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Type:

Package

Title:

Hierarchical Ordered Probit Models with Application to ReportingHeterogeneity

Version:

0.11.6

Depends:

R (≥ 3.5.0), survey (≥ 4.1-1)

Imports:

MASS, Rcpp, graphics, stats, grDevices, questionr, parallel,Rdpack (≥ 0.11.0)

LinkingTo:

Rcpp, RcppEigen

Description:

Self-reported health, happiness, attitudes, and other statuses or perceptions are often the subject of biases that may come from different sources. For example, the evaluation of an individual’s own health may depend on previous medical diagnoses, functional status, and symptoms and signs of illness; as on well as life-style behaviors, including contextual social, gender, age-specific, linguistic and other cultural factors (Jylha 2009 <doi:10.1016/j.socscimed.2009.05.013>; Oksuzyan et al. 2019 <doi:10.1016/j.socscimed.2019.03.002>). The hopit package offers versatile functions for analyzing different self-reported ordinal variables, and for helping to estimate their biases. Specifically, the package provides the function to fit a generalized ordered probit model that regresses original self-reported status measures on two sets of independent variables (King et al. 2004 <doi:10.1017/S0003055403000881>; Jurges 2007 <doi:10.1002/hec.1134>; Oksuzyan et al. 2019 <doi:10.1016/j.socscimed.2019.03.002>). The first set of variables (e.g., health variables) included in the regression are individual statuses and characteristics that are directly related to the self-reported variable. In the case of self-reported health, these could be chronic conditions, mobility level, difficulties with daily activities, performance on grip strength tests, anthropometric measures, and lifestyle behaviors. The second set of independent variables (threshold variables) is used to model cut-points between adjacent self-reported response categories as functions of individual characteristics, such as gender, age group, education, and country (Oksuzyan et al. 2019 <doi:10.1016/j.socscimed.2019.03.002>). The model helps to adjust for specific socio-demographic and cultural differences in how the continuous latent health is projected onto the ordinal self-rated measure. The fitted model can be used to calculate an individual predicted latent status variable, a latent index, and standardized latent coefficients; and makes it possible to reclassify a categorical status measure that has been adjusted for inter-individual differences in reporting behavior.

License:

GPL-3

Encoding:

UTF-8

LazyData:

TRUE

RoxygenNote:

7.2.2

Suggests:

testthat (≥ 3.0.0), R.rsp (≥ 0.43.0), usethis (≥ 1.5.0),knitr (≥ 1.20), rmarkdown (≥ 1.12), qpdf, roxygen2 (≥ 6.1.1)

VignetteBuilder:

R.rsp, knitr

RdMacros:

Rdpack

Config/testthat/edition:

NeedsCompilation:

yes

Packaged:

2024-01-29 11:30:06 UTC; maciej

Author:

Maciej J. Danko

[aut, cre]

Maintainer:

Maciej J. Danko <Maciej.Danko@gmail.com>

Repository:

CRAN

Date/Publication:

2024-01-29 13:50:09 UTC

Extracting the Akaike Information Criterion from the fitted model

Description

Extract the Akaike Information Criterion (AIC) from a fittedhopit model.

Usage

## S3 method for class 'hopit'AIC(object, ..., k = 2L)

Arguments

object

ahopit object.

...

additional objects of the classhopit.

k

a penalty per parameter to be used; the default k = 2 is theclassical AIC.

Author(s)

Maciej J. Danko

Likelihood Ratio Test Tables

Description

Perform the likelihood ratio test(s) for two or morehopit objects.

Usage

## S3 method for class 'hopit'anova(object, ..., method = c("sequential","with.most.complex", 'with.least.complex'),direction = c("decreasing", "increasing"))

Arguments

object

an object containing the results returned by ahopit.

...

an additional object(s) of the same type.

method

the method of ordered model comparisons. Choose"sequential"for 1-2, 2-3, 3-4, ... comparisons or"with.most.complex" for 1-2, 1-3, 1-4, ... comparisons,where 1 is the most complex model (the least complex for"with.least.complex").

direction

determine if the complexity of listed models is"increasing" or"decreasing" (default).

Value

a vector or a matrix with the results of the test(s).

Author(s)

Maciej J. Danko

Examples

# DATAdata(healthsurvey)# the order of response levels decreases from the best health to# the worst health; hence the hopit() parameter decreasing.levels# is set to TRUElevels(healthsurvey$health)# Example 1 ---------------------# fitting two nested modelsmodel1 <- hopit(latent.formula = health ~ hypertension + high_cholesterol +                heart_attack_or_stroke + poor_mobility + very_poor_grip +                depression + respiratory_problems +                IADL_problems + obese + diabetes + other_diseases,              thresh.formula = ~ sex + ageclass + country,              decreasing.levels = TRUE,              control = list(trace = FALSE),              data = healthsurvey)# a model with an interaction between hypertension and high_cholesterolmodel2 <- hopit(latent.formula = health ~ hypertension * high_cholesterol +                heart_attack_or_stroke + poor_mobility + very_poor_grip +                depression + respiratory_problems +                IADL_problems + obese + diabetes + other_diseases,              thresh.formula = ~ sex + ageclass + country,              decreasing.levels = TRUE,              control = list(trace = FALSE),              data = healthsurvey)# a likelihood ratio testlrt1 <- anova(model1, model2)lrt1# print results in a shorter formprint(lrt1, short = TRUE)# or equivalentlylrt.hopit(model2, model1)# Example 2 ---------------------# fitting additional nested modelsmodel3 <- hopit(latent.formula = health ~ hypertension * high_cholesterol +                heart_attack_or_stroke + poor_mobility + very_poor_grip +                depression + respiratory_problems +                IADL_problems + obese * diabetes + other_diseases,              thresh.formula = ~ sex + ageclass + country,              decreasing.levels = TRUE,              control = list(trace = FALSE),              data = healthsurvey)model4 <- hopit(latent.formula = health ~ hypertension * high_cholesterol +                heart_attack_or_stroke + poor_mobility + very_poor_grip +                depression + respiratory_problems +                IADL_problems + obese * diabetes + other_diseases,              thresh.formula = ~ sex * ageclass + country,              decreasing.levels = TRUE,              control = list(trace = FALSE),              data = healthsurvey)# sequential likelihood ratio tests# model complexity increases so direction = "increasing"anova(model1, model2, model3, model4,      direction = "increasing", method = "sequential")# likelihood ratio tests of the most complex model with the rest of the modelsanova(model1, model2, model3, model4,      direction = "increasing", method = "with.most.complex")# likelihood ratio tests of the least complex model with the rest of the modelsanova(model1, model2, model3, model4,      direction = "increasing", method = "with.least.complex")

Bootstrapping hopit model

Description

boot_hopit performs the bootstrap of a function dependent on a fitted model.In each of the bootstrap repetitions, a set of new model coefficients is drawn from the multivariate normal distribution,assuming the originally estimated model coefficients (seecoef.hopit)as a mean and using the model variance-covariance matrix (seevcov.hopit).The drawn coefficients are then used to calculate the measure of interest using a function delivered by thefunc parameter.

