Dear Statalisters,
I have contributed this module to SSC (thanks to Kit Baum):
cdfquantreg: Stata module for estimating generalized linear models for doubly-bounded random variables with cdf-quantile distributions.
cdfquantreg estimates generalized linear models with cdf-quantile distributions for doubly-bounded random variables (Smithson & Shou, 2017). It assumes that the dependent variable's values are in the (0,1) interval. These two-parameter distributions are especially useful for modeling quantiles, and have very flexible shapes. They enable a wide variety of quantile regression models with predictors for the location and dispersion parameters, and simple interpretations of those parameters. Users may specify separate submodels for the location and for the dispersion parameters, with different or overlapping sets of predictors in each. This module has similar capabilities to its counterpart package in R (Shou & Smithson, 2019).
For example, Yu et al. (2015) present a study of depressive symptoms in Chinese university students, using the Beck Depression Inventory (BDI). The BDI has a lower and upper bound, so we linearly transform the BDI scores to the (0,1) interval. The data-set is available in the online supplementary materials for the book by Smithson and Shou (2019). Among the potential predictors of depression for the students is a three-category indicator of the quality of their parental relationship: 3 = "good", 2 = "moderate", and 1 = "poor". A cdf-quantile model predicting BDI scores from parental relationship quality, using the logit-logistic distribution, yields two results. The eq1 output is the location submodel, and it indicates that the median BDI score is significantly lower for students whose parental relationship is scored "3" than for those with a parental relationship score of "1". The eq2 output is the scale (or disperesion) submodel, and indicates that the spread of BDI scores is significantly greater for students whose parental relationship is scored "3" than for those with a parental relationship score of "1".
In addition to the usual post-estimation utilities there is a helper program that provides estimates of user-specified conditional quantiles of the dependent variable. In the examples below we produce predicted values for the 75th and 25th quantiles. The two commented lines of calculations at the end show that the odds-ratio of these quantiles is greater in the "good" than in the "poor" parental relationship category, as indicated by the positive dispersion submodel coefficient in the eq2 output.
The following help files are included in this module:
cdfquantreg.sthlp, cdfquantreg_postestimation.sthlp, cdfquantreg_margins.sthlp
I am grateful to Bill Rising for his considerable advice and help on this project, but I hasten to add that any faults or errors in the module are mine alone. I welcome comments and suggestions, and an appropriate citation would be greatly appreciated if you end up using this module in your own research.
References:
Smithson, M. & Shou, Y. (2017). CDF-quantile distributions for modeling random variables on the unit interval. British Journal of Mathematical and Statistical Psychology, 70(3), 412-438 .
Shou, Y. & Smithson, M. (2019). cdfquantreg: An R package for CDF-Quantile Regression. Journal of Statistical Software, 88, 1-30.
Smithson, M. & Shou, Y. (2019). Generalized Linear Models for Bounded and Limited Quantitative Variables. Quantitative Applications in the Social Sciences Series. Belmont, CA: Sage.
Yu, Y., Yang, X., Yang, Y., Chen, L., Qiu, X., Qiao, Z., ... & He, J. (2015). The role of family environment in depressive symptoms among university students: a large sample survey in China. PloS One, 10(12), e0143612.
I have contributed this module to SSC (thanks to Kit Baum):
cdfquantreg: Stata module for estimating generalized linear models for doubly-bounded random variables with cdf-quantile distributions.
cdfquantreg estimates generalized linear models with cdf-quantile distributions for doubly-bounded random variables (Smithson & Shou, 2017). It assumes that the dependent variable's values are in the (0,1) interval. These two-parameter distributions are especially useful for modeling quantiles, and have very flexible shapes. They enable a wide variety of quantile regression models with predictors for the location and dispersion parameters, and simple interpretations of those parameters. Users may specify separate submodels for the location and for the dispersion parameters, with different or overlapping sets of predictors in each. This module has similar capabilities to its counterpart package in R (Shou & Smithson, 2019).
Code:
ssc install cdfquantreg
Code:
. cdfquantreg trbdi i.parentrel, cdf(logit) quantile(logistic) zvarlist(i.parentrel) nolog
Number of obs = 4,582
Wald chi2(2) = 71.46
Log likelihood = 4675.7358 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
trbdi | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
eq1 |
parentrel |
2 | -.0167766 .1381178 -0.12 0.903 -.2874826 .2539294
3 | -.5778559 .1268643 -4.55 0.000 -.8265054 -.3292063
|
_cons | -2.027631 .1220459 -16.61 0.000 -2.266836 -1.788425
-------------+----------------------------------------------------------------
eq2 |
parentrel |
2 | -.0225056 .069397 -0.32 0.746 -.1585212 .11351
3 | .1646371 .0625629 2.63 0.008 .0420161 .2872581
|
_cons | .0670706 .0607738 1.10 0.270 -.0520438 .186185
------------------------------------------------------------------------------
Code:
. cdfquantreg_m parentrel, pctle(0.75)
Adjusted predictions Number of obs = 4,582
Model VCE : OIM
Expression : Linear prediction, predict(equation(#1))
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
parentrel |
1 | -2.027631 .1220459 -16.61 0.000 -2.266836 -1.788425
2 | -2.044407 .0646633 -31.62 0.000 -2.171145 -1.917669
3 | -2.605487 .0346319 -75.23 0.000 -2.673364 -2.537609
------------------------------------------------------------------------------
(results modresults are active now)
Adjusted predictions Number of obs = 4,582
Model VCE : OIM
Expression : Linear prediction, predict(equation(#2))
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
parentrel |
1 | .0670706 .0607738 1.10 0.270 -.0520438 .186185
2 | .044565 .0335035 1.33 0.183 -.0211007 .1102307
3 | .2317077 .0148547 15.60 0.000 .202593 .2608224
------------------------------------------------------------------------------
(results modresults are active now)
parentrel
.75 quantile factor level
--------------------------
.29884445 1bn.parentrel
.28992918 2.parentrel
.22786434 3.parentrel
. cdfquantreg_m parentrel, pctle(0.25)
* [SNIP] *
parentrel
.25 quantile factor level
--------------------------
.03907345 1bn.parentrel
.03942672 2.parentrel
.01815365 3.parentrel
* (.29884445/(1-.29884445))/(.03907345/(1-.03907345)) = 10.48188
* (.22786434/(1-.22786434))/(.01815365/(1-.01815365)) = 15.96108
cdfquantreg.sthlp, cdfquantreg_postestimation.sthlp, cdfquantreg_margins.sthlp
I am grateful to Bill Rising for his considerable advice and help on this project, but I hasten to add that any faults or errors in the module are mine alone. I welcome comments and suggestions, and an appropriate citation would be greatly appreciated if you end up using this module in your own research.
References:
Smithson, M. & Shou, Y. (2017). CDF-quantile distributions for modeling random variables on the unit interval. British Journal of Mathematical and Statistical Psychology, 70(3), 412-438 .
Shou, Y. & Smithson, M. (2019). cdfquantreg: An R package for CDF-Quantile Regression. Journal of Statistical Software, 88, 1-30.
Smithson, M. & Shou, Y. (2019). Generalized Linear Models for Bounded and Limited Quantitative Variables. Quantitative Applications in the Social Sciences Series. Belmont, CA: Sage.
Yu, Y., Yang, X., Yang, Y., Chen, L., Qiu, X., Qiao, Z., ... & He, J. (2015). The role of family environment in depressive symptoms among university students: a large sample survey in China. PloS One, 10(12), e0143612.
