Effect Displays for Nested Logit Models

Description

Computes effects (in the sense of the effects package—see, in particular, Effect )—for "nestedLogit" models, which then can be used with other functions in the effects package, for example, predictorEffects and to produce effect plots.

Usage

## S3 method for class 'nestedLogit'
Effect(
 focal.predictors,
 mod,
 confidence.level = 0.95,
 fixed.predictors = NULL,
 ...
)

Arguments

Value

an object of class "effpoly" (see Effect ).

Author(s)

John Fox

References

John Fox and Sanford Weisberg (2019). An R Companion to Applied Regression, 3rd Edition. Sage, Thousand Oaks, CA.

John Fox, Sanford Weisberg (2018). Visualizing Fit and Lack of Fit in Complex Regression Models with Predictor Effect Plots and Partial Residuals. Journal of Statistical Software, 87(9), 1-27.

See Also

Effect , plot.effpoly , predictorEffects

Examples

data("Womenlf", package = "carData")
comparisons <- logits(work=dichotomy("not.work",
 working=c("parttime", "fulltime")),
 full=dichotomy("parttime", "fulltime"))
m <- nestedLogit(partic ~ hincome + children,
 dichotomies = comparisons,
 data=Womenlf)
peff.women <- effects::predictorEffects(m)
plot(peff.women)
plot(peff.women, axes=list(y=list(style="stacked")))
summary(peff.women)
dichots <- logits(AB_CD = dichotomy(c("A", "B"), c("C", "D")),
 A_B = dichotomy("A", "B"),
 C_D = dichotomy("C", "D"))
m.health <- nestedLogit(product4 ~ age + gender*household + position_level,
 dichotomies = dichots, data = HealthInsurance)
eff.gen.hh <- effects::Effect(c("gender", "household"), m.health,
 xlevels=list(household=0:7))
eff.gen.hh
plot(eff.gen.hh, axes=list(x=list(rug=FALSE)))
plot(eff.gen.hh, axes=list(x=list(rug=FALSE), 
 y=list(style="stacked")))

Data From the U.S. General Social Survey 1972-2016

Description

This data set is drawn from the U.S. General Social Survey (GSS) for years between 1972 and 2016.

Usage

data("GSS", package = "nestedLogit")

Format

A data frame with 44091 rows and 3 columns.

parentdeg

A factor representing parents' attained level of education (highest "degree" obtained), recording the higher of mother's and father's education, with levels "l.t.highschool", "highschool", "college", and "graduate".

degree

The respondent's level of education, a factor with the same levels as parentdeg.

year

The year of the survey, between 1972 and code2016.

Source

General Social Survey, NORC, The University of Chicago https://www.norc.org/Research/Projects/Pages/general-social-survey.aspx.

See Also

nestedLogit .

Examples

round(100*with(GSS, prop.table(table(degree, parentdeg), 2)))
m.GSS <- nestedLogit(degree ~ parentdeg*year,
 continuationLogits(c("l.t.highschool", "highschool",
 "college", "graduate")),
 data=GSS)
car::Anova(m.GSS)
summary(m.GSS)

Choice of Health Insurance Product

Description

A company recently introduced a new health insurance provider for its employees. At the beginning of the year the employees had to choose one of three (or four) different health plan products from this provider to best suit their needs.

This dataset was modified from its original source (McNulty, 2022) for the present purposes by adding a fourth choice, sampled randomly from the original three.

Usage

data("HealthInsurance", package = "nestedLogit")

Format

A data frame with 1448 rows and 7 columns.

product

Choice among three products, a factor with levels "A", "B", and "C".

product4

Choice among four products, a factor with levels "A", "B", "C", and "D".

age

The age of the individual, in years.

household

The number of people living with the individual in the same household.

position_level

Position level in the company at the time the choice was made, where 1 is is the lowest level and 5 is the highest, a numeric vector.

gender

The gender of the individual, a factor with levels "Female" and "Male".

absent

The number of days the individual was absent from work in the year prior to the choice,

Source

Originally taken from McNulty, K. (2022). Handbook of Regression Modeling in People Analytics, https://peopleanalytics-regression-book.org/data/health_insurance.csv.

See Also

nestedLogit .

