Package 'UPCM'

Uncertainty in Partial Credit Models

Description

Performs UPCM, a method to model uncertainty in (Generalized) Partial Credit Models

Author(s)

Gunther Schauberger
[email protected]
https://www.sg.tum.de/epidemiologie/team/schauberger/

References

Tutz, Gerhard and Schauberger, Gunther (2020): Uncertainty in Latent Trait Models, Applied Psychological Measurement, https://journals.sagepub.com/doi/abs/10.1177/0146621620920932?journalCode=apma

See Also

UPCM

Examples

data(tenseness)

Y <- data.matrix(tenseness[,1:4])
X <- model.matrix(~ Gender + Age, data = tenseness)[,-1]

m_upcm <- UPCM(Y = Y, X = X, cores = 2, GPCM = FALSE)
m_upcm
plot(m_upcm)

---

Plot function for UPCM

Description

Plot function for a UPCM or a UGPCM object. Plots show coefficient estimates together with confidence intervals displayed as star plots.

Usage

## S3 method for class 'UPCM'
plot(x, sig = 0.05, KIfactor = 0.9, xlim, ylim, ...)

Arguments

x	UPCM object
sig	Significance level for confidence intervals, default is sig = 0.05.
KIfactor	Parameter to regulate the shape of the resulting star.
xlim	See xlim in plot.default.
ylim	See ylim in plot.default.
...	Further plot arguments.

Value

No return value, called for side effects

Author(s)

Gunther Schauberger
[email protected]
https://www.sg.tum.de/epidemiologie/team/schauberger/

References

Tutz, Gerhard and Schauberger, Gunther (2020): Uncertainty in Latent Trait Models, Applied Psychological Measurement, https://journals.sagepub.com/doi/abs/10.1177/0146621620920932?journalCode=apma

See Also

UPCM

Examples

data(tenseness)

Y <- data.matrix(tenseness[,1:4])
X <- model.matrix(~ Gender + Age, data = tenseness)[,-1]

m_upcm <- UPCM(Y = Y, X = X, cores = 2, GPCM = FALSE)
m_upcm
plot(m_upcm)

---

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)

---

Uncertainty in (Generalized) Partial Credit Models

Description

Performs UPCM, a method to model uncertainty in (Generalized) Partial Credit Models

Usage

UPCM(
  Y,
  X = NULL,
  GPCM = TRUE,
  Q = 10,
  cores = 2,
  lambda = 0.01,
  se = TRUE,
  method = c("nlminb", "L-BFGS-B"),
  ctrl.nlminb = list(eval.max = 200, iter.max = 150, abs.tol = 1e-08, rel.tol = 1e-08,
    trace = 0, step.min = 0.1, x.tol = 1e-08, xf.tol = 1e-08)
)

Arguments

Y	Matrix containing the ordinal item response data (as ordered factors), one row per observation, one column per item.
X	Matrix containing explanatory variables which are used both for trait parameters and uncertainty parameters, one row per observation, one column per variable.
GPCM	Specifies the baseline model. GPCM = TRUE results in a UGPCM while GPCM = FALSE results in a UPCM.
Q	Number of nodes to be used (per dimension) in two-dimensional Gauss-Hermite-Quadrature.
cores	Number of cores to be used in parallelized computation
lambda	Tuning parameter for ridge penalty on all coefficients except sigma/slope parameters. Should be small, only used to stabilize results.
se	Should standard errors be computed? Standard errors are necessary for plot.UPCM. Computation is time-consuming because numerical optimization methods are used.
method	Specifies optimization algorithm used , either nlminb or L-BFGS-B (optim).
ctrl.nlminb	List of control arguments for optimization procedure nlminb.

Value

delta	Matrix containing all item parameters for the UPCM pr UGPCM model, one row per item, one column per category.
Sigma	2*2 covariance matrix for both random effects, namely the trait parameters theta and the uncertainty parameters alpha.
xi	Estimates for covariate effects on trait parameters.
alpha	Estimates for covariate effects on uncertainty parameters.
slopes	Estimates item slope parameters (only for GPCM = TRUE).
se.delta
se.xi	Estimates of standard errors for covariate effects on trait parameters.
se.alpha	Estimates of standard errors for covariate effects on uncertainty parameters.
se.sigma	Estimates of standard errors for covariance parameters. Attention: First and third parameter are estimates of se for both variances, the variance of theta and the variance of alpha. Second parameter is the estimate for correlation coefficient between theta and alpha, NOT of the corresponding covariance.
se.slopes	Estimates of standard errors of item slope parameters (only for GPCM = TRUE).
delta.GPCM	Estimates of item parameters theta in the PCM or GPCM model.
sigma.GPCM	Estimate of variance of trait parameters theta in the PCM or GPCM model.
slopes.GPCM	Estimates of slope parameters in the GPCM (only for GPCM = TRUE).
Y	Matrix containing the ordinal item response data, one row per obeservation, one column per item.
loglik	Marginal log-likelihood
coefs	Complete vector of all estimated parameters (for internal use).
se.vec	Complete vector of all estimated standard errors (for internal use).

Author(s)

Gunther Schauberger
[email protected]
https://www.sg.tum.de/epidemiologie/team/schauberger/

References

Tutz, Gerhard and Schauberger, Gunther (2020): Uncertainty in Latent Trait Models, Applied Psychological Measurement, https://journals.sagepub.com/doi/abs/10.1177/0146621620920932?journalCode=apma

See Also

plot.UPCM UPCM-package

Examples

data(tenseness)

Y <- data.matrix(tenseness[,1:4])
X <- model.matrix(~ Gender + Age, data = tenseness)[,-1]

m_upcm <- UPCM(Y = Y, X = X, cores = 2, GPCM = FALSE)
m_upcm
plot(m_upcm)

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