Quantile Regression for Random Variables on the Unit Interval

Description

Employs a two-parameter family of distributions for modelling random variables on the (0, 1) interval by applying the cumulative distribution function (cdf) of one parent distribution to the quantile function of another.

Details

The cdfquantreg package includes 36 members of a two-parameter family of distributions for modelling random variables on the (0, 1) interval (see cdfqrFamily). This family has explicit pdfs, cdfs, and quantile functions. The two parameters consist of a location parameter and a dispersion parameter. The location parameter models the median and the dispersion parameter models the spread of other quantiles around the median (see Smithson and Shou, 2016, for details about the distribution family and the models). Separate submodels may be specified for the location and for the dispersion parameters, permitting different or overlapping sets of predictors in each.

The package offers maximum likelihood (see cdfquantreg)and bootstrap (see qrBoot) estimation methods. All model functions return S3 objects. In addition to the usual goodness of fit information, the package provides root-mean-squared errors in both the raw and logit scales, and the gradient. Model diagnostics include raw, Pearson, and deviance residuals (see residuals.cdfqr), and dfbetas (see influence.cdfqr).

For each distribution, the package provides evaluations of the pdf (dq), cdf (pq), and quantile (qq), as well as random samples from any of them (rq). Evaluations of skew and kurtosis (qrPwlm) also are available using probability-weighted L-moments.

Author(s)

Yiyun Shou and Michael Smithson

Maintainer: Yiyun Shou (yiyun.shou@anu.edu.au)

References

Shou, Y. and Smithson, M., (2019). cdfquantreg: An R Package for CDF-Quantile Regression. Journal of Statistical Software,88(1), pp.1–30, doi: 10.18637/jss.v088.i01

See Also

cdfqrFamily

Ambiguity-Conflict data

Description

A data from a study that investigates the judgment under ambiguity and conflict

Usage

Ambdata

Format

A data frame with 166 rows and 2 variables:

ID

subject ID

value

Rating in each judgment scenario

scenario

Index for judgment scenarios

Source

https://pubmed.ncbi.nlm.nih.gov/16594767/

Stress-Anxiety data

Description

A data from a study that investigates the relationship between stress and anxiety.

Usage

AnxStrData

Format

A data frame with 166 rows and 2 variables:

Anxiety

Scores on Anxiety subscale

Stress

Scores on Stress subscale

Source

https://pubmed.ncbi.nlm.nih.gov/16594767/

Extinction Study data-set

Description

Probability of Human Extinction Study

Usage

ExtEvent

Format

A data frame with 1170 rows and 11 variables:

ID

Subject ID

gend

Gender of subjects, '0'is male, '1'is female

nation

The nation of the participants come from

UK

effect coding for nation

IND

effect coding for nation

political

political orientation of subjects

format

The format of probability elicitation

order

the order of probability judgement task.

SECS_6

Social conservativsm question on attitude toward gun ownership.

EQ1_P

Probability estimates for general threats.

EQ3_P

Probability estimates for the greatest threat.

Source

https://www.michaelsmithson.online/

IPCC data-set

Description

The IPCC data-set comprises the lower, best, and upper estimates for the phrases "likely" and "unlikely" in six IPCC report sentences.

Usage

IPCC

Format

A data frame with 4014 rows and 8 variables:

subj

Subject ID number

treat

Experimental conditions

valence

Valence of the sentences

prob

raw probability estimates

probm

Linear transformed prob into (0, 1) interval

mid

Distinguish lower, best and upper estiamtes

high

Distinguish lower, best and upper estiamtes

Question

IPCC question number

Source

https://pubmed.ncbi.nlm.nih.gov/19207697/

IPCC data-set - Australian data

Description

The IPCC-AUS data-set comprises the best estimates for the phrases in IPCC report sentences.

Usage

IPCCAUS

Format

A data frame with 4014 rows and 8 variables:

ID

Subject ID

gender

Gender of subjects, '0'is male, '1'is female

age

age of subjects

cfprob

personal probability.

bestprob

nominated probability.

Source

https://pubmed.ncbi.nlm.nih.gov/19207697/

IPCC data-set - Wide format

Description

The IPCC-wide data-set comprises the best estimates for the phrases "likely" and "unlikely" in six IPCC report sentences.

Usage

IPCC_Wide

Format

A data frame with 4014 rows and 8 variables:

Q4

Each column indicates the estimates for one sentence.

Q5

Each column indicates the estimates for one sentence.

