*! version 1.0.0 04jul2018

Title

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

Syntax

cdfquantreg01
varlist
,cdf(
distribution1
)
quantile(
distribution2
)
[pos(
position
)]
[func(
function
)]
[twothree(
num_parameters
)]
[zvarlist(
varlist_z
)]
[wvarlist(
varlist_w
)]
[nolog]

Description

cdfquantreg01 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 finite-tailed 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 in
a 2-parameter distribution model, and for the skew-parameter submodel in a
3-parameter distribution model. wvarlist is a non-required option
presenting the predictor variables for the dispersion submodel in a
3-parameter distribution model.

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.

The pos option is required, and specifies the inner versus outer
position type of distribution via the position name which is either "inner" or "outer".

The func option is required, and specifies the W versus V
type of skew function via the function name which is either "w" or "v".

The twothree option is required, and specifies the two- versus three-parameter
distributions via the num_parameters number which is either "2" or "3".

Also available are cdfquantreg01_p and cdfquantreg01_mf,
postestimation commands.
cdfquantreg01_p uses the specified cdf-quantile distribution to generate
the model's parameter estimates and fitted values. See the help file
for cdfquantreg_p.
cdfquantreg01_mf uses the specified cdf-quantile distribution to generate
estimates of marginal effects of each predictor in the model. See the help file
for cdfquantreg01_mf.

Distribution Names

asinh invokes the arcsinh distribution.

cauchit, cauchy invokes the Cauchy distribution.

t2 invokes the t distribution with 2 degrees of freedom.

asinh-asinh, asinh-cauchy, cauchit-asinh, cauchit-cauchy, t2-t2 are
the permissible cdf-quantile distributions.

Example 1

/* This example uses YoonData2.dta */

. generate loglosh = ln(losh)

. cdfquantreg01 pregptriage i.ambulance , cdf(cauchit) quantile(asinh) pos(outer) func(w) twothree(2) zvarlist(i.ambulance)

. estimates store A

. cdfquantreg01 pregptriage i.ambulance loglosh , cdf(cauchit) quantile(asinh) pos(outer) func(w) twothree(2) zvarlist(i.ambulance loglosh)

. estimates store B

. lrtest A B

Example 2

/* This example uses YoonData2.dta */

. generate loglosh = ln(losh)

. cdfquantreg01 pregptriage i.ambulance loglosh , cdf(cauchit) quantile(asinh) pos(outer) func(w) twothree(3) zvarlist(i.ambulance loglosh) wvarlist(i.ambulance loglosh)

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. (accepted 18/11/22). Flexible cdf-quantile distributions on the closed unit interval, with software and applications. Communications in Statistics – Theory and Methods.

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.