A demand estimate is only as reportable as its standard error. The default maximum-likelihood variance — the inverse Hessian — is correct when the model is correctly specified and choice situations are independent draws. Applied work routinely violates one or both: the same decision maker contributes several choice situations (panel and survey data), the sample was drawn by outcome (choice-based sampling), or the likelihood is at best a useful approximation. choicer treats the variance estimator as a choice you make — and can revise after estimation, without refitting.
Every MNL, MXL and NL fit exposes four estimators through one interface:
type |
Estimator | When it is the right choice |
|---|---|---|
"hessian" |
Inverse analytical Hessian | Correct specification, independent choice situations. The classical default. |
"bhhh" |
Inverse outer product of scores (BHHH/OPG) | Same asymptotic justification as the Hessian; cheap; a common companion for simulated likelihoods. |
"robust" |
Huber-White sandwich | Quasi-ML under misspecification; also the valid variance under WESML / choice-based weighting (the meat is the weight-squared score outer product). |
"cluster" |
Sandwich over within-cluster sums of scores | Dependence across choice situations from the same decision maker, market, or sampling unit. |
Here the unit is the choice situation. If the same person supplies several situations, cluster on the person. No small-sample correction is applied—not a degrees-of-freedom multiplier, leverage correction, or few-cluster reference distribution—so the number of clusters should be reasonably large. With few clusters, the asymptotic cluster sandwich can be seriously anti-conservative; choicer does not currently implement CR2, a wild-cluster bootstrap, or randomization inference. Those designs require an external small-sample procedure or a research design with a defensible higher-level sampling argument.
Dependence you should expect: panel data
The cleanest way to see what clustering buys is to build data with
genuine within-person dependence. simulate_hmnl_data()
draws a panel in which each person has their own taste vector
and makes several choices with it — a stylized version of the persistent
within-person dependence in a survey or scanner panel.
sim <- simulate_hmnl_data(N = 500, T = 8, J = 4, seed = 3)We deliberately fit a plain multinomial logit. Because a homogeneous
logit is misspecified for this random-coefficients DGP, its point
estimates target the pseudo-true homogeneous-logit projection, not
generally the population mean
.
Its likelihood also treats all 500 * 8 = 4000 choice
situations as independent — which they are not, because each person’s
taste deviation persists across their eight tasks. Passing
cluster_col supplies the person labels at fit time and
selects cluster-robust standard errors for summary():
fit <- run_mnlogit(
data = sim$data,
id_col = "task",
alt_col = "alt",
choice_col = "choice",
covariate_cols = c("x1", "x2"),
cluster_col = "pid",
include_outside_option = TRUE
)
#> Optimization run time 0h:0m:0.06s
summary(fit)
#> Multinomial Logit (MNL) model
#>
#> Parameter Estimate Std.Error z-value Pr(>|z|)
#> x1 0.740484 0.044384 16.6835 0.00e+00 ***
#> x2 -0.537569 0.044763 -12.0092 0.00e+00 ***
#> ASC_1 0.943559 0.054241 17.3956 0.00e+00 ***
#> ASC_2 -0.198141 0.068933 -2.8744 4.05e-03 **
#> ASC_3 0.766699 0.054849 13.9783 0.00e+00 ***
#> ASC_4 0.708742 0.055895 12.6798 0.00e+00 ***
#> ---
#> Signif. codes: '***' 0.001 '**' 0.01 '*' 0.05
#>
#> Std. Errors: Cluster-robust sandwich
#> Log-likelihood: -5748.24
#> AIC: 11508.5 | BIC: 11546.2
#> McFadden R2: 0.107 (adj: 0.106) | Hit rate: 0.400
#> N: 4000 | Parameters: 6
#> Optimization time: 0.06 s
#> Convergence: 3 ( NLOPT_FTOL_REACHED: Optimization stopped because ftol_rel or ftol_abs (above) was reached. )How much did it matter? vcov(fit, type = ) recomputes
any of the four estimators from the stored per-situation scores:
se_of <- function(V) sqrt(diag(V))
tab <- cbind(
hessian = se_of(vcov(fit, type = "hessian")),
bhhh = se_of(vcov(fit, type = "bhhh")),
robust = se_of(vcov(fit, type = "robust")),
cluster = se_of(vcov(fit, type = "cluster"))
)
round(tab, 4)
#> hessian bhhh robust cluster
#> x1 0.0356 0.0349 0.0364 0.0444
#> x2 0.0352 0.0342 0.0363 0.0448
#> ASC_1 0.0565 0.0566 0.0564 0.0542
#> ASC_2 0.0701 0.0701 0.0700 0.0689
#> ASC_3 0.0579 0.0579 0.0579 0.0548
#> ASC_4 0.0584 0.0583 0.0585 0.0559
round(tab[, "cluster"] / tab[, "hessian"], 2)
#> x1 x2 ASC_1 ASC_2 ASC_3 ASC_4
#> 1.25 1.27 0.96 0.98 0.95 0.96The clustered standard errors on the slope coefficients are about 25%
wider than the Hessian ones; those on the alternative-specific constants
differ little. That pattern is the fingerprint of the data-generating
process: the persistent component is each person’s taste
deviation, so it is the slope scores that are correlated within person.