Q6

Each column indicates the estimates for one sentence.

Q8

Each column indicates the estimates for one sentence.

Q9

Each column indicates the estimates for one sentence.

Q10

Each column indicates the estimates for one sentence.

Source

https://pubmed.ncbi.nlm.nih.gov/19207697/

Juror data

Description

Juror Judgment Study.

Usage

JurorData

Format

A data frame with 104 rows and 3 variables:

crc99

The ratings of confidence levels with rescaling into the (0, 1) interval to avoide 1 and 0 values.

vert

was the dummy variable for coding the conditions of verdict types, whereas

confl

was the dummy variable for coding the conflict conditions

Source

doi:10.1375/pplt.2004.11.1.154

Model comparison test for fitted cdfqr models

Description

Likelihood Ratio Tests for fitted cdfqr Objects.

Usage

## S3 method for class 'cdfqr'
anova(object, ..., test = "LRT")

Arguments

Examples

data(cdfqrExampleData)
fit_null <- cdfquantreg(crc99 ~ 1 | 1, 't2','t2', data = JurorData)
fit_mod1 <- cdfquantreg(crc99 ~ vert | confl, 't2','t2', data = JurorData)
anova(fit_null, fit_mod1)

Likelihood Functions for Generating OpenBUGS Model File

Description

Likelihood functions for generating OpenBUGS model file.

Usage

bugsLikelihood(fd, sd)

Arguments

Value

A string to be written in the BUGS model file.

Examples

bugsLikelihood('t2','t2')

Generating OpenBUGS Model File

Description

Generating OpenBUGS model file

Usage

bugsModel(formula, fd, sd, random = NULL, modelname = "bugmodel", wd = getwd())

Arguments

Value

A model ‘.txt’ file is generated in the specified working directory. The function also returns a list of values:

init1,init2

Default initial values for MCMC two chain procedure.

vars

A list of variables that are included in the estimation.

nodes_sample

a list of characters that specify the nodes to be monitored.

Examples

## Not run: 
# Need write access in the working directory before executing the code.
# No random component
bugsModel(y ~ x1 | x2, 't2','t2', random = NULL)
# Random component as subject ID
bugsModel(y ~ x1 | x2, 't2','t2', random = 'ID')

## End(Not run)

The Family of Finite-Tailed Distributions

Description

Density function, distribution function, quantile function, and random generation of variates for a specified cdf-quantile distribution.

Usage

cdfft(q, sigma, theta, fd, sd, mu = NULL, inner = TRUE, version)

pdfft(y, sigma, theta, fd, sd, mu = NULL, inner = TRUE, version)

qqft(p, sigma, theta, fd, sd, mu = NULL, inner = TRUE, version)

rqft(n, sigma, theta, fd, sd, mu = NULL, inner = TRUE, version)

Arguments

Value

pdfft gives the density, rqft generates random variate, qqft gives the quantile function, and cdfft gives the cumulative density of specified distribution.

Control Optimization Parameters for CDF-Quantile Probability Distributions

Description

Control Optimization Parameters for CDF-Quantile Probability Distributions.

Usage

cdfqr.control(method = "BFGS", maxit = 5000, trace = FALSE)

Arguments

Value

A list with the arguments specified.

Examples

data(cdfqrExampleData)
fit <- cdfquantreg(crc99 ~ vert | confl, 't2', 't2', 
data = JurorData,control = cdfqr.control(trace = TRUE))

Overview of the family of distributions

Description

The cdfquantreg family consists of the currently available distributions that can be used to fit quantile regression models via the cdfquantreg() function.

Usage

cdfqrFamily(shape = "all")

Arguments

Details

The cdfquantreg package includes a two-parameter family of distributions for modeling random variables on the (0, 1) interval by applying the cumulative distribution function (cdf) of one “parent” distribution to the quantile function of another.
The naming of these distributions is “parent - child” or “fd - sd”, where “fd” is the parent distribution, and “sd” is the child distribution.
The distributions have four characteristic shapes: Logit-logistic, bimodal, trimodal, and finite-tailed. Here is the list of currently available distributions.

Bimodal Shape Distributions

Trimodal Shape Distributions

Logit-logistic Shape Distributions

Finite-tailed Shape Distributions

Kumaraswamy Distribution

Value

A list of distributions that are available in the current version of package.

Examples

cdfqrFamily()

CDF-Quantile Probability Distributions

Description

cdfquantreg is the main function to fit a cdf quantile regression with a variety of distributions.

