pairSE {pairwise} | R Documentation |
Item Parameter Calculation with Standard Errors
Description
Calculation of the item parameters for dichotomous (difficulty) or polytomous items (thurstonian thresholds) and their standard errors (SE) respectively. All parameters are calculated using a generalization (see Heine & Tarnai, 2015) of the pairwise comparison algorithm (Choppin, 1968, 1985). Missing values up to an high amount in data matrix are allowed, as long as items are proper linked together.
Usage
pairSE(
daten,
m = NULL,
w = NULL,
nsample = 30,
size = 0.5,
seed = "no",
pot = TRUE,
zerocor = TRUE,
verbose = TRUE,
likelihood = NULL,
pot2 = 2,
delta = TRUE,
conv = 1e-04,
maxiter = 3000,
progress = TRUE,
init = NULL,
zerosum = TRUE,
...
)
Arguments
daten |
a data.frame or matrix with optionaly named colums (names of items), potentially with missing values, comprising polytomous or dichotomous (or mixted category numbers) responses of |
m |
an integer (will be recycled to a vector of length k) or a vector giving the number of response categories for all items - by default |
w |
an optional vector of case weights. |
nsample |
numeric specifying the number of subsamples sampled from data, which is the number of replications of the parameter calculation.
WARNING! specifying high values for |
size |
numeric with valid range between 0 and 1 (but not exactly 0 or 1) specifying the size of the subsample of |
seed |
numeric used for |
pot |
either a logical or an integer >= 2 defining the power to compute of the pairwise comparison matrix. If TRUE (default) a power of three of the pairwise comparison matrix is used for further calculations. If FALSE no powers are computed. |
zerocor |
either a logical or an numeric value between >0 and <=1. If (in case of a logical) zerocor is set to TRUE (default) unobserved combinations (1-0, 0-1) in the data for each pair of items are given a frequency of one conf. proposal by Alexandrowicz (2011, p.373). As an alternative option a numeric value between >0 and <=1 can be assigned to unobserved combinations (1-0, 0-1) in the data for each pair of items (conf. to personal communication with A. Robitzsch; 29-03-2021). |
verbose |
logical, if |
likelihood |
see |
pot2 |
see |
delta |
see |
conv |
see |
maxiter |
see |
progress |
see |
init |
see |
zerosum |
see |
... |
additional parameters passed through. |
Details
Parameter calculation is based on the construction of a paired comparison matrix Mnicjc with entries ficjc, representing the number of respondents who answered to item i in category c and to item j in category c-1 widening Choppin's (1968, 1985) conditional pairwise algorithm to polytomous item response formats. This algorithm is simply realized by matrix multiplication.
Estimation of standard errors is done by repeated calculation of item parameters for sub samples of the given data.
To avoid numerical problems with off diagonal zeros when constructing the pairwise comparison matrix Mnicjc, powers of the Mnicjc matrix, can be used (Choppin, 1968, 1985). Using powers k of Mnicjc, argument pot=TRUE
(default), replaces the results of the direct comparisons between i and j with the sum of the indirect comparisons of i and j through an intermediate k.
In general, it is recommended to use the argument with default value pot=TRUE
.
Value
A (list) object of class c("pairSE","list")
containing the item category thresholds, difficulties sigma and their standard errors.
A note on standard errors
Estimation of standard errors is done by repeated calculation of item parameters for subsamples of the given data. This procedure is mainly controlled by the arguments nsample
and size
(see arguments). With regard to calculation time, the argument nsample
may be the 'time killer'. On the other hand, things (estimation of standard errors) will not necessarily get better when choosing large values for nsample
. For example choosing nsample=400
will only result in minimal change for standard error estimation in comparison to (nsample=30
) which is the default setting (see examples).
References
Choppin, B. (1968). Item Bank using Sample-free Calibration. Nature, 219(5156), 870-872.
Choppin, B. (1985). A fully conditional estimation procedure for Rasch model parameters. Evaluation in Education, 9(1), 29-42.
Heine, J. H. & Tarnai, Ch. (2015). Pairwise Rasch model item parameter recovery under sparse data conditions. Psychological Test and Assessment Modeling, 57(1), 3–36.
Alexandrowicz, R. W. (2011). 'GANZ RASCH': A Free Software for Categorical Data Analysis. Social Science Computer Review, 30(3), 369-379.
Wright, B. D., & Masters, G. N. (1982). Rating Scale Analysis. Chicago: MESA Press.
Examples
data(bfiN) # loading example data set
# calculating item parameters and their SE for 5 neuroticism items with 6 answer categories (0-5).
neuro_itempar<-pairSE(daten = bfiN, m = 6)
summary(neuro_itempar) # summary for result
# plotting item thresholds with with their CI = 95%
plot(neuro_itempar)
plot(neuro_itempar,sortdif=TRUE)
###### example from details section 'Some Notes on Standard Errors' ########
neuro_itempar_400<-pairSE(daten = bfiN, m = 6,nsample=400)
plot(neuro_itempar)
plot(neuro_itempar_400)