Package 'GPCMlasso'

Title: Differential Item Functioning in Generalized Partial Credit Models
Description: Provides a framework to detect Differential Item Functioning (DIF) in Generalized Partial Credit Models (GPCM) and special cases of the GPCM as proposed by Schauberger and Mair (2019) <doi:10.3758/s13428-019-01224-2>. A joint model is set up where DIF is explicitly parametrized and penalized likelihood estimation is used for parameter selection. The big advantage of the method called GPCMlasso is that several variables can be treated simultaneously and that both continuous and categorical variables can be used to detect DIF.
Authors: Gunther Schauberger
Maintainer: Gunther Schauberger <[email protected]>
License: GPL (>= 2)
Version: 0.1-7
Built: 2024-11-24 06:54:20 UTC
Source: CRAN

Help Index

Find DIF in Generalized Partial Credit Models

Description

Performs GPCMlasso, a method to identify DIF in Generalized Partial Credit Models. A joint parametric model is set up based on an IRT model chosen by the user. Several variables can be considered simultaneously. For each pair between variable and item, a parametric DIF effect is introduced which indicates DIF if the respective parameter is selected (estimated to be unequal zero). Parameter selection is done using a lasso-type penalization term.

Author(s)

Gunther Schauberger
[email protected]

References

Schauberger, Gunther and Mair, Patrick (2019): A Regularization Approach for the Detection of Differential Item Functioning in Generalized Partial Credit Models, Behavior Research Methods, https://link.springer.com/article/10.3758/s13428-019-01224-2

See Also

GPCMlasso

Examples

data(tenseness_small)

## formula for simple model without covariates
form.0 <- as.formula(paste("cbind(",paste(colnames(tenseness_small)[1:5],collapse=","),")~0"))

######
## fit simple RSM where loglikelihood and score function are evaluated parallel on 2 cores
rsm.0 <- GPCMlasso(form.0, tenseness_small, model = "RSM", 
control= ctrl_GPCMlasso(cores=2))
rsm.0

## Not run: 
## formula for model with covariates (and DIF detection)
form <- as.formula(paste("cbind(",paste(colnames(tenseness_small)[1:5],collapse=","),")~."))

######
## fit GPCM model with 10 different tuning parameters
gpcm <- GPCMlasso(form, tenseness_small, model = "GPCM", 
                  control = ctrl_GPCMlasso(l.lambda = 10))
gpcm
plot(gpcm)
pred.gpcm <- predict(gpcm)
trait.gpcm <- trait.posterior(gpcm)

######
## fit RSM, detect differential step functioning (DSF)
rsm.DSF <- GPCMlasso(form, tenseness_small, model = "RSM", DSF = TRUE, 
                     control = ctrl_GPCMlasso(l.lambda = 10))
rsm.DSF
plot(rsm.DSF)

## create binary data set
tenseness_small_binary <- tenseness_small
tenseness_small_binary[,1:5][tenseness_small[,1:5]>1] <- 2

######
## fit and cross-validate Rasch model
set.seed(1860)
rm.cv <- GPCMlasso(form, tenseness_small_binary, model = "RM", cv = TRUE, 
                   control = ctrl_GPCMlasso(l.lambda = 10))
rm.cv
plot(rm.cv)

## End(Not run)

Control function for GPCMlasso

Description

Control parameters for penalty terms and for tuning the fitting algorithm.

Usage

ctrl_GPCMlasso(
  log.lambda = TRUE,
  lambda = NULL,
  l.lambda = 50,
  lambda.min = 0.1,
  adaptive = TRUE,
  weight.penalties = TRUE,
  ada.lambda = 1e-04,
  ada.power = 1,
  Q = 15,
  lambda2 = 1e-04,
  cvalue = 1e-05,
  trace = TRUE,
  folds = 10,
  cores = 25,
  null_thresh = 0.01,
  gradtol = 1e-06,
  steptol = 1e-06,
  iterlim = 500,
  precision = 3,
  all.dummies = FALSE
)

Arguments

log.lambda

Should the grid of tuning parameters be created on a log scale?
lambda

Optional argument to specify a vector of tuning parameters. If lambda = NULL, a vector of length l.lambda is created automatically.
l.lambda