Usage

cdfquantreg(
  formula,
  fd = NULL,
  sd = NULL,
  data,
  family = NULL,
  start = NULL,
  control = cdfqr.control(...),
  ...
)

Arguments

Details

The cdfquantreg function fits a quantile regression model with a distributions from the cdf-quantile family selected by the user (Smithson and Shou, 2015). The model is specified in a two-part formula, one part containing the predictors of the location parameter, and the second part containing the predictors of the dispersion parameter. The models are fitted in two stages, the first of which uses the Nelder-Mead algorithm and the second of which takes the estimates from the first stage and applies the BFGS algorithm to refine the estimates.

Value

An object of class cdfquantreg will be returned. Generic functions such as summary,print (e.g., print.cdfqr) and coef can be used to extract output (see summary.cdfqr for more details about the generic functions that can be used). Class of object is a list with the following output:

coefficients

A named vector of coefficients.

residuals

Raw residuals, the difference between the fitted values and the data.

fitted

The fitted values, including full model fitted values, fitted values for the mean component, and fitted values for the dispersion component.

rmse

The model root mean squared errors

rmseLogit

The root mean squared errors between the logit of the fitted values, and the logit of the response values.

vcov

The variance-covariance matrix of the coefficient estimates.

AIC, BIC

Akaike's Information Criterion and Bayesian Information Criterion.

deviance

The deviance for the model.

Examples

data(cdfqrExampleData)
fit <- cdfquantreg(crc99 ~ vert | confl, fd ='t2',sd ='t2', data = JurorData)

summary(fit)

Censored CDF-Quantile Probability Distributions

Description

cdfquantregC is the a function to fit a censored cdf quantile regression with a variety of distributions .

Usage

cdfquantregC(
  formula,
  fd = NULL,
  sd = NULL,
  data,
  family = NULL,
  censor = "DB",
  c1 = NULL,
  c2 = NULL,
  start = NULL,
  control = cdfqr.control(...),
  ...
)

Arguments

Details

The cdfquantreg function fits a quantile regression model with a distributions from the cdf-quantile family selected by the user (Smithson and Shou, 2015). The model is specified in a two-part formula, one part containing the predictors of the location parameter, and the second part containing the predictors of the dispersion parameter. The models are fitted in two stages, the first of which uses the Nelder-Mead algorithm and the second of which takes the estimates from the first stage and applies the BFGS algorithm to refine the estimates.

Value

An object of class cdfquantreg will be returned. Generic functions such as summary,print (e.g., print.cdfqr) and coef can be used to extract output (see summary.cdfqr for more details about the generic functions that can be used). Class of object is a list with the following output:

coefficients

A named vector of coefficients.

residuals

Raw residuals, the difference between the fitted values and the data.

fitted

The fitted values, including full model fitted values, fitted values for the mean component, and fitted values for the dispersion component.

rmse

The model root mean squared errors

rmseLogit

The root mean squared errors between the logit of the fitted values, and the logit of the response values.

vcov

The variance-covariance matrix of the coefficient estimates.

AIC, BIC

Akaike's Information Criterion and Bayesian Information Criterion.

deviance

The deviance for the model.

Examples

data(cdfqrExampleData)
fit <- cdfquantregC(crc99 ~ vert | confl, c1 = 0.001, c2= 0.999, 
fd ='t2',sd ='t2', data = JurorData)

summary(fit)

CDF-Quantile Finite Tailed Probability Distributions

Description

cdfquantregFT is a function to fit a cdf quantile regression with a variety of finite tailed distributions. It can account for data that has boundary values.

Usage

cdfquantregFT(
  formula,
  fd = NULL,
  sd = NULL,
  mu.fo = NULL,
  inner = FALSE,
  version = "V",
  data,
  family = NULL,
  start = NULL,
  ssn = 20,
  control = cdfqr.control(...),
  ...
)

Arguments

Details

The cdfquantregFT function fits a quantile regression model with a distributions from the cdf-quantile finite tailed distributions. Here is the list of currently available distributions.

Bimodal Shape Distributions

Value

An object of class cdfqrFT will be returned. Generic functions such as summary,print and coef can be used to extract output (see summary.cdfqr for more details about the generic functions that can be used). Class of object is a list with the following output:

coefficients

A named vector of coefficients.

residuals

Raw residuals, the difference between the fitted values and the data.

fitted

The fitted values, including full model fitted values, fitted values for the mean component, and fitted values for the dispersion component.

rmse

The model root mean squared errors

rmseLogit

The root mean squared errors between the logit of the fitted values, and the logit of the response values.

vcov

The variance-covariance matrix of the coefficient estimates.