Usage

boot_hopit(  model,  func,  data = model$frame,  nboot = 500,  unlist = TRUE,  boot.only.latent = TRUE,  parallel.flag = FALSE,  parallel.nb_cores = NULL,  parallel.packages = NULL,  parallel.variables = NULL,  robust.vcov,  ...)

Arguments

model

a fittedhopit model.

func

a function to be bootstrapped of the formfunc(model, ...).

data

data used to fit the model.

nboot

a number of bootstrap replicates.

unlist

a logical indicating whether to unlist the boot object.

boot.only.latent

a logical indicating whether to perform the bootstrap on latent variables only.

parallel.flag

a logical if to use parallel computations.

parallel.nb_cores

number of cores (<= number of CPU cores on the current host).

parallel.packages

list of packages needed to run "func".

parallel.variables

list of global variables and functions needed to run "func".

robust.vcov

seevcov.hopit.

...

other parameters passed to thefunc.

Value

a list with bootstrapped elements.

Author(s)

Maciej J. Danko

Examples

# DATAdata(healthsurvey)# the order of response levels decreases from the best health to# the worst health; hence the hopit() parameter decreasing.levels# is set to TRUElevels(healthsurvey$health)# fit a modelmodel1 <- hopit(latent.formula = health ~ hypertension + high_cholesterol +                heart_attack_or_stroke + poor_mobility + very_poor_grip +                depression + respiratory_problems +                IADL_problems + obese + diabetes + other_diseases,              thresh.formula = ~ sex + ageclass + country,              decreasing.levels = TRUE,              control = list(trace = FALSE),              data = healthsurvey)# Example 1 ---------------------# bootstrapping cut-points# a function to be bootstrappedcutpoints <-  function(model) getCutPoints(model)$cutpointsB <- boot_hopit(model = model1, func = cutpoints, nboot = 100)# calculate lower and upper bounds using the percentile methodcutpoints.CI <- percentile_CI(B)# print estimated cutpoints and their confidence intervalscutpoints(model1)cutpoints.CI# Example 2 ---------------------# bootstrapping differences in health levels# a function to be bootstrappeddiff_BadHealth <- function(model) {  hl <- getLevels(model = model, formula=~ sex + ageclass, sep=' ')  hl$original[,1] + hl$original[,2] - hl$adjusted[,1]- hl$adjusted[,2]}# estimate the differenceest.org <- diff_BadHealth(model = model1)# perform the bootstrapB <- boot_hopit(model = model1, func = diff_BadHealth, nboot = 100)# calculate lower and upper bounds using the percentile methodest.CI <- percentile_CI(B)# plot the difference and its (asymmetrical) confidence intervalspmar <- par('mar'); par(mar = c(9.5,pmar[2:4]))m <- max(abs(est.CI))pos <- barplot(est.org, names.arg = names(est.org), las = 3,               ylab = 'Original - Adjusted',               ylim=c(-m, m), density = 20, angle = c(45, -45),               col = c('blue', 'orange'))for (k in seq_along(pos)) lines(c(pos[k,1],pos[k,1]),                                est.CI[,k], lwd = 2, col = 2)abline(h = 0); box(); par(mar = pmar)

Extracting the model coefficients

Description

Extract the model coefficients from thehopit model.

Usage

## S3 method for class 'hopit'coef(object, aslist = FALSE, ...)

Arguments

object

ahopit object.

aslist

a logical indicating whether the model coefficients should be returnedas a list of three vectorsrelated to latent variables, threshold lambdas, and threshold gammas.

...

further arguments passed to or from other methods.

Author(s)

Maciej J. Danko

INTERNAL: Get the starting parameters

Description

INTERNAL: Get the starting parameters

Usage

get.hopit.start(object, data)

Arguments

object

ahopit object.

data

a data.frame with data used to fit the object.

Value

an updatedhopit object.

Author(s)

Maciej J. Danko

Calculate the threshold cut-points and individual adjusted responses using Jurges' method

Description

Calculate the threshold cut-points and individual adjusted responses using Jurges' method

Usage

getCutPoints(model, decreasing.levels = model$decreasing.levels, subset = NULL)

Arguments

model

a fittedhopit model.

decreasing.levels

a logical indicating whether self-reported health classes are ordered in increasing order.

subset

an optional vector specifying a subset of observations.

Value

a list with the following components:

cutpoints

cut-points for the adjusted categorical response levels with the corresponding percentiles of the latent index.

adjusted.levels

adjusted categorical response levels for each individual.

Author(s)

Maciej J. Danko

References

Jurges H (2007).“True health vs response styles: exploring cross-country differences in self-reported health.”Health Economics,16(2), 163-178.doi:10.1002/hec.1134.

Oksuzyan A, Danko MJ, Caputo J, Jasilionis D, Shkolnikov VM (2019).“Is the story about sensitive women and stoical men true? Gender differences in health after adjustment for reporting behavior.”Social Science & Medicine,228, 41-50.doi:10.1016/j.socscimed.2019.03.002.

Examples

# DATAdata(healthsurvey)# the order of response levels decreases from the best health to# the worst health; hence the hopit() parameter decreasing.levels# is set to TRUElevels(healthsurvey$health)# Example 1 ---------------------# fit a modelmodel1 <- hopit(latent.formula = health ~ hypertension + high_cholesterol +                heart_attack_or_stroke + poor_mobility + very_poor_grip +                depression + respiratory_problems +                IADL_problems + obese + diabetes + other_diseases,              thresh.formula = ~ sex + ageclass + country,              decreasing.levels = TRUE,              control = list(trace = FALSE),              data = healthsurvey)# calculate the health index cut-pointsz <- getCutPoints(model = model1)z$cutpointsplot(z)# tabulate the adjusted health levels for individuals (Jurges method):rev(table(z$adjusted.levels))# tabulate the original health levels for individualstable(model1$y_i)# tabulate the predicted health levelstable(model1$Ey_i)

Summarize the adjusted and the original self-rated response levels

Description

Summarize the adjusted and the original self-rated response levels.

Usage

getLevels(  model,  formula = model$thresh.formula,  data = model$frame,  sep = "_",  decreasing.levels = model$decreasing.levels,  sort.flag = FALSE,  weight.original = TRUE)

Arguments

model

a fittedhopit model.

formula

a formula containing the grouping variables. It is by default set to threshold formula.

data

data used to fit the model.

sep

a separator for the level names.

decreasing.levels

a logical indicating whether self-reported health classes are ordered in increasing order.

sort.flag

a logical indicating whether to sort the levels.

weight.original

a logical indicating if use survey weights for calcualtion of original responses.