Specifies the length of the grid of tuning parameters.
lambda.min

Minimal value used if the grid of tuning parameters is created automatically.
adaptive

Should adaptive lasso be used? Default is TRUE.
weight.penalties

Should penalties be weightes accoreding to the number of penalty term and the number of parameters corresponding to one pair between item and covariate. Only relevant if both DSF = TRUE and the number of response categories differs across items (because only then these values can differ).
ada.lambda

Size of tuning parameter for Ridge-regularized estimation of parameters used for adaptive weights.
ada.power

By default, 1st power of absolute values of Ridge-regularized estimates are used. Could be changed to squared values by ada-power = 2.
Q

Number of nodes to be used in Gauss-Hermite quadrature.
lambda2

Tuning parameter for ridge penalty on all coefficients except sigma/slope parameters. Should be small, only used to stabilize results.
cvalue

Internal parameter for the quadratic approximation of the L1 penalty. Should be sufficiently small.
trace

Should the trace of the progress (current tuning parameter) be printed?
folds

Number of folds for cross-validation. Only relevant if cv = TRUE in GPCMlasso.
cores

Number of cores to be used parallel when fitting the model.
null_thresh

Threshold which is used to distinguih between values equal and unequal to zero.
gradtol

Parameter to tune optimization accuracy, for details see nlm.
steptol

Parameter to tune optimization accuracy, for details see nlm.
iterlim

Parameter to tune optimization accuracy, for details see nlm.
precision

Number of decimal places used to round coefficient estimates.
all.dummies

Should (in case of factors with more than 2 categories) the dummy variables for all categories be included in the design matrix? If all.dummies = TRUE, the dependence on the reference category is eliminated for multi-categorical covariates.

Author(s)

Gunther Schauberger
[email protected]

References

Schauberger, Gunther and Mair, Patrick (2019): A Regularization Approach for the Detection of Differential Item Functioning in Generalized Partial Credit Models, Behavior Research Methods, https://link.springer.com/article/10.3758/s13428-019-01224-2

Examples

data(tenseness_small)

## formula for simple model without covariates
form.0 <- as.formula(paste("cbind(",paste(colnames(tenseness_small)[1:5],collapse=","),")~0"))

######
## fit simple RSM where loglikelihood and score function are evaluated parallel on 2 cores
rsm.0 <- GPCMlasso(form.0, tenseness_small, model = "RSM", 
control= ctrl_GPCMlasso(cores=2))
rsm.0

## Not run: 
## formula for model with covariates (and DIF detection)
form <- as.formula(paste("cbind(",paste(colnames(tenseness_small)[1:5],collapse=","),")~."))

######
## fit GPCM model with 10 different tuning parameters
gpcm <- GPCMlasso(form, tenseness_small, model = "GPCM", 
                  control = ctrl_GPCMlasso(l.lambda = 10))
gpcm
plot(gpcm)
pred.gpcm <- predict(gpcm)
trait.gpcm <- trait.posterior(gpcm)

######
## fit RSM, detect differential step functioning (DSF)
rsm.DSF <- GPCMlasso(form, tenseness_small, model = "RSM", DSF = TRUE, 
                     control = ctrl_GPCMlasso(l.lambda = 10))
rsm.DSF
plot(rsm.DSF)

## create binary data set
tenseness_small_binary <- tenseness_small
tenseness_small_binary[,1:5][tenseness_small[,1:5]>1] <- 2

######
## fit and cross-validate Rasch model
set.seed(1860)
rm.cv <- GPCMlasso(form, tenseness_small_binary, model = "RM", cv = TRUE, 
                   control = ctrl_GPCMlasso(l.lambda = 10))
rm.cv
plot(rm.cv)

## End(Not run)

GPCMlasso

Description

Performs GPCMlasso, a method to identify differential item functioning (DIF) in Generalized Partial Credit Models. A joint parametric model is set up based on an IRT model chosen by the user. Several variables can be considered simultaneously. For each pair between variable and item, a parametric DIF effect is introduced which indicates DIF if the respective parameter is selected (estimated to be unequal zero). Parameter selection is done using a lasso-type penalization term.

