Estimates ordered probit switching regression (OPSR) models - a Heckman type selection model with an ordinal selection and continuous outcomes. Different model specifications are allowed for each treatment/regime.
# install.packages("devtools")
devtools::install_github("dheimgartner/OPSR")OPSR can be used whenever the ordinal treatment is not assigned exogenously but self-selected and one is interested in the treatment effect on a continuous outcome. The motivating example is telework frequency (conceptually, the treatment) and vehicle miles driven (the outcome of interest). We assume that two distinct processes lead people to choose a certain telework frequency and how mobile they are. Further and most importantly, the possibility of selection on unobservables exists. I.e., unobserved factors (as part of the errors of the two processes) might influence both the ordinal and continuous outcome. This leads to error correlation which needs to be accounted for in the modeling effort in spirit of Heckman.
library(OPSR)
#> To cite package 'OPSR' in publications use:
#>
#> Heimgartner D, Wang X (2025). "OPSR: A package for estimating ordered
#> probit switching regression models in R." Arbeitsbericht Verkehrs-
#> und Raumplanung 1907, IVT, ETH Zurich. doi:10.3929/ethz-b-000729641
#> <https://doi.org/10.3929/ethz-b-000729641>.
#>
#> Wang X, Mokhtarian PL (2024). "Examining the treatment effect of
#> teleworking on vehicle-miles driven: Applying an ordered probit
#> selection model and incorporating the role of travel stress."
#> _Transportation Research Part A_, *186*, 104072.
#> doi:10.1016/j.tra.2024.104072
#> <https://doi.org/10.1016/j.tra.2024.104072>.
#>
#> To see these entries in BibTeX format, use 'print(<citation>,
#> bibtex=TRUE)', 'toBibtex(.)', or set
#> 'options(citation.bibtex.max=999)'.
f <-
## ordinal and continuous outcome
twing_status | vmd_ln ~
## selection model
edu_2 + edu_3 + hhincome_2 + hhincome_3 +
flex_work + work_fulltime + twing_feasibility +
att_proactivemode + att_procarowning +
att_wif + att_proteamwork +
att_tw_effective_teamwork + att_tw_enthusiasm + att_tw_location_flex |
## outcome model NTW
female + age_mean + age_mean_sq +
race_black + race_other +
vehicle + suburban + smalltown + rural +
work_fulltime +
att_prolargehouse + att_procarowning +
region_waa |
## outcome model NUTW
edu_2 + edu_3 + suburban + smalltown + rural +
work_fulltime +
att_prolargehouse + att_proactivemode + att_procarowning |
## outcome model UTW
female + hhincome_2 + hhincome_3 +
child + suburban + smalltown + rural +
att_procarowning +
region_waa
fit <- opsr(f, telework_data, printLevel = 0)
summary(fit)
#>
#> Call:
#> opsr(formula = f, data = telework_data, printLevel = 0)
#>
#> BFGS maximization, 182 iterations
#> Return code 0: successful convergence
#> Runtime: 5.28 secs
#> Number of regimes: 3
#> Number of observations: 1584 (535, 322, 727)
#> Estimated parameters: 56
#>
#> Log-Likelihood: -3538.757
#> AIC: 7189.513
#> BIC: 7490.105
#> Pseudo R-squared (EL): 0.4868
#> Pseudo R-squared (MS): 0.462
#> Multiple R-squared: 0.2367 (0.1787, 0.1806, 0.1244)
#>
#> Estimates:
#> Estimate Std. error t value Pr(> t)
#> kappa1 1.1466204 0.1696082 6.760 1.38e-11 ***
#> kappa2 2.3801501 0.1771205 13.438 < 2e-16 ***
#> s_edu_2 0.2443606 0.1376536 1.775 0.075867 .
#> s_edu_3 0.4023184 0.1308658 3.074 0.002110 **
#> s_hhincome_2 0.0895885 0.1131361 0.792 0.428440
#> s_hhincome_3 0.2807199 0.1110217 2.529 0.011455 *
#> s_flex_work 0.2828764 0.0975378 2.900 0.003730 **
#> s_work_fulltime 0.2536533 0.0999697 2.537 0.011171 *
#> s_twing_feasibility 0.1326350 0.0057808 22.944 < 2e-16 ***
#> s_att_proactivemode 0.0815302 0.0398707 2.045 0.040868 *
#> s_att_procarowning -0.0779199 0.0404062 -1.928 0.053803 .
