*! version 1.0.0 04jul2018

Title

cdfquantreg -- General linear models using cdf-quantile distributions for variables on the unit interval

Syntax

cdfquantreg
varlist
,cdf(
distribution1
)
quantile(
distribution2
)
[zvarlist(
varlist_z
)]
[nolog]

Description

cdfquantreg invokes maximum likelhood estimation using ml with
a linear form. A general linear model is estimated for a dependent variable
on the unit (0,1) interval, using a member of the cdf-quantile distributon family.

varlist must include at least the dependent variable, and also may include the
predictor variables for the location submodel. zvarlist is a non-required option
presenting the predictor variables for the dispersion submodel.

The cdf and quantile options are required, and they specify the
cdf-quantile distribution to be used in the model. Likewise, distribution1
and distribution2 are names chosen from the Distributions list below.

Also available is cdfquantreg_p, a postestimation command, which uses the specified
cdf-quantile distribution to generate the model's parameter estimates and
fitted values. See the help file for cdfquantreg_p.

Distribution Names

Distributions

asinh invokes the arcsinh distribution.

burr7 invokes the Burr 7 distribution.

burr8 invokes the Burr 8 distribution.

cauchit, cauchy invokes the Cauchy distribution.

logit, logistic invokes the logistic distribution.

t2 invokes the t distribution with 2 degrees of freedom.

CDF-Quantile Distributions

CDF-Quantile Distributions

asinhasinh invokes the arcsinh-arcsinh distribution (finite-tailed subfamily).

asinhburr7 invokes the arcsinh-Burr7 distribution (trimodal subfamily).

asinhburr8 invokes the arcsinh-Burr8 distribution (trimodal subfamily).

asinhcauchy invokes the arcsinh-Cauchy distribution (finite-tailed subfamily).

asinhlogistic invokes the arcsinh-logistic distribution (trimodal subfamily).

asinht2 invokes the arcsinh-t2 distribution (trimodal subfamily).

burr7asinh invokes the Burr7-arcsinh distribution (bimodal subfamily).

burr7burr7 invokes the Burr7-Burr7 distribution (logit-logistic subfamily).

burr7cauchy invokes the Burr7-Cauchy distribution (bimodal subfamily).

burr7logistic invokes the Burr7-logistic distribution (logit-logistic subfamily).

burr7t2 invokes the Burr7-t2 distribution (bimodal subfamily).

burr8asinh invokes the Burr8-arcsinh distribution (bimodal subfamily).

burr8burr7 invokes the Burr8-Burr7 distribution (logit-logistic subfamily).

burr8burr8 invokes the Burr8-Burr8 distribution (logit-logistic subfamily).

burr8cauchy invokes the Burr8-Cauchy distribution (bimodal subfamily).

burr8logistic invokes the Burr8-logistic distribution (logit-logistic subfamily).

burr8t2 invokes the Burr8-t2 distribution (bimodal subfamily).

cauchitasinh invokes the Cauchit-arcsinh distribution (finite-tailed subfamily).

cauchitburr7 invokes the Cauchit-Burr7 distribution (trimodal subfamily).

cauchitburr8 invokes the Cauchit-Burr8 distribution (trimodal subfamily).

cauchitcauchy invokes the Cauchit-Cauchy distribution (finite-tailed subfamily).

cauchitlogistic invokes the Cauchit-logistic distribution (trimodal subfamily).

cauchitt2 invokes the Cauchit-t2 distribution (trimodal subfamily).

logitasinh invokes the logit-arcsinh distribution (bimodal subfamily).

logitburr7 invokes the logit-Burr7 distribution (logit-logistic subfamily).

logitburr8 invokes the logit-Burr8 distribution (logit-logistic subfamily).

logitcauchy invokes the logit-Cauchy distribution (bimodal subfamily).

logitlogistic invokes the logit-logistic distribution (logit-logistic subfamily).

logitt2 invokes the logit-t2 distribution (bimodal subfamily).

t2asinh invokes the t2-arcsinh distribution (bimodal subfamily).

t2burr7 invokes the t2-Burr7 distribution (trimodal subfamily).

t2burr8 invokes the t2-Burr8 distribution (trimodal subfamily).

t2cauchy invokes the t2-Cauchy distribution (bimodal subfamily).

t2logistic invokes the t2-logistic distribution (trimodal subfamily).

t2t2 invokes the t2-t2 distribution (finite-tailed subfamily).

Example

/* This example uses ch6_probguiltstudy1.dta */

. cdfquantreg crguilt crvd1 crvd2, cdf(logit) quantile(logistic)

. estimates store A

. cdfquantreg crguilt crvd1 crvd2, cdf(logit) quantile(logistic) zvarlist(crvd1 crvd2)

. estimates store B

. lrtest A B

Author

Michael Smithson, Research School of Psychology, The Australian National University,
Canberra, A.C.T. Australia
Michael.Smithson@anu.edu.au

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.