Note also that "robust" alone recovers almost none of this
— the Huber-White sandwich guards against misspecification of each
situation’s likelihood, not against dependence across
situations. If the same decision maker appears repeatedly,
robust-without-clustering is the wrong comfort.
Post hoc, without refitting
Nothing above required deciding at fit time. Any fit stored with
keep_data = TRUE (the default) can be re-inferenced later —
useful when the clustering level is itself a robustness question:
fit0 <- run_mnlogit(
data = sim$data,
id_col = "task",
alt_col = "alt",
choice_col = "choice",
covariate_cols = c("x1", "x2"),
include_outside_option = TRUE
)
#> Optimization run time 0h:0m:0.06s
# one cluster label per choice situation, named by choice-situation id
task_person <- unique(sim$data[, c("task", "pid")])
cl <- setNames(task_person$pid, task_person$task)
se_of(vcov(fit0, type = "cluster", cluster = cl))
#> x1 x2 ASC_1 ASC_2 ASC_3 ASC_4
#> 0.04438 0.04476 0.05424 0.06893 0.05485 0.05590The cluster vector has one entry per choice situation —
here, one pid per task — and is named by the
choice-situation id. choicer uses those names to realign labels safely
to its prepared order.
Clustering repairs inference, not the estimand
A caveat that matters for the mixed logit. run_mxlogit()
maximizes a cross-sectional simulated likelihood: each choice
situation’s probability is integrated over the mixing distribution
separately, rather than holding each simulation draw fixed across a
person’s tasks before integrating their joint probability. On panel
data, type = "cluster" makes the standard errors robust to
within-person dependence around its pseudo-true target, but the point
estimates still target that cross-sectional model — clustering does not
turn the fit into a panel mixed logit, in which one taste draw is shared
across a person’s choices. When the panel structure is the object of
interest — individual-level tastes, their distribution, persistence —
estimate the panel model instead: the hierarchical Bayesian logit
(run_hmnlogit() with person_col), covered in
the hierarchical Bayes vignette.
Choice-based sampling
When the sample was drawn by outcome (interviewing travellers at the
terminal of the mode they chose, oversampling rare hospitals), the
weights are not optional and the variance choice is forced: under WESML
weighting the inverse weighted Hessian and the ordinary BHHH variance
are both invalid, and type = "robust" — whose meat carries
the squared weights — is the correct estimator, conditional on the
supplied population shares Q. If weighted observations are
also dependent within sampling units, use the weighted cluster sandwich
instead; if Q is estimated, its uncertainty requires an
additional resampling or sensitivity layer. The choice-based sampling vignette develops the full
workflow, from population shares to weighted fit.
References
Berndt, E., Hall, B., Hall, R. and Hausman, J. (1974). Estimation and inference in nonlinear structural models. Annals of Economic and Social Measurement, 3(4), 653-665.
Cameron, A. C. and Miller, D. L. (2015). A practitioner’s guide to cluster-robust inference. Journal of Human Resources, 50(2), 317-372.
Manski, C. F. and Lerman, S. R. (1977). The estimation of choice probabilities from choice based samples. Econometrica, 45(8), 1977-1988.
White, H. (1982). Maximum likelihood estimation of misspecified models. Econometrica, 50(1), 1-25.