Qualitative response models

Binary, ordinal and multinomial logit and probit models, conditional logit and simultaneous probit.

Usage

TDA_QRMODELS

tda_qreg(
  formula,
  data,
  model = "logit",
  nq = NULL,
  waves = NULL,
  min_waves = NULL,
  intercept = NULL,
  control = NULL,
  nintegral = NULL,
  tol_integral = NULL,
  parameterization = NULL,
  standardized = FALSE,
  predictions = FALSE,
  constraints = NULL,
  start = NULL,
  weights = NULL,
  options = list(),
  dir = tempfile("tda"),
  ...
)

Arguments

formula: a two-sided formula.
data: a data frame.
model: a name from TDA_QRMODELS or a TDA model number.
nq: number of categories, for models 5 and 6. Filled in from the data if not given.
waves, min_waves: the number of waves and, of those, the minimum with valid data required per case (nw=/pmin=); only meaningful for models 7 and 8 (see the Panel models section).
intercept: whether to include an intercept. Defaults to whatever the formula itself says (y ~ 0 + x or y ~ x - 1 already mean no intercept, the ordinary R way, and are honoured); set explicitly to override that.
control: convergence settings from tda_control.
nintegral, tol_integral: for models needing numerical integration (6-8), the integration control and its accuracy (qreg's nhp=/eps=).
parameterization: for models 6-8, how the between-wave correlation matrix is parameterised during estimation – 1 (default) direct; 2 a logistic-style transform keeping each correlation in $[-1, 1]$ by construction; 3 a Cholesky-style factorisation. A numerical-stability choice for the optimiser, not something that changes what the fitted correlations mean; qreg's opt=.
standardized: for a binary logit or probit model (model = "logit"/"probit") fit to cross-sectional data (no waves), also compute standardized coefficients – qreg's res=1. A separate table, in $standardized: each coefficient in standard-deviation units (Coeff), its exponential (Exp(C)), the exponential of the coefficient times the predictor's standard deviation (Exp(C*SD)), and that standard deviation itself (Std.Dev.). Only works for these two, cross-sectional models (TDA silently skips res= for any other), so requesting it for a different model errors here instead.
predictions: also write out each case's fitted probabilities – qreg's df=/dtda=. A separate table, in $predictions: case and wave identifiers, the response, predictors, weight (if given), and PROB/PROB0, PROB1, ... (one PROBn per outcome category the model has). Unlike standardized, model-agnostic: works for every model, each getting whichever PROB* columns it actually computes.
constraints: for model 6 (multivariate_probit) or 8 (simultaneous_probit), linear constraints on the model's parameters, in TDA's bN numbering – qreg's con=, the same linear-constraint machinery tda_lsreg's equality/inequality use, just addressed by number rather than by name. bN is the same numbering tda_estimates()'s Idx column already shows, so a first run without constraints tells you which number is which parameter. These two models introduce a correlation parameter for every pair of outcome categories ($\binom{nq}{2}$ of them) on top of the regular regression coefficients, and are usually only identified with most of them fixed – examples/exam/qr6.cf's worked example fixes all ten (nq = 5) to zero, constraints = paste0("b", 9:18, " = 0") here, reproduced exactly. model's formula and variable list stay exactly the shape every other model already uses: a single response, one row per case.
start: optional starting values, in TDA's parameter order (the same order bN in constraints refers to, and tda_estimates()'s Idx) – qreg's xp=. Often needed in practice for models 6/8: TDA's automatic starting-value generator is not always good enough for these two models' extra correlation parameters, and a fit that converges cleanly with good starting values can fail outright without them.
weights: optional case weights, a column name in data or a vector as long as the data – TDA's cwt = W;, a separate, standalone command (not a per-command option), the same convention tda_ple/tda_ltb use.
options: a named list of further TDA options, passed through: the output files.
dir: working directory.
...: passed to tda_run.

Value

An object of class tda_fit. For the multivariate and simultaneous probits (models 6 and 8) it carries correlation, the estimated correlation matrix among the latent equations, which TDA computes only when asked for a parameter file. It additionally carries categories, the (weighted) count and percentage of each response category as qreg itself tabulates them before estimating. Cases with missing values are dropped before the fit, with a message (see ?tdaR).

Models

model takes a name from TDA_QRMODELS, matched partially, or a TDA model number:

1	`logit`	binary logit
2	`probit`	binary probit
3	`ordinal_logit`	needs three or more categories
4	`ordinal_probit`	needs three or more categories
5	`multinomial_logit`	needs `nq`
6	`multivariate_probit`	needs `nq`
7	`conditional_logit`	panel: needs `waves` (2+) and `cbind()` terms – see Panel models
8	`simultaneous_probit`	panel: needs `waves` (2+) and `cbind()` terms – see Panel models

Panel models (waves)

Models 7 and 8 are TDA's panel models, taking each variable once per wave in a horizontal layout. Write each variable's per-wave columns as cbind(): cbind(y1, y2) ~ cbind(x1, x2) with waves = 2. A term with a single column is a time-constant predictor and is repeated across waves for you. Both models are fit without an intercept option (TDA's design; model 8 estimates one intercept per wave anyway, printed against Term = "W <k>", with the between-wave correlations as Sigma rows).

Missing data follows TDA's unbalanced-panel rule: a case whose response is missing in a wave simply has that wave dropped from its likelihood contribution (min_waves – TDA's pmin= – then sets how many valid waves a case needs to be used at all), while a missing predictor value has no such rule and drops the case, with a message.

conditional_logit is Chamberlain's fixed-effects logit; on two-wave data it agrees with survival::clogit stratified by case to full printed precision (pinned in the tests). simultaneous_probit fits one binary probit per wave with free cross-wave error correlations – for two waves, a bivariate probit. TDA's help text for this is incomplete: it names only model 5 as needing nq, though models 5 and 6 both require it, and it lists only the first five models, though eight are implemented – the table above is the full set. The binary models agree with glm: a binary logit is a binomial glm with a logit link, a binary probit one with a probit link.

Examples

set.seed(23)
d <- data.frame(x = round(rnorm(200), 3))
d$y <- rbinom(200, 1, plogis(-0.5 + 1.4 * d$x))
qf <- tda_qreg(y ~ x, d, model = "logit")
coef(qf)
#>  Intercept          x 
#> -0.6819166  1.7243012 
coef(glm(y ~ x, d, family = binomial()))  # matches: a binary logit is a
#> (Intercept)           x 
#>  -0.6819166   1.7243012 
                                           # binomial glm with a logit link
head(predict(qf))                         # fitted values, no newdata needed
#> [1] -0.3491264 -1.4319876  0.8923705  2.4097556  1.0372118  1.2268849