Value

a list with the following components:

original

frequencies of original response levels for selected groups/categories.

adjusted

frequencies of adjusted response levels (Jurges 2007 method) for selected groups/categories.

N.original

the number of original response levels for selected groups/categories.

N.adjusted

the number of adjusted response levels (Jurges 2007 method) for selected groups/categories.

categories

selected groups/categories used in summary.

tab

an original vs. an adjusted contingency table.

mat

a matrix with columns: grouping variables, original response levels, adjusted response levels.Each row corresponds to a single individual from the data used to fit the model.

Author(s)

Maciej J. Danko

References

Examples

# DATAdata(healthsurvey)# the order of response levels decreases from the best health to# the worst health; hence the hopit() parameter decreasing.levels# is set to TRUElevels(healthsurvey$health)# fit a modelmodel1 <- hopit(latent.formula = health ~ hypertension + high_cholesterol +                heart_attack_or_stroke + poor_mobility + very_poor_grip +                depression + respiratory_problems +                IADL_problems + obese + diabetes + other_diseases,              thresh.formula = ~ sex + ageclass + country,              decreasing.levels = TRUE,              control = list(trace = FALSE),              data = healthsurvey)# Example 1 ---------------------# calculate a summary by countryhl <- getLevels(model=model1, formula=~ country, sep=' ')plot(hl, las=1, mar = c(3,2,1.5,0.5))# differences between frequencies of original and adjusted health levelsround(100*(hl$original - hl$adjusted),2)# extract good and bad health levels (combined levels)Org <- cbind(bad = rowSums(hl$original[,1:2]),             good = rowSums(hl$original[,4:5]))Adj <- cbind(bad = rowSums(hl$adjusted[,1:2]),             good = rowSums(hl$adjusted[,4:5]))round(100*(Org - Adj),2)# plot the differencesbarplot(t(Org - Adj), beside = TRUE, density = 20, angle = c(-45, 45),        col = c('pink4', 'green2'),        ylab = 'Original - adjusted reported health frequencies')abline(h = 0); box()legend('top', c('Bad health','Good health'),       density = 20, angle = c(-45, 45),       fill = c('pink4', 'green2'), bty = 'n', cex = 1.2)# in country X, bad health seems to be over-reported while good health# is under-reported; in country Z, good health is highly over-reported.# Example 2 ---------------------# summary by gender and agehl <- getLevels(model = model1, formula=~ sex + ageclass, sep=' ')plot(hl)# differences between frequencies of original and adjusted health levelsround(100*(hl$original - hl$adjusted),2)# extract good health levels (combined "Very good" and "Excellent" levels)Org <- rowSums(hl$original[,4:5])Adj <- rowSums(hl$adjusted[,4:5])round(100*(Org - Adj),2)pmar <- par('mar'); par(mar = c(9.5, pmar[2:4]))barplot(Org-Adj,        ylab = 'Original - adjusted reported good health frequencies',        las = 3,        density = 20, angle = c(45, -45), col = c('blue', 'orange'))abline(h = 0); box(); par(mar = pmar)legend('top', c('Man','Woman'), density = 20, angle = c(-45, 45),       fill = c('blue', 'orange'), bty = 'n', cex = 1.2)# results show that women in general tend to over-report good health,# while men aged 50-59 greatly under-report good health.# more examples can be found in the description of the boot_hopit() function.

Artificially generated health survey data

Description

A dataset containing artificially generated survey data

Usage

healthsurvey

Format

A data frame with 10000 rows and 11 variables:

ID: personal identification number.
health: reported health, 5 levels.
diabetes: has diabetes? "yes" or "no".
obese: is obese? "yes" or "no".
IADL_problems: has problems with Instrumental Activities of Daily Living? "yes" or "no".
hypertension: has hypertension? "yes" or "no".
high_cholesterol: has high cholesterol? "yes" or "no".
respiratory_problems: has respiratory problems? "yes" or "no".
heart_attack_or_stroke: had a stroke or a heart attack? "yes" or "no".
poor_mobility: has poor mobility? "yes" or "no".
very_poor_grip: cannot perform grip strength test? "yes" or "no".
depression: has depression? "yes" or "no".
other_diseases: has other diseases? "yes" or "no".
sex: sex/gender: "woman" or "man".
ageclass: categorized age: [50,60), [60,70), [70,80), [80,120).
education: two levels of education: primary or lower ("prim-") and secondary or higher ("sec+".
country: country: "X", "Y", or "Z".
csw: cross-sectional survey weights.
psu: primary statistical unit.

Source

healthsurvey is a completely artificial data set simulated using distributions ofsome major health and socio-demographic characteristics. The distributions and the datastructure are roughly based on the WAVE1 SHARE database (DOIs: 10.6103/SHARE.w1.600); see(Borsch-Supan et al. 2013) for technical details.None of the records represent any part of the true data.

The SHARE data collection has been primarily funded by the European Commission through FP5 (QLK6-CT-2001-00360), FP6 (SHARE-I3: RII-CT-2006-062193, COMPARE: CIT5-CT-2005-028857, SHARELIFE: CIT4-CT-2006-028812) and FP7 (SHARE-PREP: N°211909, SHARE-LEAP: N°227822, SHARE M4: N°261982). Additional funding from the German Ministry of Education and Research, the Max Planck Society for the Advancement of Science, the U.S. National Institute on Aging (U01_AG09740-13S2, P01_AG005842, P01_AG08291, P30_AG12815, R21_AG025169, Y1-AG-4553-01, IAG_BSR06-11, OGHA_04-064, HHSN271201300071C) and from various national funding sources is gratefully acknowledged (see www.share-project.org).

References

Borsch-Supan A, Brandt M, Hunkler C, Kneip T, Korbmacher J, Malter F, Schaan B, Stuck S, Zuber S (2013).“Data Resource Profile: The Survey of Health, Ageing and Retirement in Europe (SHARE).”International Journal of Epidemiology,42(4), 992-1001.doi:10.1093/ije/dyt088.

Examples

# load *healthsurvey* datasetdata(healthsurvey)# horizontal view of the dataset (omitting ID)print(t(healthsurvey[1:6,-1]), quote=FALSE, na.print='NA', right=TRUE)

Generalized hierarchical ordered threshold models.

Description

The ordered response data classify a measure of interest into ordered categoriescollected during a survey. For example, if the dependent variable is a happinessrating, a respondent typically answers a question such as: “Taking all thingstogether, would you say you are ... ?" and then selects from response optionsalong the lines of: "very happy", "pretty happy", "not too happy", and "very unhappy"(Liao et al. 2005). Similarly, if interviewees are asked to evaluate theirhealth in general (e.g., “Would you say your health is ... ?”) they, can typically choose amongseveral categories, such as "very good", "good", "fair", "bad", and "very bad"(King et al. 2004; Jurges 2007; Rebelo and Pereira 2014; Oksuzyan et al. 2019). In political science, a respondentmay be asked for an opinion about recent legislation (e.g. “Rate your feelings aboutthe proposed legislation.") and asked to choose among categories like: "stronglyoppose", "mildly oppose", "indifferent", "mildly support", and "strongly support"(Greene and Hensher 2010). It is easy to imagine other multi-level ordinalvariables that might be used during a survey and to which the methodology describedbelow could be applied.