Usage

GPCMlasso(
  formula,
  data,
  DSF = FALSE,
  model = c("PCM", "RSM", "GPCM", "GRSM", "RM", "2PL"),
  control = ctrl_GPCMlasso(),
  cv = FALSE,
  main.effects = TRUE
)

Arguments

formula

Formula to indicate which items are considered and which covariates should be used to find DIF. Items are considered to be the response and are concatenated by cbind(). If the RHS of the formula is ~0, simply the model specified in model is calulated.
data

Data frame containing the ordinal item response data (as ordered factors) and all covariates.
DSF

Should Differential Step Functioning (DSF) be considered? If DSF = TRUE, one parameter per step between two response categories is introduced. For binary items, DSF and DIF conincide.
model

Specify the underlying basic model. Currently, you can choose between the partial credit model and the rating scale model and the respective generalized versions of both models called 'PCM', 'RSM', 'GPCM' and 'GRSM'. Generalized models allow for different discrimination parameters between items.
control

Control argument to specify further arguments for the algorithm and numerical optimization, specified by ctrl_GPCMlasso.
cv

Should cross-validation be performed? Cross-validation can be used as an alternative to BIC to select the optimal tuning parameter.
main.effects

Should also main effects of the variables be included in the model? Default is TRUE. Here, positive parameter estimates correspond to an increase of the respective trait if the variable increases.

Value

coefficients

Matrix containing all parameters for the GPCMlasso model, one row per tuning parameter lambda. Due to the penalty the parameters are scaled and, therefore, are comparable with respect to their size.
logLik

Vector of log-likelihoods, one value per tuning parameter lambda.
call

The function call of GPCMlasso
cv_error

Vector of cv_errors, one per tuning parameter. Only relevant if cv = TRUE.
model

Basic IRT model chosen by user.
data

Data from call.
control

Control list.
DSF

DSF from call.
formula

Formula from call.
item.names

Item names.
Y

Matrix containing item responses.
design_list

List containing several helpful objects for internal use.
AIC

Vector of AIC values, one per tuning parameter.
BIC

Vector of BIC values, one per tuning parameter.
cAIC

Vector of corrected AIC values, one per tuning parameter.
df

Vector of degrees of freedom, one per tuning parameter.
coef.rescal

Matrix containing all rescaled parameters for the GPCMlasso model, one row per tuning parameter lambda. In contrast to coefficients, all parameters are rescaled back to their original scales.

Author(s)

Gunther Schauberger
[email protected]

References

Schauberger, Gunther and Mair, Patrick (2019): A Regularization Approach for the Detection of Differential Item Functioning in Generalized Partial Credit Models, Behavior Research Methods, https://link.springer.com/article/10.3758/s13428-019-01224-2

See Also

GPCMlasso-package, ctrl_GPCMlasso, print.GPCMlasso, plot.GPCMlasso, predict.GPCMlasso, trait.posterior

Examples

data(tenseness_small)

## formula for simple model without covariates
form.0 <- as.formula(paste("cbind(",paste(colnames(tenseness_small)[1:5],collapse=","),")~0"))

######
## fit simple RSM where loglikelihood and score function are evaluated parallel on 2 cores
rsm.0 <- GPCMlasso(form.0, tenseness_small, model = "RSM", 
control= ctrl_GPCMlasso(cores=2))
rsm.0

## Not run: 
## formula for model with covariates (and DIF detection)
form <- as.formula(paste("cbind(",paste(colnames(tenseness_small)[1:5],collapse=","),")~."))

######
## fit GPCM model with 10 different tuning parameters
gpcm <- GPCMlasso(form, tenseness_small, model = "GPCM", 
                  control = ctrl_GPCMlasso(l.lambda = 10))
gpcm
plot(gpcm)
pred.gpcm <- predict(gpcm)
trait.gpcm <- trait.posterior(gpcm)

######
## fit RSM, detect differential step functioning (DSF)
rsm.DSF <- GPCMlasso(form, tenseness_small, model = "RSM", DSF = TRUE, 
                     control = ctrl_GPCMlasso(l.lambda = 10))
rsm.DSF
plot(rsm.DSF)

## create binary data set
tenseness_small_binary <- tenseness_small
tenseness_small_binary[,1:5][tenseness_small[,1:5]>1] <- 2

