zeligchoice-ologit¶

Syntax¶

First load packages:

library("Zelig")
library("ZeligChoice")

With reference classes:

z5 <- zologit$new()
z5$zelig(as.factor(Y) ~ X1 + X2, data = mydata)
z5$setx()
z5$sim()

With the Zelig 4 compatibility wrappers:

z.out <- zelig(as.factor(Y) ~ X1 + X23,
               model = "ologit", data = mydata)
x.out <- setx(z.out)
s.out <- sim(z.out, x = x.out, x1 = NULL)

If Y takes discrete integer values, the as.factor() command will order automatically order the values. If Y takes on values composed of character strings, such as “strongly agree”, “agree”, and “disagree”, as.factor() will order the values in the order in which they appear in Y. You will need to replace your dependent variable with a factored variable prior to estimating the model through zelig(). See Section [factors] for more information on creating ordered factors and Example [ord.fact] below.

Example¶

data(sanction)

sanction$ncost <- factor(sanction$ncost, ordered = TRUE,
                         levels = c("net gain", "little effect", "modest loss", "major loss"))

z.out <- zelig(ncost ~ mil + coop, model = "ologit",
               data = sanction)

## Warning in readLines(zeligmixedmodels): incomplete final line found on
## '/usr/lib64/R/library/ZeligMultilevel/JSON/zelig5mixedmodels.json'

## How to cite this model in Zelig:
##   William N. Venables, and Brian D. Ripley. 2011.
##   ologit: Ordinal Logit Regression for Ordered Categorical Dependent Variables
##   in Christine Choirat, Christopher Gandrud, James Honaker, Kosuke Imai, Gary King, and Olivia Lau,
##   "Zelig: Everyone's Statistical Software," http://zeligproject.org/

summary(z.out)

## Model:
## Call:
## z5$zelig(formula = ncost ~ mil + coop, data = sanction)
##
## Coefficients:
##         Value Std. Error  t value
## mil  -0.00131      0.732 -0.00179
## coop  1.04055      0.262  3.96607
##
## Intercepts:
##                           Value  Std. Error t value
## net gain|little effect     1.260  0.482      2.617
## little effect|modest loss  3.936  0.698      5.636
## modest loss|major loss     5.609  0.899      6.236
##
## Residual Deviance: 153.07
## AIC: 163.07
## Next step: Use 'setx' method

x.out <- setx(z.out)

s.out <- sim(z.out, x = x.out)

summary(s.out)

##
##  sim x :
##  -----
## ev
##                 mean     sd    50%     2.5% 97.5%
## net gain      0.3498 0.0555 0.3464 2.49e-01 0.458
## little effect 0.4944 0.1517 0.5225 1.63e-01 0.711
## modest loss   0.0831 0.0697 0.0705 8.95e-06 0.244
## major loss    0.0727 0.1102 0.0180 6.76e-09 0.384
## pv
##      mean    sd 50% 2.5% 97.5%
## [1,] 1.91 0.842   2    1     4

plot(s.out)

z.out <- zelig(as.factor(cost) ~ mil + coop, model = "ologit",
               data = sanction)

## Warning in readLines(zeligmixedmodels): incomplete final line found on
## '/usr/lib64/R/library/ZeligMultilevel/JSON/zelig5mixedmodels.json'

## How to cite this model in Zelig:
##   William N. Venables, and Brian D. Ripley. 2011.
##   ologit: Ordinal Logit Regression for Ordered Categorical Dependent Variables
##   in Christine Choirat, Christopher Gandrud, James Honaker, Kosuke Imai, Gary King, and Olivia Lau,
##   "Zelig: Everyone's Statistical Software," http://zeligproject.org/

summary(z.out)

## Model:
## Call:
## z5$zelig(formula = as.factor(cost) ~ mil + coop, data = sanction)
##
## Coefficients:
##         Value Std. Error  t value
## mil  -0.00131      0.732 -0.00179
## coop  1.04055      0.262  3.96607
##
## Intercepts:
##     Value  Std. Error t value
## 1|2  1.260  0.482      2.617
## 2|3  3.936  0.698      5.636
## 3|4  5.609  0.899      6.236
##
## Residual Deviance: 153.07
## AIC: 163.07
## Next step: Use 'setx' method

x.low <- setx(z.out, coop = 1)
x.high <- setx(z.out, coop = 4)

s.out2 <- sim(z.out, x = x.low, x1 = x.high)
summary(s.out2)