In practice, it is assumed that when responding to a survey question about their generalhappiness, health, feelings, attitudes or other status, participants areassessing their true value of this unobserved continuous variable, andproject it onto the discrete scale provided. The thresholds that individualsuse to categorize their true status by selecting a specific response optionmay be affected by the reference group chosen, their earlier life experiences,and cross-cultural differences in using scales. Thus, the responses ofindividuals may differ depending on their gender, age, cultural background,education, and personality traits; among other factors(King et al. 2004; Jurges 2007; Oksuzyan et al. 2019).
From the perspective of reporting behavior modeling, one of the main tasksresearchers face is to compute this continuous estimate of the underlying,latent measures of individuals based on several specific characteristicsof the responses considered (e.g., health variables or happiness variables),and to account for variations in reporting across socio-demographic andcultural groups. More specifically, to build a latent, underlying measure,a generalized hierarchical ordered threshold model is fitted that regressesthe reported status/attitude/feeling on two sets of independent variables(Boes and Winkelmann 2006; Greene et al. 2014). When the dependent reported orderedvariable is self-rated health status, then the first set of variables –i.e., health variables – assess specific aspects of individuals’ health,such as measures of chronic conditions, mobility, difficulties with a rangeof daily activities, grip strength, anthropometric characteristics, andlifestyle behaviors. Using the second set of independent variables(threshold variables), the model also adjusts for differences acrosssocio-demographic and cultural groups, such as differences in culturalbackground, gender, age, and education(King et al. 2004; Jurges 2007; Oksuzyan et al. 2019).

Ordered threshold models are used to fit ordered categorical dependent variables.The generalized ordered threshold models (Ierza 1985; Boes and Winkelmann 2006; Greene et al. 2014)are an extension of the ordered threshold models (McKelvey and Zavoina 1975).Whereas in the latter models, the thresholds are constant, in the generalized models thethresholds are allowed to be dependent on covariates.Greene and Hensher (2010); Greene et al. (2014) pointed out that for amodel to make sense, the thresholds must also be ordered.This observation motivated Greene and coauthors to call these modelsHOPIT, which standsfor hierarchical ordered probit models.

The fittedhopit model is used to analyze heterogeneity in reporting behavior.SeestandardizeCoef,latentIndex,getCutPoints,getLevels, andboot_hopit.

Usage

hopit(  latent.formula,  thresh.formula = ~1,  data,  decreasing.levels,  start = NULL,  fit.sigma = FALSE,  design = list(),  weights = NULL,  link = c("probit", "logit"),  control = list(),  na.action = na.fail)

Arguments

latent.formula

a formula used to model the latent variable. It should not contain any threshold variable.To specify the interactions between the latent and the threshold variables, see details.

thresh.formula

a formula used to model the threshold variable. It should not contain any latent variable.To specify interactions between the latent and the threshold variables, see details.Any dependent variable (left side of "~" in the formula) will be ignored.

data

a data frame that includes all modeled variables.

decreasing.levels

a logical indicating whether self-reported health classes are ordered in decreasing order.

start

a vector with starting coefficient values in the formc(latent_parameters, threshold_lambdas, threshold_gammas) orc(latent_parameters, threshold_lambdas, threshold_gammas, logSigma) if thefit.sigma == TRUE.

fit.sigma

a logical indicating whether to fit an additional parameter sigma,which models a standard deviation of the error term (e.g., the standard deviation of the cumulative normal distribution in the probit model).

design

an optional survey design. Use thesvydesign function to specify the design.The design cannot be specified together with parameterweights.

weights

optional model weights. Use design parameter to construct survey weights.

link

a link function. The possible values are"probit" (default) and"logit".

control

a list with control parameters. Seehopit.control.

na.action

a function that indicates what should happen when thedata containNAs.The default isna.fail,which generates an error if any missing value is found. The alternative isna.omit(orna.exclude equivalently), which removes rows with missingvalues from thedata. Usingna.pass will lead to an error.

Details

The function fits generalized hierarchical ordered threshold models.

latent.formula models the latent variable.If the response variable is self-rated health, then the latent measure can depend on different healthconditions and diseases (latent variables are called health variables).Latent variables are modeled with the parallel regression assumption. According to this assumption, the coefficientsthat describe the relationship between the lowest response category and all of the higher response categories, are the same as the coefficientsthat describe the relationship between another (e.g., adjacent) lowest response category and the remaining higher response categories.The predicted latent variable is modeled as a linear function of the health variables and the corresponding coefficients.

thresh.formula models the threshold variable.The thresholds (cut-points,alpha) are modeled by the threshold variablesgamma and the interceptslambda.It is assumed that they model the contextual characteristics of the respondent (e.g., country, gender, and age).The threshold variables are modeled without the parallel regression assumption; thus, each threshold is modeled bya variable independently (Boes and Winkelmann 2006; Greene et al. 2014).Thehopit() function uses the parameterization of thresholds proposed by Jurges (2007).

decreasing.levels it is the logical that determines the ordering of the levels of the categorical response variable.It is always advisable to first check the ordering of the levels before starting (see example 1)

It is possible to model the interactions, including interactions between the latent and the threshold variables. The interactions added to the latent formulaonly model the latent measure, and the interactions modeled in the threshold formula only model the thresholds.The general rule for modeling any kind of interaction is to use "*" to specify interactions within a latent (or threshold) formula and touse ':' to specify interactions between the latent and the threshold variables. In the latter case, the main effects of an interaction must also be specified;i.e., the main latent effects must be specified in the latent formula, and the main threshold effect must be speciffied in the threshold formula.See alsoExample 3 below.

For more details, please see the package vignette, which is also available under this link:vig_hopit.pdf

Value

ahopit object used by other functions and methods. The object is a list with the following components:

control

a list with control parameters. Seehopit.control.

link

a link function used.

hasdisp

a logical indicating whether fit.sigma was modeled.

use.weights

a logical indicating whether any weights were used.

weights

a vector with model weights.

frame

a model frame.

latent.formula

a latent formula used to fit the model.

latent.mm

a latent model matrix.

latent.terms

latent variables used, and their interactions.

cross.inter.latent

a part of the latent formula used for modeling cross-interactions in the latent model

thresh.formula

a threshold formula used to fit the model.

thresh.mm

a threshold model matrix.

thresh.extd

an extended threshold model matrix.

thresh.terms

threshold variables used, and their interactions.

cross.inter.thresh

a part of the threshold formula used for modeling cross-interactions in the threshold model

thresh.no.cov

a logical indicating whether gamma parameters are present.

parcount

a 3-element vector with a number of parameters for the latent variables (beta),the threshold intercepts (lambda), and the threshold covariates (gamma).

coef

a vector with model coefficients.

coef.ls

model coefficients as a list.

start

a vector with the starting values of the coefficients.

alpha

estimated individual-specific thresholds.

y_i

a vector with individual responses - the response variable.

y_latent_i

a vector with predicted latent measures for each individual.