AIC, BIC

Akaike's Information Criterion and Bayesian Information Criterion.

deviance

The deviance for the model.

Examples

data(cdfqrExampleData)
fit <- cdfquantregFT(pnurse ~ Ambulance |Ambulance ,
 fd = "arcsinh", sd = "arcsinh",  inner = FALSE, version = "V", data = yoon)
summary(fit)

Zero/One inflated CDF-Quantile Probability Distributions

Description

cdfquantregH is the a function to fit a Zero/One inflated CDF-Quantile regression with a variety of distributions .

Usage

cdfquantregH(
  formula,
  zero.fo = ~1,
  one.fo = ~1,
  fd = NULL,
  sd = NULL,
  data,
  family = NULL,
  type = "ZI",
  start = NULL,
  control = cdfqr.control(...),
  ...
)

Arguments

Details

The cdfquantreg function fits a quantile regression model with a distributions from the cdf-quantile family selected by the user (Smithson and Shou, 2015). The model is specified in a two-part formula, one part containing the predictors of the location parameter, and the second part containing the predictors of the dispersion parameter. The models are fitted in two stages, the first of which uses the Nelder-Mead algorithm and the second of which takes the estimates from the first stage and applies the BFGS algorithm to refine the estimates.

Value

An object of class cdfqrH will be returned. Generic functions such as summary,print (e.g., print.cdfqr) and coef can be used to extract output (see summary.cdfqr for more details about the generic functions that can be used). Class of object is a list with the following output:

coefficients

A named vector of coefficients.

residuals

Raw residuals, the difference between the fitted values and the data.

fitted

The fitted values, including full model fitted values, fitted values for the mean component, and fitted values for the dispersion component.

vcov

The variance-covariance matrix of the coefficient estimates.

AIC, BIC

Akaike's Information Criterion and Bayesian Information Criterion.

Examples

data(cdfqrExampleData)
# For one-inflated model
ipcc_high <- subset(IPCC, mid == 1 & high == 1 & prob!=0)
fit <- cdfquantregH(prob ~ valence | valence,one.fo = ~valence,
  fd ='t2',sd ='t2', type = "OI", data = ipcc_high)

summary(fit)

# For zero-inflated model
ipcc_low <- subset(IPCC, mid == 0 & high == 0 & prob!=1)
fit <- cdfquantregH(prob ~ valence | valence, zero.fo = ~valence,
  fd ='t2',sd ='t2', type = "ZI", data = ipcc_low)
 
 
# For zero &one-inflated model
ipcc_mid <- subset(IPCC, mid == 1 & high == 0)
fit <- cdfquantregH(prob ~ valence | valence, zero.fo = ~valence,
  one.fo = ~valence,
  fd ='t2',sd ='t2', type = "ZO", data = ipcc_mid)
 
  

The Family of Distributions

Description

Density function, distribution function, quantile function, and random generation of variates for a specified cdf-quantile distribution.

Usage

dq(x, mu, sigma, fd, sd)

rq(n, mu, sigma, fd, sd)

qq(p, mu, sigma, fd, sd)

pq(q, mu, sigma, fd, sd)

Arguments

Value

dq gives the density, rq generates random variates, qq gives the quantile function, and pq gives the cumulative density of specified distribution.

Examples

x <- rq(5, mu = 0.5, sigma = 1, 't2','t2'); x

dq(x, mu = 0.5, sigma = 1, 't2','t2')

qtil <- pq(x, mu = 0.5, sigma = 1, 't2','t2');qtil

qq(qtil , mu = 0.5, sigma = 1, 't2','t2')

Influence Diagnosis For Fitted Cdfqr Object

Description

Influence Diagnosis (dfbetas) For Fitted Cdfqr Object

Usage

## S3 method for class 'cdfqr'
influence(
  model,
  method = "dfbeta",
  type = c("full", "location", "dispersion", "skew", "zero", "one"),
  what = "full",
  plot = FALSE,
  id = FALSE,
  ...
)

## S3 method for class 'cdfqr'
dfbeta(
  model,
  type = c("full", "location", "dispersion", "skew", "zero", "one"),
  what = "full",
  ...
)

## S3 method for class 'cdfqr'
dfbetas(
  model,
  type = c("full", "location", "dispersion", "skew", "zero", "one"),
  what = "full",
  ...
)

Arguments

Value

A matrix, each row of which contains the estimated influence on parameters when that row's observation is removed from the sample.