##
##  sim x :
##  -----
## ev
##     mean     sd     50%     2.5% 97.5%
## 1 0.5492 0.0689 0.55423 4.05e-01 0.677
## 2 0.3568 0.0808 0.36539 1.59e-01 0.493
## 3 0.0492 0.0475 0.03584 4.67e-05 0.165
## 4 0.0448 0.0765 0.00816 1.65e-08 0.268
## pv
##      mean   sd 50% 2.5% 97.5%
## [1,] 1.64 0.83   1    1     4
##
##  sim x1 :
##  -----
## ev
##     mean     sd    50%     2.5% 97.5%
## 1 0.0607 0.0382 0.0523 1.57e-02 0.158
## 2 0.4600 0.2831 0.4043 8.12e-02 0.974
## 3 0.2319 0.1556 0.2114 3.94e-03 0.579
## 4 0.2475 0.2498 0.1570 1.11e-06 0.758
## pv
##      mean    sd 50% 2.5% 97.5%
## [1,] 2.71 0.904   3    1     4
## fd
##     mean     sd     50%      2.5%  97.5%
## 1 -0.488 0.0841 -0.4937 -6.36e-01 -0.311
## 2  0.103 0.2473  0.0232 -2.20e-01  0.605
## 3  0.183 0.1470  0.1660 -1.46e-02  0.504
## 4  0.203 0.1929  0.1450  1.09e-06  0.582

plot(s.out2)

Model¶

Let be the ordered categorical dependent variable for observation that takes one of the integer values from to where is the total number of categories.

• The stochastic component begins with an unobserved continuous variable, , which follows the standard logistic distribution with a parameter ,

  to which we add an observation mechanism

  where (for ) are the threshold parameters with for all and and .

• The systematic component has the following form, given the parameters and , and the explanatory variables :

  which implies:

Quantities of Interest¶

• The expected values (qi$ev) for the ordinal logit model are simulations of the predicted probabilities for each category:

  given a draw of from its sampling distribution.

• The predicted value (qi$pr) is drawn from the logit distribution described by , and observed as one of discrete outcomes.

• The difference in each of the predicted probabilities (qi$fd) is given by

• In conditional prediction models, the average expected treatment effect (att.ev) for the treatment group is

  where is a binary explanatory variable defining the treatment () and control () groups, and is the number of treated observations in category .

• In conditional prediction models, the average predicted treatment effect (att.pr) for the treatment group is

  where is a binary explanatory variable defining the treatment () and control () groups, and is the number of treated observations in category .

Output Values¶

The output of each Zelig command contains useful information which you may view. For example, if you run z.out <- zelig(y ~ x, model = ologit, data), then you may examine the available information in z.out by using names(z.out), see the coefficients by using z.out$coefficients, and a default summary of information through summary(z.out). Other elements available through the $ operator are listed below.

• From the zelig() output object z.out, you may extract:
  • coefficients: parameter estimates for the explanatory variables.
  • zeta: a vector containing the estimated class boundaries .
  • deviance: the residual deviance.
  • fitted.values: the matrix of in-sample fitted values.
  • df.residual: the residual degrees of freedom.
  • edf: the effective degrees of freedom.
  • Hessian: the Hessian matrix.
  • zelig.data: the input data frame if save.data = TRUE.
• From summary(z.out), you may extract:
  • coefficients: the parameter estimates with their associated standard errors, and -statistics.

See also¶

The ordinal logit model is part of the MASS package by William N. Venable and Brian D. Ripley. Advanced users may wish to refer to help(polr).

Venables WN and Ripley BD (2002). Modern Applied Statistics with S, Fourth edition. Springer, New York. ISBN 0-387-95457-0, <URL: http://www.stats.ox.ac.uk/pub/MASS4>.