Ey_i

a vector with predicted categorical responses for each individual.

J

a number of response levels.

N

a number of observations.

deviance

a deviance.

LL

a log likelihood.

AIC

an AIC for models without a survey design.

vcov

a variance-covariance matrix.

vcov.basic

a variance-covariance matrix that ignores the survey design.

hessian

a Hessian matrix.

estfun

a gradient (a vector of partial derivatives) of the log likelihood function at the estimated coefficient values.

YYY1,YYY2,YYY3

an internal objects used for the calculation of gradient and Hessian functions.

Author(s)

Maciej J. Danko

References

Boes S, Winkelmann R (2006).“Ordered response models.”Allgemeines Statistisches Archiv,90(1), 167–181.ISSN 1614-0176,doi:10.1007/s10182-006-0228-y.

Greene W, Harris MN, Hollingsworth B, Weterings TA (2014).“Heterogeneity in Ordered Choice Models: A Review with Applications to Self-Assessed Health.”Journal of Economic Surveys,28(1), 109-133.doi:10.1111/joes.12002.

Greene W, Hensher D (2010).Modeling Ordered Choices.Cambridge University Press.

Ierza JV (1985).“Ordinal probit: A generalization.”Communications in Statistics - Theory and Methods,14(1), 1-11.ISSN 0361-0926,doi:10.1080/03610928508828893.

Jurges H (2007).“True health vs response styles: exploring cross-country differences in self-reported health.”Health Economics,16(2), 163-178.doi:10.1002/hec.1134.

King G, Murray CJL, Salomon JA, Tandon A (2004).“Enhancing the Validity and Cross-Cultural Comparability of Measurement in Survey Research.”American Political Science Review,98(1), 191–207.doi:10.1017/S000305540400108X.

Liao P, Fu Y, Yi C (2005).“Perceived quality of life in Taiwan and Hong Kong: an intra-culture comparison.”Journal of Happiness Studies,6(1), 43–67.ISSN 1573-7780,doi:10.1007/s10902-004-1753-6.

McKelvey RD, Zavoina W (1975).“A Statistical Model for the Analysis of Ordinal Level Dependent Variables.”Journal of Mathematical Sociology,4(1), 103–120.

Oksuzyan A, Danko MJ, Caputo J, Jasilionis D, Shkolnikov VM (2019).“Is the story about sensitive women and stoical men true? Gender differences in health after adjustment for reporting behavior.”Social Science & Medicine,228, 41-50.doi:10.1016/j.socscimed.2019.03.002.

Rebelo LP, Pereira NS (2014).“Assessing health endowment, access and choice determinants: Impact on retired Europeans' (in)activity and quality of life.”Social Indicators Research,119(3), 1411-1446.doi:10.1007/s11205-013-0542-1.

Examples

# DATAdata(healthsurvey)# first determine the order of the levels of the dependent variablelevels(healthsurvey$health)# the order of response levels decreases from the best health to# the worst health; hence the hopit() parameter decreasing.levels# is set to TRUE# Example 1 ---------------------# fitting the model:model1 <- hopit(latent.formula = health ~ hypertension + high_cholesterol +                heart_attack_or_stroke + poor_mobility + very_poor_grip +                depression + respiratory_problems +                IADL_problems + obese + diabetes + other_diseases,              thresh.formula = ~ sex + ageclass + country,              decreasing.levels = TRUE,              control = list(trace = FALSE),              data = healthsurvey)# summarize the fit:summary(model1)# extract parameters in the form of a listcm1 <- coef(model1, aslist = TRUE)# names of the returned coefficientsnames(cm1)# extract the latent health coefficientscm1$latent.params# check the fitprofile(model1)# Example 2 ---------------------# incorporate the survey designdesign <- svydesign(ids = ~ country + psu, weights = healthsurvey$csw,data = healthsurvey)model2 <- hopit(latent.formula = health ~ hypertension + high_cholesterol +                  heart_attack_or_stroke + poor_mobility +                  very_poor_grip + depression + respiratory_problems +                  IADL_problems + obese + diabetes + other_diseases,                thresh.formula = ~ sex + ageclass + country,                decreasing.levels = TRUE,                design = design,                control = list(trace = FALSE),                data = healthsurvey)# compare the latent variablescbind('No survey design' = coef(model1, aslist = TRUE)$latent.par,'Has survey design' = coef(model2, aslist = TRUE)$latent.par)# Example 3 ---------------------# defining the interactions between the threshold and the latent variables# correctly defined interactions:model3 <- hopit(latent.formula = health ~ hypertension + high_cholesterol +                heart_attack_or_stroke + poor_mobility * very_poor_grip +                depression + respiratory_problems +                IADL_problems + obese + diabetes + other_diseases +                sex : depression + sex : diabetes + ageclass:obese,              thresh.formula = ~ sex * ageclass + country + sex : obese,              decreasing.levels = TRUE,              control = list(trace = FALSE),              data = healthsurvey)## Not run: # badly defined interactions:# 1) lack of a main effect of "other_diseases" in any formula# it can be solved by adding " + other_diseases" to the latent formulamodel3a <- hopit(latent.formula = health ~ hypertension + high_cholesterol +                heart_attack_or_stroke + poor_mobility + very_poor_grip +                depression + respiratory_problems +                IADL_problems + obese + diabetes + other_diseases : sex,              thresh.formula = ~ sex + ageclass + country,              decreasing.levels = TRUE,              control = list(trace = FALSE),              data = healthsurvey)# 2) the main effect of sex is present in both formulas.# it can be solved by replacing "*" with ":" in "other_diseases * sex"model3b <- hopit(latent.formula = health ~ hypertension + high_cholesterol +                heart_attack_or_stroke + poor_mobility + very_poor_grip +                depression + respiratory_problems +                IADL_problems + obese + diabetes + other_diseases * sex,              thresh.formula = ~ sex + ageclass + country,              decreasing.levels = TRUE,              control = list(trace = FALSE),              data = healthsurvey)## End(Not run)# Example 4 ---------------------# construct a naive continuous variable:hs <- healthsurveyhs$cont_var <- sample(5000:5020,nrow(hs),replace=TRUE)latent.formula = health ~ hypertension + high_cholesterol +  heart_attack_or_stroke + poor_mobility + very_poor_grip +  depression + respiratory_problems +  IADL_problems + obese + diabetes + other_diseases# in some cases, when continuous variables are used, the hopit:::get.hopit.start() function# do not find starting parameters (R version 3.4.4 (2018-03-15)):## Not run: model4 <- hopit(latent.formula = latent.formula,                thresh.formula = ~ sex + cont_var,                decreasing.levels = TRUE,                data = hs)## End(Not run)# one of the solutions is to transform one or more continuous variables:hs$cont_var_t <- hs$cont_var-min(hs$cont_var)model4b <- hopit(latent.formula = latent.formula,                 thresh.formula = ~ sex + cont_var_t,                 decreasing.levels = TRUE,                 data = hs)# this can also be done automatically using the the control parametermodel4c <- hopit(latent.formula = latent.formula,                 thresh.formula = ~ sex + cont_var,                 decreasing.levels = TRUE,                 control = list(transform.thresh = 'min',                                transform.latent = 'none'),                 data = hs)model4d <- hopit(latent.formula = latent.formula,                 thresh.formula = ~ sex + cont_var,                 decreasing.levels = TRUE,                 control = list(transform.thresh = 'scale_01',                                transform.latent = 'none'),                 data = hs)model4e <- hopit(latent.formula = latent.formula,                 thresh.formula = ~ sex + cont_var,                 decreasing.levels = TRUE,                 control = list(transform.thresh = 'standardize',                                transform.latent = 'none'),                 data = hs)model4f <- hopit(latent.formula = latent.formula,                 thresh.formula = ~ sex + cont_var,                 decreasing.levels = TRUE,                 control = list(transform.thresh = 'standardize_trunc',                                transform.latent = 'none'),                 data = hs)round(t(rbind(coef(model4b),              coef(model4c),              coef(model4d),              coef(model4e),              coef(model4f))),4)