######
## fit and cross-validate Rasch model
set.seed(1860)
rm.cv <- GPCMlasso(form, tenseness_small_binary, model = "RM", cv = TRUE, 
                   control = ctrl_GPCMlasso(l.lambda = 10))
rm.cv
plot(rm.cv)

## End(Not run)

Plot function for GPCMlasso

Description

Plot function for a GPCMlasso object. Plots show coefficient paths of DIF (or DSF) parameters along (a transformation of) the tuning parameter lambda. One plot per item is created, every single parameter corresponding to this item is depicted by a single path. The optimal model is highlighted with a red dashed line.

Usage

## S3 method for class 'GPCMlasso'
plot(x, select = c("BIC", "AIC", "cAIC", "cv"),
log.lambda = TRUE, items_per_page = 1, items = "all", 
columns = NULL, ask_new = TRUE, lambda.lines = TRUE,
equal_range = TRUE, ...)

Arguments

x

GPCMlasso object
select

Specifies which criterion to use for the optimal model, we recommend the default value "BIC". If cross-validation was performed, automatically the optimal model according to cross-validation is used. The chosen optimal model is highlighted with a red dashed line.
log.lambda

A logical value indicating whether lambda or a log-transformation of lambda should be used as x-axis in the plots.
items_per_page

By default, each plot/item is put on a separate page. For example, items_per_page=4 would put four plots/items on one page.
items

By default, all items are plotted. If items=c(1,3), only the first and the third item are plotted.
columns

Specifies the number of columns to use when several plots are on one page. Only relevant if items_per_page>1.
ask_new

If TRUE, the user is asked to confirm before the next item is plotted.
lambda.lines

A logical value indicating whether a thin gray line plotted for each value from the vector of tuning parameters from object
equal_range

A logical value indicating whether for each plot equal limits on the y-axis shall be used.
...

Further plot arguments.

Author(s)

Gunther Schauberger
[email protected]

References

Schauberger, Gunther and Mair, Patrick (2019): A Regularization Approach for the Detection of Differential Item Functioning in Generalized Partial Credit Models, Behavior Research Methods, https://link.springer.com/article/10.3758/s13428-019-01224-2

See Also

GPCMlasso

Examples

data(tenseness_small)

## formula for simple model without covariates
form.0 <- as.formula(paste("cbind(",paste(colnames(tenseness_small)[1:5],collapse=","),")~0"))

######
## fit simple RSM where loglikelihood and score function are evaluated parallel on 2 cores
rsm.0 <- GPCMlasso(form.0, tenseness_small, model = "RSM", 
control= ctrl_GPCMlasso(cores=2))
rsm.0

## Not run: 
## formula for model with covariates (and DIF detection)
form <- as.formula(paste("cbind(",paste(colnames(tenseness_small)[1:5],collapse=","),")~."))

######
## fit GPCM model with 10 different tuning parameters
gpcm <- GPCMlasso(form, tenseness_small, model = "GPCM", 
                  control = ctrl_GPCMlasso(l.lambda = 10))
gpcm
plot(gpcm)
pred.gpcm <- predict(gpcm)
trait.gpcm <- trait.posterior(gpcm)

######
## fit RSM, detect differential step functioning (DSF)
rsm.DSF <- GPCMlasso(form, tenseness_small, model = "RSM", DSF = TRUE, 
                     control = ctrl_GPCMlasso(l.lambda = 10))
rsm.DSF
plot(rsm.DSF)

## create binary data set
tenseness_small_binary <- tenseness_small
tenseness_small_binary[,1:5][tenseness_small[,1:5]>1] <- 2

######
## fit and cross-validate Rasch model
set.seed(1860)
rm.cv <- GPCMlasso(form, tenseness_small_binary, model = "RM", cv = TRUE, 
                   control = ctrl_GPCMlasso(l.lambda = 10))
rm.cv
plot(rm.cv)

## End(Not run)

Predict function for GPCMlasso

Description

Predict function for a GPCMlasso object. Predictions can be linear predictors or probabilities separately for each person and each item.