Examples

lbinary <- logits(AB_CD = dichotomy(c("A", "B"), c("C", "D")),
 A_B = dichotomy("A", "B"),
 C_D = dichotomy("C", "D"))
as.matrix(lbinary)
health.nested <- nestedLogit(product4 ~ age + gender * household + position_level,
 dichotomies = lbinary, data = HealthInsurance)
 car::Anova(health.nested)
coef(health.nested)

Convert a Predicted Objects to a data.frame

Description

These functions provide simple ways to convert the results of predict.nestedLogit to a data frame in a consistent format for plotting and other actions.

Usage

## S3 method for class 'predictNestedLogit'
as.data.frame(x, row.names = NULL, optional = FALSE, ...)

Arguments

Value

• For predict(..., model="nested") (the default), returns a data frame containing the values of predictors along with the columns response, p, se.p, logit, se.logit.

• For predict(..., model="dichotomies"), returns a data frame containing the values of predictors along with the columns response, logit, and se.logit.

Examples

data("Womenlf", package = "carData")
comparisons <- logits(work=dichotomy("not.work", c("parttime", "fulltime")),
 full=dichotomy("parttime", "fulltime"))
wlf.nested <- nestedLogit(partic ~ hincome + children,
 dichotomies = comparisons,
 data=Womenlf)
# get predicted values for a grid of `hincome` and `children`
new <- expand.grid(hincome=seq(0, 45, length=10),
 children=c("absent", "present"))
pred.nested <- predict(wlf.nested, new)
plotdata <- as.data.frame(pred.nested)
str(plotdata)
# Predicted logit values for the dichotomies
pred.dichot <- predict(wlf.nested, new, model = "dichotomies")
plotlogit <- as.data.frame(pred.dichot)
str(plotlogit)

Broom Related Methods

Description

These functions give compact summaries of a "nestedLogit" object

glance

Construct a single row summaries for the dichotomies "nestedLogit" model.

tidy

Summarizes the terms in "nestedLogit" model.

Usage

## S3 method for class 'nestedLogit'
glance(x, ...)
## S3 method for class 'nestedLogit'
tidy(x, ...)

Arguments

Value

• glance returns a tibble containing one row of fit statistics for each dichotomy, labeled response. See glance for details.

• tidy returns a tibble containing coefficient estimates and test statistics for the combinations of response and term. See tidy for details.

See Also

nestedMethods , glance , tidy

Examples

data("Womenlf", package = "carData")
m <- nestedLogit(partic ~ hincome + children,
 dichotomies = logits(work=dichotomy("not.work",
 working=c("parttime", "fulltime")),
 full=dichotomy("parttime", "fulltime")),
 data=Womenlf)
# one-line summaries
broom::glance(m)
# coefficients and tests
broom::tidy(m)

Extract Binary Logit Models from a nestedLogit Object

Description

models is used to extract "glm" objects representing binary logit models from a "nestedLogit" object.

Usage

models(model, select, as.list = FALSE)
## S3 method for class 'nestedLogit'
models(model, select, as.list = FALSE)

Arguments

Value

model returns either a single "glm" object (see glm ) or a list of "glm" objects, each representing a binary logit model.

Examples

 data("Womenlf", package = "carData")
 comparisons <- logits(work=dichotomy("not.work",
 working=c("parttime", "fulltime")),
 full=dichotomy("parttime", "fulltime"))
 m <- nestedLogit(partic ~ hincome + children,
 dichotomies = comparisons,
 data=Womenlf)
 # extract a binomial logit model
 models(m, "work")
 # use that to plot residuals
 plot(density(residuals(models(m, "work"))))

Hypothesis-Testing and Related Methods for "nestedLogit" Objects

Description

Various methods for testing hypotheses about nested logit models.

Anova

Calculates type-II or type-III analysis-of-variance tables for "nestedLogit" objects; see Anova in the car package.

anova

Computes sequential analysis of variance (or deviance) tables for one or more fitted "nestedLogit" objects; see anova .

linearHypothesis

Computes Wald tests for linear hypotheses; see linearHypothesis in the car package.

logLik

Returns the log-likelihood and degrees of freedom for the nested-dichotomies model. (and through it AIC and BIC model-comparison statistics).

