sirt (version 1.5-0)

conf.detect: Confirmatory DETECT and polyDETECT Analysis

Description

This function computes the DETECT statistics for dichotomous item responses and the polyDETECT statistic for polytomous item responses under a confirmatory specification of item clusters (Stout, Habing, Douglas & Kim, 1996; Zhang & Stout, 1999a, 1999b; Zhang, 2007). Item responses in a multi-matrix design are allowed (Zhang, 2013).

Usage

conf.detect(data, score, itemcluster, bwscale = 1.1, progress = TRUE, 
        thetagrid = seq(-3, 3, len = 200))

Arguments

data

An $N \times I$ data frame of dichotomous or polytomous responses. Missing responses are allowed.

score

An ability estimate, e.g. the WLE

itemcluster

Item cluster for each item. The order of entries must correspond to the columns in data.

bwscale

Bandwidth factor for calculation of conditional covariance (see ccov.np)

progress

Display progress?

thetagrid

A vector which contains theta values where conditional covariances are evaluated.

Value

• A list with following entries:
• detect
  Data frame with statistics DETECT, ASSI and RATIO
• ccovtable
  Individual contributions to conditional covariance
• ccov.matrix
  Evaluated conditional covariance

Details

The result of DETECT are the indices DETECT, ASSI and RATIO (see Zhang 2007 for details) calculated for the options unweighted and weighted. The option unweighted means that all conditional covariances of item pairs are equally weighted, weighted means that these covariances are weighted by the sample size of item pairs. In case of multi matrix item designs, both types of indices can differ. The classification scheme of these indices are as follows (Jang & Roussos, 2007; Zhang, 2007): ll{ Strong multidimensionality DETECT > 1.00 Moderate multidimensionality .40 < DETECT < 1.00 Weak multidimensionality .20 < DETECT < .40 Essential unidimensionality DETECT < .20 } lll{ Maximum value under simple structure ASSI=1 RATIO=1 Essential deviation from unidimensionality ASSI > .25 RATIO > .36 Essential unidimensionality ASSI < .25 RATIO < .36 }

References

Jang, E. E., & Roussos, L. (2007). An investigation into the dimensionality of TOEFL using conditional covariance-based nonparametric approach. Journal of Educational Measurement, 44, 1-21. Stout, W., Habing, B., Douglas, J., & Kim, H. R. (1996). Conditional covariance-based nonparametric multidimensionality assessment. Applied Psychological Measurement, 20, 331-354. Zhang, J., & Stout, W. (1999a). Conditional covariance structure of generalized compensatory multidimensional items. Psychometrika, 64, 129-152. Zhang, J., & Stout, W. (1999b). The theoretical DETECT index of dimensionality and its application to approximate simple structure. Psychometrika, 64, 213-249. Zhang, J. (2007). Conditional covariance theory and DETECT for polytomous items. Psychometrika, 72, 69-91. Zhang, J. (2013). A procedure for dimensionality analyses of response data from various test designs. Psychometrika, 78, 37-58.

See Also

For a download of the free DIM-Pack software (DIMTEST, DETECT) see http://psychometrictools.measuredprogress.org/home.

Examples

#############################################################################
# EXAMPLE 1: TIMSS mathematics data set (dichotomous data)
#############################################################################
data(data.timss)

# extract data
dat <- data.timss$data
dat <- dat[ , substring( colnames(dat),1,1) == "M" ]
# extract item informations
iteminfo <- data.timss$item
# estimate Rasch model
mod1 <- rasch.mml2( dat )
# estimate WLEs
wle1 <- wle.rasch( dat , b = mod1$item$b )$theta

# DETECT for content domains
detect1 <- conf.detect( data = dat , score = wle1 ,
                    itemcluster = iteminfo$Content.Domain )
  ##          unweighted weighted
  ##   DETECT      0.316    0.316
  ##   ASSI        0.273    0.273
  ##   RATIO       0.355    0.355

# DETECT cognitive domains
detect2 <- conf.detect( data = dat , score = wle1 ,
                    itemcluster = iteminfo$Cognitive.Domain )
  ##          unweighted weighted
  ##   DETECT      0.251    0.251
  ##   ASSI        0.227    0.227
  ##   RATIO       0.282    0.282

# DETECT for item format 
detect3 <- conf.detect( data = dat , score = wle1 ,
                    itemcluster = iteminfo$Format )
  ##          unweighted weighted
  ##   DETECT      0.056    0.056
  ##   ASSI        0.060    0.060
  ##   RATIO       0.062    0.062

# DETECT for item blocks
detect4 <- conf.detect( data = dat , score = wle1 ,
                    itemcluster = iteminfo$Block )
  ##          unweighted weighted
  ##   DETECT      0.301    0.301
  ##   ASSI        0.193    0.193
  ##   RATIO       0.339    0.339

# Exploratory DETECT: Application of a cluster analysis employing the Ward method
detect5 <- expl.detect( data = dat , score = wle1  , 
                nclusters = 10 , N.est = nrow(dat)  )
# Plot cluster solution
pl <- plot( detect5$clusterfit , main = "Cluster solution" )
rect.hclust(detect5$clusterfit, k=4, border="red")

#############################################################################
# EXAMPLE 2: Big 5 data set (polytomous data)
#############################################################################

# attach Big5 Dataset
data(data.big5)

# select 6 items of each dimension
dat <- data.big5
dat <- dat[, 1:30]

# estimate person score by simply using a transformed sum score
score <- qnorm( ( rowMeans( dat )+.5 )  / ( 30 + 1 ) )

# extract item cluster (Big 5 dimensions)
itemcluster <- substring( colnames(dat) , 1 , 1 )

# DETECT Item cluster
detect1 <- conf.detect( data = dat , score = score , itemcluster = itemcluster )
  ##        unweighted weighted
  ## DETECT      1.256    1.256
  ## ASSI        0.384    0.384
  ## RATIO       0.597    0.597

# Exploratory DETECT
detect5 <- expl.detect( data = dat , score = score  , 
                     nclusters = 9 , N.est = nrow(dat)  )
  ## DETECT (unweighted)
  ## Optimal Cluster Size is  6  (Maximum of DETECT Index)
  ##   N.Cluster N.items N.est N.val      size.cluster DETECT.est ASSI.est RATIO.est
  ## 1         2      30   500     0              6-24      1.073    0.246     0.510
  ## 2         3      30   500     0           6-10-14      1.578    0.457     0.750
  ## 3         4      30   500     0         6-10-11-3      1.532    0.444     0.729
  ## 4         5      30   500     0        6-8-11-2-3      1.591    0.462     0.757
  ## 5         6      30   500     0       6-8-6-2-5-3      1.610    0.499     0.766
  ## 6         7      30   500     0     6-3-6-2-5-5-3      1.557    0.476     0.740
  ## 7         8      30   500     0   6-3-3-2-3-5-5-3      1.540    0.462     0.732
  ## 8         9      30   500     0 6-3-3-2-3-5-3-3-2      1.522    0.444     0.724

# Plot Cluster solution
pl <- plot( detect5$clusterfit , main = "Cluster solution" )
rect.hclust(detect5$clusterfit, k=6, border="red")