Usage

## S3 method for class 'GPCMlasso'
predict(
  object,
  coefs = NULL,
  newdata = NULL,
  type = c("link", "response"),
  ...
)

Arguments

object

GPCMlasso object
coefs

Optional vector of coefficients, can be filled with a specific row from object$coefficients. If not specified, coefs are specififed to be the BIC-optimal coefficients or, if cross-validation was performed, the optimal coefficients according to cross-validation.
newdata

List possibly containing slots Y, X, Z1 and Z2 to use new data for prediction.
type

Type "link" gives vectors of linear predictors for separate categories (of length $k_i-1$) and type "response" gives the respective probabilities (of length $k_i$).
...

Further predict arguments.

Details

Results are lists of vectors with length equal to the number of response categories $k_i$ in case of probabilities (type="response") or $k_i-1$ in case of linear predictors (type="link").

Author(s)

Gunther Schauberger
[email protected]

See Also

GPCMlasso

Examples

data(tenseness_small)

## formula for simple model without covariates
form.0 <- as.formula(paste("cbind(",paste(colnames(tenseness_small)[1:5],collapse=","),")~0"))

######
## fit simple RSM where loglikelihood and score function are evaluated parallel on 2 cores
rsm.0 <- GPCMlasso(form.0, tenseness_small, model = "RSM", 
control= ctrl_GPCMlasso(cores=2))
rsm.0

## Not run: 
## formula for model with covariates (and DIF detection)
form <- as.formula(paste("cbind(",paste(colnames(tenseness_small)[1:5],collapse=","),")~."))

######
## fit GPCM model with 10 different tuning parameters
gpcm <- GPCMlasso(form, tenseness_small, model = "GPCM", 
                  control = ctrl_GPCMlasso(l.lambda = 10))
gpcm
plot(gpcm)
pred.gpcm <- predict(gpcm)
trait.gpcm <- trait.posterior(gpcm)

######
## fit RSM, detect differential step functioning (DSF)
rsm.DSF <- GPCMlasso(form, tenseness_small, model = "RSM", DSF = TRUE, 
                     control = ctrl_GPCMlasso(l.lambda = 10))
rsm.DSF
plot(rsm.DSF)

## create binary data set
tenseness_small_binary <- tenseness_small
tenseness_small_binary[,1:5][tenseness_small[,1:5]>1] <- 2

######
## fit and cross-validate Rasch model
set.seed(1860)
rm.cv <- GPCMlasso(form, tenseness_small_binary, model = "RM", cv = TRUE, 
                   control = ctrl_GPCMlasso(l.lambda = 10))
rm.cv
plot(rm.cv)

## End(Not run)

Print function for GPCMlasso

Description

Print function for a GPCMlasso object. Prints parameters estimates for all model components for the optimal model chosen by a specific criterion (by default BIC).

Usage

## S3 method for class 'GPCMlasso'
print(x, select = c("BIC", "AIC", "cAIC", "cv"), ...)

Arguments

x

GPCMlasso object
select

Specifies which criterion to use for the optimal model, we recommend the default value "BIC". If cross-validation was performed, automatically the optimal model according to cross-validation is used. Only the parameter estimates from the chosen optimal model are printed.
...

Further print arguments.

Author(s)

Gunther Schauberger
[email protected]

References

Schauberger, Gunther and Mair, Patrick (2019): A Regularization Approach for the Detection of Differential Item Functioning in Generalized Partial Credit Models, Behavior Research Methods, https://link.springer.com/article/10.3758/s13428-019-01224-2

See Also

GPCMlasso

Examples

data(tenseness_small)

## formula for simple model without covariates
form.0 <- as.formula(paste("cbind(",paste(colnames(tenseness_small)[1:5],collapse=","),")~0"))

######
## fit simple RSM where loglikelihood and score function are evaluated parallel on 2 cores
rsm.0 <- GPCMlasso(form.0, tenseness_small, model = "RSM", 
control= ctrl_GPCMlasso(cores=2))
rsm.0

## Not run: 
## formula for model with covariates (and DIF detection)
form <- as.formula(paste("cbind(",paste(colnames(tenseness_small)[1:5],collapse=","),")~."))