Usage

## S3 method for class 'nestedLogit'
Anova(mod, ...)
## S3 method for class 'Anova.nestedLogit'
print(x, ...)
## S3 method for class 'nestedLogit'
linearHypothesis(model, ...)
## S3 method for class 'nestedLogit'
anova(object, object2, ...)
## S3 method for class 'anova.nestedLogit'
print(x, ...)
## S3 method for class 'nestedLogit'
logLik(object, ...)

Arguments

Value

• The Anova and anova methods return objects of class "Anova.nestedLogit" and "anova.nestedLogit", respectively, each of which contains a list of "anova" objects (see anova ) and is usually printed.

• The linearHypothesis method is called for its side effect, printing the result of linear hypothesis tests, and invisibly returns NULL.

• The logLik method returns an object of class "logLik" (see logLik ).

Author(s)

John Fox

See Also

Anova , anova , linearHypothesis , logLik , AIC , BIC

Examples

# define continuation dichotomies for level of education
cont.dichots <- continuationLogits(c("l.t.highschool",
 "highschool",
 "college",
 "graduate"))
# fit a nested model for the GSS data examining education degree in relation to parent & year
m <- nestedLogit(degree ~ parentdeg + year,
 cont.dichots,
 data=GSS)
# Anova and anova tests
car::Anova(m) # type-II (partial) tests
anova(update(m, . ~ . - year), m) # model comparison
# Wald test
car::linearHypothesis(m, c("parentdeghighschool", "parentdegcollege",
 "parentdeggraduate"))
# log-liklihood, AIC, and BIC
logLik(m)
AIC(m)
BIC(m)

Binary Logit Models for Nested Dichotomies

Description

Fit a related set of binary logit models via the glm function to nested dichotomies, comprising a model for the polytomy. A polytomous response with m categories can be analyzed using m-1 binary logit comparisons. When these comparisons are nested, the m-1 sub-models are statistically independent. Therefore, the likelihood chi-square statistics for the sub-models are additive and give overall tests for a model for the polytomy. This method was introduced by Fienberg (1980),and subsequently illustrated by Fox(2016) and Friendly & Meyer (2016).

dichotomy and logits are helper functions to construct the dichotomies.

continuationLogits constructs a set of m-1 logit comparisons, called continuation logits, for an ordered response. With m=4 levels, say, A, B, C, D, considered low to high: The first contrasts B, C, D against A. The second ignores A and contrasts C, D against B. The second ignores A, B and contrasts D against C.

Usage

nestedLogit(formula, dichotomies, data, subset = NULL, contrasts = NULL, ...)
logits(...)
dichotomy(...)
continuationLogits(levels, names, prefix = "above_")

Arguments

Details

A dichotomy for a categorical variable is a comparison of one subset of levels against another subset. A set of dichotomies is nested, if after an initial dichotomy, all subsequent ones are within the groups of levels lumped together in earlier ones. Nested dichotomies correspond to a binary tree of the successive divisions.

For example, for a 3-level response, a first dichotomy could be {A}, {B, C} and then the second one would be just {B}, {C}. Note that in the second dichotomy, observations with response A are treated as NA.

The function dichotomy constructs a single dichotomy in the required form, which is a list of length 2 containing two character vectors giving the levels defining the dichotomy. The function logits is used to create the set of dichotomies for a response factor. Alternatively, the nested dichotomies can be specified more compactly as a nested (i.e., recursive) list with optionally named elements; for example, list(air="plane", ground=list(public=list("train", "bus"), private="car")).

The function continuationLogits provides a convenient way to generate all dichotomies for an ordered response. For an ordered response with m=4 levels, say, A, B, C, D, considered low to high: The dichotomy first contrasts B, C, D against A. The second ignores A and contrasts C, D against B. The second ignores A, B and contrasts D against C.

Value

nestedLogit returns an object of class "nestedLogit" containing the following elements:

• models, a named list of (normally) m - 1 "glm" objects, each a binary logit model for one of the m - 1 nested dichotomies representing the m-level response.

• formula, the model formula for the nested logit models.

• dichotomies, the "dichotomies" object defining the nested dichotomies for the model.

• data.name, the name of the data set to which the model is fit, of class "name".