See Also

lm.influence, influence.measures

Examples

data(cdfqrExampleData)
fit <- cdfquantreg(crc99 ~ vert | confl, 't2', 't2', data = JurorData)
#It takes some time especially the data is large.
influcne <- influence(fit)
plot(influcne[,2])

## Not run: 
# Same as influence(fit)
dfbetval <- dfbetas(fit)

## End(Not run)

Plot Fitted Values/Residuals of A Cdfqr Object or Distribution

Description

Plot Fitted Values/Residuals of A cdfqr Object or Distribution

Usage

## S3 method for class 'cdfqr'
plot(
  x,
  mu = NULL,
  sigma = NULL,
  theta = NULL,
  fd = NULL,
  sd = NULL,
  n = 10000,
  inner = TRUE,
  version = "V",
  type = c("fitted"),
  ...
)

Arguments

Examples

data(cdfqrExampleData)
fit <- cdfquantreg(crc99 ~ vert | confl, 't2','t2', data = JurorData)
plot(fit)

Methods for Cdfqr Objects

Description

Methods for obtaining the fitted/predicted values for a fitted cdfqr object.

Usage

## S3 method for class 'cdfqr'
predict(
  object,
  newdata = NULL,
  type = c("full", "mu", "sigma", "theta", "one", "zero"),
  quant = 0.5,
  ...
)

## S3 method for class 'cdfqr'
fitted(
  object,
  type = c("full", "mu", "sigma", "theta", "one", "zero"),
  plot = FALSE,
  ...
)

Arguments

Examples

data(cdfqrExampleData)
fit <- cdfquantreg(crc99 ~ vert | confl, 't2','t2', data = JurorData)

plot(predict(fit))
plot(predict(fit))

Bootstrapping for cdf quantile regression

Description

qrBoot provides a simple bootstrapping method for estimating the parameters of a cdf quantile regression model.

Usage

qrBoot(object, rn, f = coef, R = 500, ci = 0.95)

Arguments

Value

A matrix that includes the original statistics, bootstrap means, and bootstrap confidence intervals

Examples

data(cdfqrExampleData)
fit <- cdfquantreg(crc99 ~ vert | confl, 't2', 't2', data = JurorData)
qrBoot(fit, rn = 50, R = 50)

Give the Gradient Function for CDF-Quantile Distribution Models

Description

Give the Gradient Function for CDF-Quantile Distribution models

Usage

qrGrad(fd, sd)

Arguments

Value

grad The gradient function of parameter estimates, given a specified cdf-quantile distribution

Examples

qrGrad('t2','t2')

Log Likelihood for Fitting Cdfquantile Distributions

Description

Function to give the (negative) log likelihood for fitting cdfquantile distributions.

Usage

qrLogLik(y, mu, sigma, fd, sd, total = TRUE)

Arguments

Value

The negative log likelihood for fitting the data with a cdfquantile distribution.

Examples

y <- rbeta(20, 0.5, 0.5)
qrLogLik(y, mu = 0.5, sigma = 1, 't2','t2')

Probability Weighted L-moment Skewness and Kurtosis

Description

Calculate the skew and kurtosis statistics based on probability weighted moments, via simulation method.

Usage

qrPwlm(x, n = NULL, mu = NULL, sigma = NULL, fd = NULL, sd = NULL)

Arguments

Details

This function computes the L-moment measures of skew and kurtosis, which may be computed via linear combinations of probability-weighted moments (Greenwood, Landwehr, Matalas and Wallis, 1979).

Value

The tau3(skew) and tau4(kurtosis) values of the L-moment.

References

Greenwood, J. A., Landwehr, J. M., Matalas, N. C., & Wallis, J. R. (1979). Probability weighted moments: definition and relation to parameters of several distributions expressable in inverse form. Water Resources Research, 15(5), 1049-1054.

Examples

qrPwlm(n = 1000, mu = 0.5, sigma = 1, fd = 't2', sd = 't2')

Starting Value Generation for CDF quantile Regressions

Description

qrStart is the function for generating starting values for a cdf-quantile GLM null model.

Usage

qrStart(ydata, fd = NULL, sd = NULL, skew = FALSE)

Arguments

Details

The start values for the location parameter in a null model are the median of the empirical distribution, and a starting value for the dispersion parameter based on a specific quantile of the empirical distribution, specified according to the theoretical distribution on which the model is based. The start values for all new predictor coefficients in both the location and dispersion submodels are assigned the value 0.1.