Auxiliary for controlling the fitting of a`hopit` model

Description

An auxiliary function for controlling the fitting of ahopit model.Use this function to set the controlparameters of thehopit and other related functions.

Usage

hopit.control(  grad.eps = 3e-05,  bgfs.maxit = 10000,  cg.maxit = 10000,  nlm.maxit = 150,  bgfs.reltol = 5e-10,  cg.reltol = 5e-10,  nlm.gradtol = 1e-07,  nlm.steptol = 1e-07,  fit.methods = "BFGS",  nlm.fit = FALSE,  trace = TRUE,  transform.latent = "none",  transform.thresh = "none")

Arguments

grad.eps

an epsilon parameter ("a very small number") used to calculate the Hessian from the gradient function.

bgfs.maxit,cg.maxit,nlm.maxit

the maximum number of iterations.Seeoptim andnlm for details.

bgfs.reltol,cg.reltol

the relative convergence tolerances for the BFGS and the CG methods.Seeoptim for details.

nlm.gradtol,nlm.steptol

a tolerance at which the scaled gradient isconsidered close enough to zero anda minimum allowable relative step length for the nlm method. Seenlm.

fit.methods

"CG", "BFGS", or both. If both, the CG is run first, followed by the BFGS. Seeoptim.

nlm.fit

a logical; if FALSE (default) thenlm optimization methodis omitted and only the BFGS and/or the CG methods are run.

trace

a logical for whether to trace the process of model fitting.

transform.latent,transform.thresh

a type of transformation applied tothe all of the latent's or all of the threshold's numeric variables. Possible values:

"none" : no transformation
"min" : subtract the minimum from a variable
"scale_01" : transform the variable to fit the range from 0 to 1
"standardize" or "standardise" : subtract the mean from a variable then divide it by its standard deviation
"standardize_trunc" or "standardise_trunc" : subtract the minimum from a variable then divide it by its standard deviation

Author(s)

Maciej J. Danko

INTERNAL: Calculate the predicted continuous latent measure (h_i).

Description

INTERNAL: Calculate the predicted continuous latent measure (h_i).

Usage

hopit_Latent(latent.params, model = NULL)

Arguments

latent.params

vectors with model parameters.

model

ahopit object

Author(s)

Maciej J. Danko

INTERNAL: Calculate the model cut-points (alpha)

Description

INTERNAL: Calculate the model cut-points (alpha)

Usage

hopit_Threshold(thresh.lambda, thresh.gamma, model)

Arguments

thresh.lambda,thresh.gamma

vectors with model parameters.

model

ahopit object.

Author(s)

Maciej J. Danko

INTERNAL: The gradient of the log likelihood function

Description

INTERNAL: The gradient of the log likelihood function

Usage

hopit_derivLL(  parameters = model$coef,  model,  collapse = TRUE,  use_weights,  negative = FALSE)

Arguments

parameters

model parameters (optional). If the parameters not delivered, they are taken from themodel$coef.

model

ahopit object.

collapse

a logical indicating whether to sum individual LL contributions.

use_weights

a logical indicating whether to use model weights.

negative

a logical indicating whether the function should return negative LL.

Author(s)

Maciej J. Danko

INTERNAL: Fit a`hopit` model given the starting parameters

Description

Fit the model.

Usage

hopit_fitter(model, start = model$start, use_weights)

Arguments

model

ahopit object.

start

starting parameters.

use_weights

a logical indicating whether to use model weights.

Author(s)

Maciej J. Danko

INTERNAL: The log likelihood function

Description

INTERNAL: The log likelihood function

Usage

hopit_negLL(  parameters = model$coef,  model,  collapse = TRUE,  use_weights,  negative = TRUE)

Arguments

parameters

model parameters (optional). If the parameters are not delivered, they are taken frommodel$coef.

model

ahopit object.

collapse

a logical indicating whether to sum the individual LL contributions.

use_weights

a logical indicating whether to use model weights.

negative

a logical indicating whether the function should return negative.

Author(s)

Maciej J. Danko

Calculate the latent index

Description

Calculate the latent index from the fitted model. The latent index is a standardized latent measure that takes values from 0 to 1, where0 refers to the worst predicted state (the maximal observed value for the latent measure) and 1 refersto the best predicted state (the minimal observed value for the latent measure).

Usage

latentIndex(model, subset = NULL)healthIndex(model, subset = NULL)

Arguments

model

a fittedhopit model.

subset

an optional vector that specifies a subset of observations.

Value

a vector with a latent index for each individual.