######
## fit GPCM model with 10 different tuning parameters
gpcm <- GPCMlasso(form, tenseness_small, model = "GPCM", 
                  control = ctrl_GPCMlasso(l.lambda = 10))
gpcm
plot(gpcm)
pred.gpcm <- predict(gpcm)
trait.gpcm <- trait.posterior(gpcm)

######
## fit RSM, detect differential step functioning (DSF)
rsm.DSF <- GPCMlasso(form, tenseness_small, model = "RSM", DSF = TRUE, 
                     control = ctrl_GPCMlasso(l.lambda = 10))
rsm.DSF
plot(rsm.DSF)

## create binary data set
tenseness_small_binary <- tenseness_small
tenseness_small_binary[,1:5][tenseness_small[,1:5]>1] <- 2

######
## fit and cross-validate Rasch model
set.seed(1860)
rm.cv <- GPCMlasso(form, tenseness_small_binary, model = "RM", cv = TRUE, 
                   control = ctrl_GPCMlasso(l.lambda = 10))
rm.cv
plot(rm.cv)

## End(Not run)

Tenseness data from the Freiburg Complaint Checklist

Description

Data from the Freiburg Complaint Checklist. The data contain all 8 items corresponding to the scale Tenseness for 2042 participants of the standardization sample of the Freiburg Complaint Checklist.

Format

A data frame containing data from the Freiburg Complaint Checklist with 1847 observations. All items refer to the scale Tenseness and are measured on a 5-point Likert scale where low numbers correspond to low frequencies or low intensitites of the respective complaint and vice versa.

Clammy_hands

Do you have clammy hands?

Sweat_attacks

Do you have sudden attacks of sweating?

Clumsiness

Do you notice that you behave clumsy?

Wavering_hands

Are your hands wavering frequently, e.g. when lightning a cigarette or when holding a cup?

Restless_hands

Do you notice that your hands are restless?

Restless_feet

Do you notice that your feet are restless?

Twitching_eyes

Do you notice unvoluntary twitching of your eyes?

Twitching_mouth

Do you notice unvoluntary twitching of your mouth?

Gender

Gender of the person

Household

Does the person live alone in a household or together with somebody?

Income

Income, categorized to levels from 1 (low income) to 11(high income). For simplicity, due to the high number of categories income can be treated as a metric variable.

WestEast

Is the person from East Germany (former GDR)?

Abitur

Does the person have Abitur (A-levels)?

Age

Age of the person

Source

ZPID (2013). PsychData of the Leibniz Institute for Psychology Information ZPID. Trier: Center for Research Data in Psychology.

Fahrenberg, J. (2010). Freiburg Complaint Checklist [Freiburger Beschwerdenliste (FBL)]. Goettingen, Hogrefe.

Examples

data(tenseness)

Subset of tenseness data from the Freiburg Complaint Checklist

Description

Data from the Freiburg Complaint Checklist. The data contain 5 items (out of 8) corresponding to the scale Tenseness for a subset of 200 participants of the standardization sample of the Freiburg Complaint Checklist.

Format

A data frame containing data from the Freiburg Complaint Checklist a subset of 200 observations. The complete data set with 1847 observations can be found in tenseness. All items refer to the scale Tenseness and are measured on a 5-point Likert scale where low numbers correspond to low frequencies or low intensitites of the respective complaint and vice versa.

Clammy_hands

Do you have clammy hands?

Sweat_attacks

Do you have sudden attacks of sweating?

Clumsiness

Do you notice that you behave clumsy?

Wavering_hands

Are your hands wavering frequently, e.g. when lightning a cigarette or when holding a cup?

Restless_hands

Do you notice that your hands are restless?

Gender

Gender of the person

Age

Age of the person

Source

ZPID (2013). PsychData of the Leibniz Institute for Psychology Information ZPID. Trier: Center for Research Data in Psychology.

Fahrenberg, J. (2010). Freiburg Complaint Checklist [Freiburger Beschwerdenliste (FBL)]. Goettingen, Hogrefe.