• data, the data set to which the model is fit.

• subset, a character representation of the subset argument or "NULL" if the argument isn't specified.

• contrasts, the contrasts argument or NULL if the argument isn't specified.

• contrasts.print a character representation of the contrasts argument or "NULL" if the argument isn't specified.

logits and continuationLogits return objects of class "dichotomies" and c("continuationDichotomies" "dichotomies"), respectively, which are two-elements lists, each element containing a list of two character vectors representing a dichotomy. dichotomy returns a list of two character vectors representing a dichotomy.

Author(s)

John Fox

References

S. Fienberg (1980). The Analysis of Cross-Classified Categorical Data, 2nd Edition, MIT Press, Section 6.6.

J. Fox (2016), Applied Linear Regression and Generalized Linear Models, 3rd Edition, Sage, Section 14.2.2.

J. Fox and S. Weisberg (2011), An R Companion to Applied Regression, 2nd Edition, Sage, Section 5.8.

M. Friendly and D. Meyers (2016), Discrete Data Analysis with R, CRC Press, Section 8.2.

See Also

nestedMethods

Examples

data("Womenlf", package = "carData")
 #' Use `logits()` and `dichotomy()` to specify the comparisons of interest
 comparisons <- logits(work=dichotomy("not.work",
 working=c("parttime", "fulltime")),
 full=dichotomy("parttime", "fulltime"))
 print(comparisons)
 m <- nestedLogit(partic ~ hincome + children,
 dichotomies = comparisons,
 data=Womenlf)
 print(summary(m))
 print(car::Anova(m))
 coef(m)
 # equivalent;
 nestedLogit(partic ~ hincome + children,
 dichotomies = list("not.work",
 working=list("parttime", "fulltime")),
 data=Womenlf)
 # get predicted values
 new <- expand.grid(hincome=seq(0, 45, length=10),
 children=c("absent", "present"))
 pred.nested <- predict(m, new)
 # plot
 op <- par(mfcol=c(1, 2), mar=c(4, 4, 3, 1) + 0.1)
 plot(m, "hincome", list(children="absent"),
 xlab="Husband's Income", legend=FALSE)
 plot(m, "hincome", list(children="present"),
 xlab="Husband's Income")
 par(op)
 continuationLogits(c("none", "gradeschool", "highschool", "college"))
 continuationLogits(4)

Methods for "nestedLogit" and Related Objects

Description

Various methods for processing "nestedLogit" and related objects. Most of these are the standard methods for a model-fitting function.

coef, vcov

Return the coefficients and their variance-covariance matrix respectively.

update

Re-fit a "nestedLogit" model with a change in any of the formula, dichotomies, data, subset, or contrasts, arguments.

predict, fitted

Computes predicted values from a fitted "nestedLogit" model.

confint

Compute point-wise confidence limits for predicted response-category probabilities or logits.

glance

Construct a single row summaries for the dichotomies "nestedLogit" model.

tidy

Summarizes the terms in "nestedLogit" model.

Usage

## S3 method for class 'nestedLogit'
print(x, ...)
## S3 method for class 'nestedLogit'
summary(object, ...)
## S3 method for class 'summary.nestedLogit'
print(x, ...)
## S3 method for class 'dichotomies'
print(x, ...)
## S3 method for class 'nestedLogit'
predict(object, newdata, model = c("nested", "dichotomies"), ...)
## S3 method for class 'predictNestedLogit'
print(x, n = min(10L, nrow(x$p)), ...)
## S3 method for class 'predictNestedLogit'
confint(
 object,
 parm = c("prob", "logit"),
 level = 0.95,
 conf.limits.logit = TRUE,
 ...
)
## S3 method for class 'predictDichotomies'
print(x, n = 10L, ...)
## S3 method for class 'nestedLogit'
fitted(object, model = c("nested", "dichotomies"), ...)
## S3 method for class 'nestedLogit'
coef(object, as.matrix = TRUE, ...)
## S3 method for class 'nestedLogit'
vcov(object, as.matrix = FALSE, ...)
## S3 method for class 'nestedLogit'
update(object, formula, dichotomies, data, subset, contrasts, ...)
## S3 method for class 'dichotomies'
as.matrix(x, ...)
## S3 method for class 'dichotomies'
as.character(x, ...)
## S3 method for class 'continuationDichotomies'
as.matrix(x, ...)
as.dichotomies(x, ...)
## S3 method for class 'matrix'
as.dichotomies(x, ...)