Author(s)

Maciej J. Danko

References

Examples

# DATAdata(healthsurvey)# the order of response levels decreases from the best health to# the worst health; hence the hopit() parameter decreasing.levels# is set to TRUElevels(healthsurvey$health)# Example 1 ---------------------# fit a modelmodel1 <- hopit(latent.formula = health ~ hypertension + high_cholesterol +                  heart_attack_or_stroke + poor_mobility + very_poor_grip +                  depression + respiratory_problems +                  IADL_problems + obese + diabetes + other_diseases,                thresh.formula = ~ sex + ageclass + country,                decreasing.levels = TRUE,                control = list(trace = FALSE),                data = healthsurvey)# calculate the health indexhi <- latentIndex(model1)summary(hi)# plot a simple histogram of the function outputhist(hi, col='deepskyblue3')#plot the reported health status versus the health index.plot(hi, response = "data", ylab = 'Health index',     col='deepskyblue3', main = 'Reported health levels')# plot the model-predicted health levels versus the health index.plot(hi, response = "fitted", ylab = 'Health index',     col='deepskyblue3', main = 'Model-predicted health levels')

Extracting a log likelihood of the fitted model

Description

Extract the log likelihood of ahopit model.

Usage

## S3 method for class 'hopit'logLik(object, ...)

Arguments

object

ahopit object.

...

additional objects of the classhopit.

Author(s)

Maciej J. Danko

Likelihood ratio test for a pair of models

Description

Likelihood ratio test for a pair of models

Usage

lrt.hopit(full, nested)

Arguments

full,nested

models to be compared.

Value

a vector with the results of the test.

Author(s)

Maciej J. Danko

Examples

# DATAdata(healthsurvey)# the order of response levels decreases from the best health to# the worst health; hence the hopit() parameter decreasing.levels# is set to TRUElevels(healthsurvey$health)# Example 1 ---------------------# fitting two nested modelsmodel1 <- hopit(latent.formula = health ~ hypertension + high_cholesterol +                heart_attack_or_stroke + poor_mobility + very_poor_grip +                depression + respiratory_problems +                IADL_problems + obese + diabetes + other_diseases,              thresh.formula = ~ sex + ageclass + country,              decreasing.levels = TRUE,              control = list(trace = FALSE),              data = healthsurvey)# model with an interaction between hypertension and high_cholesterolmodel2 <- hopit(latent.formula = health ~ hypertension * high_cholesterol +                heart_attack_or_stroke + poor_mobility + very_poor_grip +                depression + respiratory_problems +                IADL_problems + obese + diabetes + other_diseases,              thresh.formula = ~ sex + ageclass + country,              decreasing.levels = TRUE,              control = list(trace = FALSE),              data = healthsurvey)# Likelihood ratio testlrt1 <- lrt.hopit(full = model2, nested = model1)lrt1# print the results in a shorter formprint(lrt1, short = TRUE)# equivalentlyprint(anova(model2, model1), short = TRUE)

Calculating the confidence intervals of the bootstrapped function using the percentile method

Description

Calculate the confidence intervals of the bootstrapped function using the percentile method.

Usage

percentile_CI(boot, alpha = 0.05, bounds = c("both", "lo", "up"))

Arguments

boot

a matrix or a list of vectors with bootstrapped elements. If it is list, then each element of the list is one replication.

alpha

a significance level.

bounds

which bounds to return; one of"both","lo","up".

Author(s)

Maciej J. Danko

Examples

# see examples in boot_hopit() function.

Plotting Cut-Points

Description

Plotting Cut-Points

Usage

## S3 method for class 'hopitCP'plot(  x,  decreasing.levels = x$decreasing.levels,  mar = c(4, 4, 1, 1),  oma = c(0, 0, 0, 0),  XLab = "Health index",  XLab.cex = 1.1,  YLab = "Counts",  YLab.cex = 1.1,  border.col = 2,  border.lty = 2,  border.lwd = 1.5,  group.labels.type = c("middle", "border", "none"),  ...)

Arguments

decreasing.levels

a logical indicating whether self-reported health classes are ordered in decreasing order.

mar,oma

graphic parameters, seepar.

XLab,XLab.cex

a label of the x axis and it's size.

YLab,YLab.cex

a label of the y axis and it's size.

border.lwd,border.lty,border.col

graphic parameters for vertical lines used to plot cut-points.

group.labels.type

a position of the legend. One ofmiddle,border, ornone.

...

further plotting arguments.

Author(s)

Maciej J. Danko

Plotting standardized coefficients

Description

Plotting standardized coefficients

Usage

## S3 method for class 'hopitDW'plot(  x,  ordered = TRUE,  show.signif = TRUE,  mar = c(10, 4, 1.5, 1),  oma = c(0, 0, 0, 0),  ylab = "Disability weight",  xlab = "",  density = 20,  angle = 45,  col = "orange",  las = 3,  ...)

Arguments

x

a object generated bystandardizeCoef function.

ordered

a logical indicating whether to sort the disability weights.

show.signif

show significance codes.

mar,oma

graphic parameters, seepar.

ylab,xlab,density,angle,col,las,...

arguments passed tobarplot.

Author(s)

Maciej J. Danko

Plotting Latent Index

Description

Plotting Latent Index

Usage

## S3 method for class 'hopitHI'plot(x, response = c("data", "fitted"), xlab = "", ylab = "Latent index", ...)

Arguments

x

a object generated bylatentIndex function.

response

X-axis plotting option; choose'data' for the raw responses and'fitted' for the responses reclassified by the model.

xlab

a label of the x-axis.

ylab

a label of the y-axis.

...

further parameters passed to theplot function.

Author(s)

Maciej J. Danko

Plotting getLevels object

Description

Plotting getLevels object

Usage

## S3 method for class 'hopitLV'plot(  x,  mar = c(7, 2, 1.5, 0.5),  oma = c(0, 3, 0, 0),  YLab = "Fraction [%]",  YLab.cex = 1.1,  legbg = grDevices::adjustcolor("white", alpha.f = 0.4),  legbty = "o",  las = 3,  ...)

Arguments

x

aobject generated bygetLevels.

mar,oma

graphic parameters, seepar.

YLab,YLab.cex

a label for the y-axis and it's size.

legbg

a legend background color. Seebg parameter inlegend.

legbty

a legend box type. Seebty parameter inlegend.

las

the style of axis labels, seepar.

...

further plotting arguments.

Author(s)

Maciej J. Danko

Plot the log likelihood profile for a profile.hopit object

Description

Plot the method for a profile.hopit object.

Usage

## S3 method for class 'profile.hopit'plot(x, ..., ylim = NULL, relative = FALSE,leg.cex = 0.85, leg.col = 'blue4')

Arguments

x

aprofile.hopit object.

...

arguments to be passed to theplot() function (seepar).

ylim

seeplot.

relative

a logical indicating whetherylim on each panel should be thesame (TRUE) or not (FALSE).

leg.cex

a character expansion factor relative to the currentpar("cex") (seelegend).

leg.col

a color used for the legend text.

Author(s)

Maciej J. Danko

Printing basic information about fitted`hopit` model

Description

Print ahopit model.

Usage

## S3 method for class 'hopit'print(x, ...)

Arguments

x

ahopit object.

...

further arguments passed to or from other methods.