See Also

GPCMlasso, ctrl_GPCMlasso, trait.posterior

Examples

data(tenseness_small)

## formula for simple model without covariates
form.0 <- as.formula(paste("cbind(",paste(colnames(tenseness_small)[1:5],collapse=","),")~0"))

######
## fit simple RSM where loglikelihood and score function are evaluated parallel on 2 cores
rsm.0 <- GPCMlasso(form.0, tenseness_small, model = "RSM", 
control= ctrl_GPCMlasso(cores=2))
rsm.0

## Not run: 
## formula for model with covariates (and DIF detection)
form <- as.formula(paste("cbind(",paste(colnames(tenseness_small)[1:5],collapse=","),")~."))

######
## fit GPCM model with 10 different tuning parameters
gpcm <- GPCMlasso(form, tenseness_small, model = "GPCM", 
                  control = ctrl_GPCMlasso(l.lambda = 10))
gpcm
plot(gpcm)
pred.gpcm <- predict(gpcm)
trait.gpcm <- trait.posterior(gpcm)

######
## fit RSM, detect differential step functioning (DSF)
rsm.DSF <- GPCMlasso(form, tenseness_small, model = "RSM", DSF = TRUE, 
                     control = ctrl_GPCMlasso(l.lambda = 10))
rsm.DSF
plot(rsm.DSF)

## create binary data set
tenseness_small_binary <- tenseness_small
tenseness_small_binary[,1:5][tenseness_small[,1:5]>1] <- 2

######
## fit and cross-validate Rasch model
set.seed(1860)
rm.cv <- GPCMlasso(form, tenseness_small_binary, model = "RM", cv = TRUE, 
                   control = ctrl_GPCMlasso(l.lambda = 10))
rm.cv
plot(rm.cv)

## End(Not run)

Calculate Posterior Estimates for Trait Parameters

Description

Calculates posterior estimates for trait/person parameters using the assumption of Gaussian distributed parameters.

Usage

trait.posterior(model, coefs = NULL, cores = 25, tol = 1e-04)

Arguments

model

Object of class GPCMlasso.
coefs

Vector of coefficients to be used for prediction. If coefs = NULL, the parameters from the BIC-optimal model will be used. If cross-validation was performed, automatically the parameters from the optimal model according to cross-validation are used.
cores

Number of cores to be used in parallelized computation.
tol

The maximum tolerance for numerical integration, for more details see pcubature.

Value

Vector containing all estimates of trait/person parameters.

Author(s)

Gunther Schauberger
[email protected]

References

Schauberger, Gunther and Mair, Patrick (2019): A Regularization Approach for the Detection of Differential Item Functioning in Generalized Partial Credit Models, Behavior Research Methods, https://link.springer.com/article/10.3758/s13428-019-01224-2

See Also

GPCMlasso GPCMlasso-package

Examples

data(tenseness_small)

## formula for simple model without covariates
form.0 <- as.formula(paste("cbind(",paste(colnames(tenseness_small)[1:5],collapse=","),")~0"))

######
## fit simple RSM where loglikelihood and score function are evaluated parallel on 2 cores
rsm.0 <- GPCMlasso(form.0, tenseness_small, model = "RSM", 
control= ctrl_GPCMlasso(cores=2))
rsm.0

## Not run: 
## formula for model with covariates (and DIF detection)
form <- as.formula(paste("cbind(",paste(colnames(tenseness_small)[1:5],collapse=","),")~."))

######
## fit GPCM model with 10 different tuning parameters
gpcm <- GPCMlasso(form, tenseness_small, model = "GPCM", 
                  control = ctrl_GPCMlasso(l.lambda = 10))
gpcm
plot(gpcm)
pred.gpcm <- predict(gpcm)
trait.gpcm <- trait.posterior(gpcm)

######
## fit RSM, detect differential step functioning (DSF)
rsm.DSF <- GPCMlasso(form, tenseness_small, model = "RSM", DSF = TRUE, 
                     control = ctrl_GPCMlasso(l.lambda = 10))
rsm.DSF
plot(rsm.DSF)

## create binary data set
tenseness_small_binary <- tenseness_small
tenseness_small_binary[,1:5][tenseness_small[,1:5]>1] <- 2

######
## fit and cross-validate Rasch model
set.seed(1860)
rm.cv <- GPCMlasso(form, tenseness_small_binary, model = "RM", cv = TRUE, 
                   control = ctrl_GPCMlasso(l.lambda = 10))
rm.cv
plot(rm.cv)

## End(Not run)