodologies' composite-variable lists: the ECH's are list(NULL, "sex", "department"). Default list(NULL).
id_unit: character vector naming the unit key that links waves (e.g. c("household","person")). Used to look up each current unit's t-1 status.
formula: the demographic auxiliary formula for x (as in step_calibrate() method = "linear"), e.g. ~ age_sex + region.
totals, count: the population totals X for x, in the same forms accepted by step_calibrate() (a named vector aligned to the model.matrix, or the tidy named list with count).
birth: expression (evaluated in the current data) that is TRUE for the birth rotation group (the units with no t-1 value to carry). If NULL, birth units are those not found in previous by id_unit.
alpha: MR1/MR2 mixing constant between 0 and 1. alpha = 0 targets the level only (MR1), alpha = 1 the change only (MR2). Default 2/3 (Chen and Liu 2002).
overlap: the overlap rate used by the MR2 carry-backward correction: "auto" (default) estimates it as the w_nr-weighted overlap fraction, or a number (e.g. 5/6, the nominal LFS/ECH rate).
on_missing_prev: how to treat non-birth units without a valid t-1 status (new household members, newly of working age): "carry_backward" (default; set z_{t-1} = z_t) or "zero" (z_{t-1} = 0).
cluster, equal_within_cluster: integrated method of weighting: with equal_within_cluster = TRUE (needs cluster) the auxiliaries x and z are averaged to the cluster so members share one weight (Lemaitre-Dufour 1987).
calfun, bounds: distance and g-bounds for the calibration, as in step_calibrate(). Use bounds = c(L, U) with a logit calfun to avoid final weights below 1.
rotation_group: optional name of the rotation-group column. When given, the step adds the equal-representation constraints both surveys impose: each rotation group must weight to the same working-age total, N / G (ECH sec. 8.4.1, sum_{i in s_g} w_i = N_PET / 6; LFS sec. 6.3.1). N is read from the intercept target in totals and G is the number of groups; the last group is left implied (its total follows from the others and N), so G - 1 constraints are added to the demographic block. NULL (default) omits them.
status_ref: the status level held as reference (dropped from each cell block to avoid the mechanical collinearity between the full status indicators and the demographic block, which pins the same cell totals). The dropped total is implied by the others plus X, so the estimator is unchanged; naming the level only sets which one is implicit (e.g. "inact" to keep employed/unemployed explicit). NULL (default) drops the last level in sorted order. One level is always dropped: keeping every level would make the block collinear with the intercept in X.
id: optional stable identifier for this step.

Value

the input weighting_spec with the CRE step appended (evaluated at prep()). Chain waves by passing each prepped wave as the previous of the next.

Details

The composite auxiliary z is known for the overlap sample (units present in t-1) and imputed for the birth rotation group (units entering at t, with no t-1 value) by combining two imputations: MR1 (mean imputation, aimed at the level) and MR2 (carry-backward, aimed at the change), mixed as z = (1 - alpha) z1 + alpha z2 with alpha = 2/3.

The composite weights are w_cre = w_nr * g, with g the GREG factor of the augmented calibration [x | z] to [X | Zhat]; the same solver as step_calibrate(). With equal_within_cluster = TRUE the auxiliaries are averaged to the household (integrated method of weighting, Lemaitre-Dufour 1987) so every household member shares one final weight.

References

Gambino J, Kennedy B, Singh MP (2001). Regression composite estimation for the Canadian Labour Force Survey. Survey Methodology 27(1):65-74. Fuller WA, Rao JNK (2001). A regression composite estimator with application to the Canadian Labour Force Survey. Survey Methodology 27(1):45-51. Instituto Nacional de Estadistica (Uruguay). Metodologia de la Encuesta Continua de Hogares, seccion 8.4 (calibracion compuesta).

Examples

# Composite (CRE) estimation on the 6-month rotating panel `panel_ine`.
# `condicion` is the previous-wave labour status (emp / unemp / inact).
t1 <- subset(panel_ine, ola == 1 & disp == "R")
t2 <- subset(panel_ine, ola == 2 & disp == "R")
t1$sexo <- factor(t1$sexo); t2$sexo <- factor(t2$sexo)
Xtot <- function(d) colSums(d$w_base * stats::model.matrix(~ sexo, data = d))

# seed wave: no previous month, so step_cre() reduces to a linear calibration to X
seed <- weighting_spec(t1, base_weights = w_base) |>
  step_cre(previous = NULL, status = condicion, formula = ~ sexo,
           totals = Xtot(t1), status_ref = "inact") |>
  prep()

# composite wave: augment X with the previous-wave status, country-level and by sex
fit2 <- weighting_spec(t2, base_weights = w_base) |>
  step_cre(previous = seed, status = condicion, composite = list(NULL, "sexo"),
           id_unit = c("id_hogar", "nper"), formula = ~ sexo, totals = Xtot(t2),
           alpha = 2/3, status_ref = "inact") |>
  prep()
fit2
#> 
#> == Weighting specification (weightflow) ==
#> Data    : 1774 cases
#> Base wts: w_base
#> Steps   :
#>   1. composite regression estimator (composite, alpha = 0.67)  [cre_1]
#> Status  : estimated (prep)
#> 
#> Stage summary:
#>             stage n_active sum_wts cv_wts deff_kish n_eff
#>              base     1774  254211  0.304     1.092  1624
#>  stage_1_step_cre     1774  254211  0.373     1.139  1557
#> 
#> deff_kish = 1 + CV^2 (Kish design effect from unequal weighting);
#> n_eff = n_active / deff_kish. Both worsen with each adjustment and
#> improve with trimming.
#>