#> s_att_wif 0.1176906 0.0384118 3.064 0.002185 **
#> s_att_proteamwork 0.0855596 0.0370847 2.307 0.021047 *
#> s_att_tw_effective_teamwork 0.3151287 0.0435362 7.238 4.54e-13 ***
#> s_att_tw_enthusiasm 0.0852045 0.0379058 2.248 0.024589 *
#> s_att_tw_location_flex 0.0816184 0.0402637 2.027 0.042653 *
#> o1_(Intercept) 3.7426043 0.2775669 13.484 < 2e-16 ***
#> o1_female -0.2084407 0.1063050 -1.961 0.049905 *
#> o1_age_mean 0.0097620 0.0037000 2.638 0.008331 **
#> o1_age_mean_sq -0.0004327 0.0002485 -1.741 0.081616 .
#> o1_race_black -0.3918706 0.2375626 -1.650 0.099036 .
#> o1_race_other -0.0192830 0.1762266 -0.109 0.912868
#> o1_vehicle 0.1314998 0.0487828 2.696 0.007026 **
#> o1_suburban 0.0094855 0.1592882 0.060 0.952514
#> o1_smalltown 0.4147294 0.1828185 2.269 0.023297 *
#> o1_rural 0.4945182 0.2327146 2.125 0.033587 *
#> o1_work_fulltime 0.4367238 0.1316097 3.318 0.000906 ***
#> o1_att_prolargehouse 0.1864675 0.0523970 3.559 0.000373 ***
#> o1_att_procarowning 0.1224735 0.0664025 1.844 0.065123 .
#> o1_region_waa -0.2397950 0.1093528 -2.193 0.028318 *
#> o2_(Intercept) 2.4193729 0.3875823 6.242 4.31e-10 ***
#> o2_edu_2 0.2221850 0.3404089 0.653 0.513949
#> o2_edu_3 0.6693748 0.3253659 2.057 0.039658 *
#> o2_suburban 0.4451185 0.1734935 2.566 0.010299 *
#> o2_smalltown 0.2200755 0.2926442 0.752 0.452037
#> o2_rural 0.8233954 0.3244967 2.537 0.011166 *
#> o2_work_fulltime 0.7052761 0.1688305 4.177 2.95e-05 ***
#> o2_att_prolargehouse 0.1648046 0.0789276 2.088 0.036794 *
#> o2_att_proactivemode -0.1758775 0.0762701 -2.306 0.021112 *
#> o2_att_procarowning 0.1697231 0.0869310 1.952 0.050892 .
#> o3_(Intercept) 2.3798672 0.2883497 8.253 < 2e-16 ***
#> o3_female -0.3709856 0.1105030 -3.357 0.000787 ***
#> o3_hhincome_2 0.4654192 0.2557430 1.820 0.068779 .
#> o3_hhincome_3 0.3013654 0.2470044 1.220 0.222434
#> o3_child 0.1892227 0.0601994 3.143 0.001671 **
#> o3_suburban 0.2852249 0.1358278 2.100 0.035738 *
#> o3_smalltown 0.3087142 0.2846410 1.085 0.278110
#> o3_rural 0.8498792 0.3280278 2.591 0.009573 **
#> o3_att_procarowning 0.2499500 0.0583057 4.287 1.81e-05 ***
#> o3_region_waa -0.2709285 0.1087091 -2.492 0.012694 *
#> sigma1 1.1772629 0.0485867 24.230 < 2e-16 ***
#> sigma2 1.2358839 0.0675020 18.309 < 2e-16 ***
#> sigma3 1.4267208 0.0427374 33.383 < 2e-16 ***
#> rho1 0.0669559 0.0960455 0.697 0.485724
#> rho2 0.1326106 0.0680882 1.948 0.051459 .
#> rho3 0.3010864 0.0703368 4.281 1.86e-05 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Wald chi2 (null): 1261.888 on 45 DF, p-value: < 0
#> Wald chi2 (rho): 21.9907 on 3 DF, p-value: < 1e-04
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