Author(s)

Maciej J. Danko

Printing an object calculated by`lrt.hopit`

Description

Printing an object calculated bylrt.hopit

Usage

## S3 method for class 'lrt.hopit'print(x, short = FALSE, ...)

Arguments

x

an object obtained fromlrt.hopit.

short

a logical indicating whether to show a shortened description.

...

further arguments passed to or from other methods.

Author(s)

Maciej J. Danko

Print method for a profile.hopit object

Description

Print method for a profile.hopit object

Usage

## S3 method for class 'profile.hopit'print(x, ..., plotf = TRUE)

Arguments

x

aprofile.hopit object.

...

arguments to be passed to theplot() function (seeplot.profile.hopit).

plotf

a logical indicating whether to plot the profile.

Author(s)

Maciej J. Danko

Calculate the log likelihood profile for the fitted`hopit` model

Description

Calculate the log likelihood profile for the fittedhopit model

Usage

## S3 method for class 'hopit'profile(fitted, ..., scope = 0.15, steps = 101)

Arguments

fitted

ahopit object (a fitted model).

...

unused now.

scope

a value (fraction) defining the plotting range for a coefficient.The range isc(coef \* (1-scope), coef \* (1+scope)).

steps

at how many equally spaced points the log likelihoodfunction is calculated for each coefficient.

Author(s)

Maciej J. Danko

Examples

# DATAdata(healthsurvey)# the order of response levels decreases from the best health to# the worst health; hence the hopit() parameter decreasing.levels# is set to TRUElevels(healthsurvey$health)# Example 1 ---------------------# fitting the model:model1 <- hopit(latent.formula = health ~ hypertension + high_cholesterol +                heart_attack_or_stroke + poor_mobility + very_poor_grip +                depression + respiratory_problems +                IADL_problems + obese + diabetes + other_diseases,              thresh.formula = ~ sex + ageclass + country,              decreasing.levels = TRUE,              control = list(trace = FALSE),              data = healthsurvey)# check the fit using the profile function (at 51 points)pr <- profile(model1, steps = 51)print(pr, plotf = FALSE)# plot profileplot(pr, relative = FALSE)# alternative plotplot(pr, relative = TRUE)

Extract the`Sigma` parameter from a`hopit` model

Description

Extract theSigma parameter from ahopit model

Usage

## S3 method for class 'hopit'sigma(object, ...)

Arguments

object

a fittedhopit model.

Author(s)

Maciej J. Danko

Standardization of the coefficients

Description

Calculate standardized the coefficients (e.g. disability weights for the health variables) usingthe predicted latent measure obtained from the model.
In the self-rated health example the standardized coefficients are called disability weights Jurges (2007)and are calculated for each health variable to provide information about the impact of a specific health measure on the latent index(seelatentIndex). The disability weight for a health variable is equal to the ratio of the corresponding health coefficientand the difference between the lowest and the highest values of the predicted latent health. In other words, the disability weight reducesthe latent index by some given amount or percentage (i.e., the latent index of every individual is reduced by the same amount if the person had a heart attack or otherheart problems)(Jurges 2007).

Usage

standardizeCoef(model, namesf = identity)standardiseCoef(model, namesf = identity)disabilityWeights(model, namesf = identity)

Arguments

model

a fittedhopit model.

namesf

a vector of the names of coefficients or one argument function that modifies the names of coefficients.

Value

a vector with standardized coefficients.

Author(s)

Maciej J. Danko

References

Examples

# DATAdata(healthsurvey)# the order of response levels decreases from the best health to# the worst health; hence the hopit() parameter decreasing.levels# is set to TRUElevels(healthsurvey$health)# Example 1 ---------------------# fit a modelmodel1 <- hopit(latent.formula = health ~ hypertension + high_cholesterol +                heart_attack_or_stroke + poor_mobility + very_poor_grip +                depression + respiratory_problems +                IADL_problems + obese + diabetes + other_diseases,              thresh.formula = ~ sex + ageclass + country,              decreasing.levels = TRUE,              control = list(trace = FALSE),              data = healthsurvey)# a function that modifies the coefficient names.txtfun <- function(x) gsub('_',' ',substr(x,1,nchar(x)-3))# calculate and plot the disability weightssc <- standardizeCoef(model1, namesf = txtfun)scsummary(sc)plot(sc)

Calculate the model summary

Description

Summarize ahopit model.

Usage

## S3 method for class 'hopit'summary(object, robust.se, ...)

Arguments

object

ahopit object.

robust.se

a logical indicating whether to use robust standard errors basedon the sandwich estimator.If a survey design is detected, then this option is ignored.Seehopit.control.

...

further arguments passed to or from other methods.

Author(s)

Maciej J. Danko

Calculation of the variance-covariance matrix for a specified survey design (experimental function)

Description

This function is an equivalent ofsurvey:::svy.varcoef. In the original approachestfun is calculated fromglm's working residuals:
estfun <- model.matrix(glm.object) * resid(glm.object, "working") * glm.object$weights
In the hopit package, estfun is directly calculated as a gradient (vector of partial derivatives) of the log likelihood function.Depending on detected design an appropriatesurvey function is called.

Usage

svy.varcoef_hopit(vcovMat, estfun, design)

Arguments

vcovMat

a variance-covariance matrix.

estfun

a gradient function of the log-likelihood function.

design

asurvey.design object.

Variance-covariance matrix from the fitted model

Description

Returns the variance-covariance matrix of the main parameters of a fittedhopit model object.

Usage

## S3 method for class 'hopit'vcov(object, robust.vcov, ...)

Arguments

object

ahopit object.

robust.vcov

a logical indicating whether to use the sandwich estimator tocalculate the variance-covariance matrix.If a survey design is detected, then this option is ignored.

...

further arguments passed to or from other methods.

Author(s)

Maciej J. Danko

Movatterモバイル変換

Extracting the Akaike Information Criterion from the fitted model

Description

Usage

Arguments

Author(s)

Likelihood Ratio Test Tables

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Bootstrapping hopit model

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Extracting the model coefficients

Description

Usage

Arguments

Author(s)

INTERNAL: Get the starting parameters

Description

Usage

Arguments

Value

Author(s)

Calculate the threshold cut-points and individual adjusted responses using Jurges' method

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Summarize the adjusted and the original self-rated response levels

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Artificially generated health survey data

Description

Usage

Format

Source

References

Examples

Generalized hierarchical ordered threshold models.

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Auxiliary for controlling the fitting of ahopit model

Description

Usage

Arguments

Author(s)

See Also

INTERNAL: Calculate the predicted continuous latent measure (h_i).

Description

Usage

Arguments

Author(s)

INTERNAL: Calculate the model cut-points (alpha)

Auxiliary for controlling the fitting of a`hopit` model

INTERNAL: Fit a`hopit` model given the starting parameters