Arguments

Details

The predict method provides predicted values for two representations of the model. model = "nested" gives the fitted probabilities for each of the response categories. model = "dichotomies" gives the fitted log odds for each binary logit models in the dichotomies.

Value

• The coef and vcov methods return either matrices or lists of regression coefficients and their covariances, respectively.

• The update method returns an object of class "nestedLogit" (see nestedLogit ) derived from the original nested-logit model.

• The predict and fitted methods return an object of class "predictNested" or "predictDichotomies", which contain the predicted probabilities, predicted logits, and other information, such as standard errors of predicted values, and, if supplied, the newdata on which predictions are based.

• The summary method returns an object of class "summary.nestedLogit", which is a list of summaries of the glm objects that comprise the nested-dichotomies model; the object is normally printed.

• The methods for as.matrix, as.character, and as.dichotomies coerce various objects to matrices, character vectors, and dichotomies objects.

• The various print methods invisibly return their x arguments.

Author(s)

John Fox and Michael Friendly

See Also

nestedLogit , plot.nestedLogit , glance.nestedLogit , tidy.nestedLogit

Examples

# define continuation dichotomies for level of education
cont.dichots <- continuationLogits(c("l.t.highschool",
 "highschool",
 "college",
 "graduate"))
# Show dichotomies in various forms
print(cont.dichots)
as.matrix(cont.dichots)
as.character(cont.dichots)
# fit a nested model for the GSS data examining education degree in relation to parent & year
m <- nestedLogit(degree ~ parentdeg + year,
 cont.dichots,
 data=GSS)
coef(m) # coefficient estimates
sqrt(diag(vcov(m, as.matrix=TRUE))) # standard errors
print(m)
summary(m)
# broom methods
broom::glance(m)
broom::tidy(m)
# predicted probabilities and ploting
predict(m) # fitted probabilities for first few cases;
new <- expand.grid(parentdeg=c("l.t.highschool", "highschool",
 "college", "graduate"),
 year=c(1972, 2016))
fit <- predict(m, newdata=new)
cbind(new, fit) # fitted probabilities at specific values of predictors
# predicted logits for dichotomies
predictions <- predict(m, newdata=new, model="dichotomies")
predictions

Plotting Nested Logit Models

Description

A plot method for "nestedLogit" objects produced by the nestedLogit function. Fitted probabilities under the model are plotted for each level of the polytomous response variable, with one of the explanatory variables on the horizontal axis and other explanatory variables fixed to particular values. By default, a 95% pointwise confidence envelope is added to the plot.

Usage

## S3 method for class 'nestedLogit'
plot(
 x,
 x.var,
 others,
 n.x.values = 100L,
 xlab = x.var,
 ylab = "Fitted Probability",
 main,
 cex.main = 1,
 digits.main = getOption("digits") - 2L,
 font.main = 1L,
 pch = 1L:length(response.levels),
 lwd = 3,
 lty = 1L:length(response.levels),
 col = palette()[1L:length(response.levels)],
 legend = TRUE,
 legend.inset = 0.01,
 legend.location = "topleft",
 legend.bty = "n",
 conf.level = 0.95,
 conf.alpha = 0.3,
 ...
)

Arguments

Value

NULL Used for its side-effect of producing a plot

Author(s)

John Fox jfox@mcmaster.ca

See Also

nestedLogit , matplot

Examples

data("Womenlf", package = "carData")
m <- nestedLogit(partic ~ hincome + children,
 logits(work=dichotomy("not.work", c("parttime", "fulltime")),
 full=dichotomy("parttime", "fulltime")),
 data=Womenlf)
plot(m, legend.location="top")
op <- par(mfcol=c(1, 2), mar=c(4, 4, 3, 1) + 0.1)
plot(m, "hincome", list(children="absent"),
 xlab="Husband's Income", legend=FALSE)
plot(m, "hincome", list(children="present"),
 xlab="Husband's Income")
par(op)