Value

A vector that consists initial values for mu and sigma.

Examples

x <- rbeta(100, 1, 2)
qrStart(x, fd='t2', sd='t2')
#[1] -0.5938286  1.3996999

Register method for cdfqr object functions

Description

Register method for cdfqr object functions.

Usage

## S3 method for class 'cdfqr'
residuals(object, type = c("raw", "pearson", "deviance"), ...)

Arguments

Value

residuals of a specified type.

Examples

data(cdfqrExampleData)
fit <- cdfquantreg(crc99 ~ vert | confl, 't2','t2', data = JurorData)

residuals(fit, "pearson")

Transform Values into (0, 1) Interval

Description

scaleTR is function that rescales values of a variable into the (0, 1) interval.

Usage

scaleTR(y, high = NULL, low = NULL, data = NULL, N = NULL, scale = 0.5)

Arguments

Details

scaleTR used the method suggested by Smithson and Verkuilen (2006) and applies linear transformation to values into the open interval (0, 1). It first transform the values from their original scale by taking y' = (y - a)/(b-a), where a is the lowest possible value of that variable and b is the highest possible value of that variable. Next, it compresses the range to avoid zeros and ones by taking y" = (y'(N - 1) + c)/N, where N is the sample size and c is the compressing parameter. The smaller value c is, the boundary values would be more approaching zeros and ones, and have greater impact on the estimation of the dispersion parameters in the cdf quantile model.

See Also

cdfquantreg

Examples

y <- rnorm(20, 0, 1)
ynew <- scaleTR(y)

S3 Methods for getting output from fitted cdfqr Objects.

Description

Give the S3 Methods for CDF-Quantile Distribution Models

Usage

## S3 method for class 'cdfqr'
summary(object, ...)

## S3 method for class 'cdfqr'
print(x, digits = max(3, getOption("digits") - 3), ...)

## S3 method for class 'cdfqr'
coef(object, type = "full", ...)

## S3 method for class 'cdfqr'
vcov(object, type = "full", ...)

## S3 method for class 'cdfqr'
update(object, formula., zero.fo., one.fo., mu.fo., ..., evaluate = TRUE)

## S3 method for class 'cdfqr'
confint(object, parm, level = 0.95, submodel = "full", ...)

## S3 method for class 'cdfqr'
formula(x, ...)

## S3 method for class 'cdfqr'
nobs(object, ...)

## S3 method for class 'cdfqr'
deviance(object, ...)

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

## S3 method for class 'cdfqrH'
confint(
  object,
  parm,
  level = 0.95,
  type = c("full", "mean", "sigma", "zero", "one"),
  ...
)

## S3 method for class 'cdfqrFT'
confint(object, parm, level = 0.95, submodel = "full", ...)

Arguments

Examples

data(cdfqrExampleData)
fit <- cdfquantreg(crc99 ~ vert | confl, 't2','t2', data = JurorData)

summary(fit)
print(fit)
logLik(fit)
coef(fit)
deviance(fit)
vcov(fit)
confint(fit)

#Update the model
fit2 <- update(fit, crc99 ~ vert*confl | confl)
summary(fit2)

Patient Time Data

Description

Data from Modeling Proportion of Patient Time in Emergency Ward Stages

Usage

yoon

Format

A data frame with 1170 rows and 11 variables:

id

case identification

Day

day of the week ( 0 = Sunday)

Ambulance

0 = walk-in; 1 = ambulance-arrival

Triage

triage level

Triage1

1 = triage level 1

Triage2

1 = triage level 2

Triage3

1 = triage level 3

Triage4

1 = triage level 4

Triage5

1 = triage level 5

Lab

1 = laboratory test(s) conducted

Xray

1 = x-ray conducted

Other

1 = other intervention

LOS

length of stay in minutes

LOSh

length of stay in hours

preg

proportion of time in registration stage

ptriage

proportion of time in triage stage

pnurse

proportion of time in nursing care stage

pphysician

proportion of time in consultation with physician(s)

pdecis

proportion of time in decisional stage

pregptriage

preg + ptriage

pphysdecis

pphysician + pdecis

prnurse

pnurse/(pnurse + pregptriage)

prphysdec

pphysdecis /(pphysdecis + pregptriage)

Source

doi:10.1017/S1481803500006539