dstudy: Conduct a Univariate or Multivariate Decision (D) Study

In gtheory: Apply Generalizability Theory with R

Description

dstudy calculates generalizability and dependability coefficients from variance components. It also provides standards errors of measurement and estimation.

Usage

dstudy(x, ...)

## S3 method for class 'components'
dstudy(x, colname.objects, ...)

## S3 method for class 'gstudy'
dstudy(x, colname.objects, data = NULL,
  colname.scores = NULL, colname.strata = NULL, weights = NULL, ...)

## S3 method for class 'dstudy'
dstudy(x, colname.objects, weights = NULL, ...)

Arguments

x	an object of class gstudy, dstudy, or components
...	ignored
colname.objects	a string naming the source of variation for the object of measurement
data	an optional data frame in long format with a column for item scores and columns for sources of variance
colname.scores	an optional string that specifies the name of the column containing scores
colname.strata	an optional string that specifies the name of the column containing strata (if conducting a multivariate G study)
weights	an optional numeric vector containg one weight per stratum for composite scoring (if conducting a multivariate G study); defaults to equal weights

Details

A typical decision (D) study starts with updating variance components from the generalizaiblity (G) with the number of facet levels from the D-study data. D-study data may or may not be the same data collected for the G study. dstudy will update the variance components when you supply decision data and specify the name of the column identifying objects of measurement. If you do not supply data or specify the score column, then dstudy will use the G-study variance components (i.e., with all n = 1) and return what is commonly known as intraclass correlation (i.e., the generalizability and dependability of a single observation). If your D-study data are unbalanced (i.e., if the number of facet levels vary from one object of measurement to another), then dstudy will return an overall components object based on the median number of levels of the main facet effects and will store object-specific variance components as attributes (i.e., to facilitate scoring).

Value

an object of class "dstudy" that lists the variance components and corresponding measures of signal and noise (i.e., generalizability and dependability coefficients, universe score variance, relative and absolute error variance, and relative and absolute standard errors of measurement and estimation).

Methods (by class)

• components: D study of a components object

• gstudy: D study of gstudy object

• dstudy: D study of a dstudy object

References

Brennan, R. L. (2001). Generalizability theory. New York: Springer.

Rajaratnam, N., Cronbach, L. J., & Gleser, G. C. (1965). Generalizability of stratified-parallel tests. Psychometrika, 30(1), 39-56.

Examples

#A univariate D study.
#Compare to results on page 116 of Brennan (2001).
data(Brennan.3.2)
formula.Brennan.3.2 <- "Score ~ (1 | Person) + (1 | Task) + (1 | Rater:Task) + 
  (1 | Person:Task)"
gstudy.out <- gstudy(data = Brennan.3.2, formula = formula.Brennan.3.2)
dstudy(gstudy.out, colname.objects = "Person", data = Brennan.3.2, colname.scores = "Score")

#A multivariate D study.
#Compare to results on pages 270-272 of Brennan (2001).
data(Rajaratnam.2)
formula.Rajaratnam.2 <- "Score ~ (1 | Person) + (1 | Item)"
gstudy.out <- gstudy(data = Rajaratnam.2, formula = formula.Rajaratnam.2, 
  colname.strata = "Subtest", colname.objects = "Person")
dstudy(gstudy.out, colname.objects = "Person", data = Rajaratnam.2, colname.scores = "Score", 
  colname.strata = "Subtest", weights = c(0.25, 0.5, 0.25))

Example output

Loading required package: lme4
Loading required package: Matrix
$components
       source        var percent  n
1 Person:Task 0.18652264    18.3  3
2  Rater:Task 0.05396091     5.3 12
3      Person 0.47314818    46.4  1
4        Task 0.10838474    10.6  3
5    Residual 0.19835391    19.4 12

$var.universe
[1] 0.4731482

$generalizability
[1] 0.5514389

$var.error.rel
[1] 0.3848765

$sem.rel
[1] 0.6203842

$see.rel
[1] 0.4606907

$dependability
[1] 0.4637024

$var.error.abs
[1] 0.5472222

$sem.abs
[1] 0.7397447

$see.abs
[1] 0.5037343

attr(,"class")
[1] "dstudy" "list"  
$within
$within$`1`
$within$`1`$components
    source       var percent n
1   Person 1.5714285    75.9 1
2     Item 0.2142857    10.3 2
3 Residual 0.2857143    13.8 2


$within$`2`
$within$`2`$components
    source        var percent n
1   Person 2.78571418    89.8 1
2     Item 0.04985119     1.6 4
3 Residual 0.26785715     8.6 4


$within$`3`
$within$`3`$components
    source       var percent n
1   Person 1.8571429    80.9 1
2     Item 0.2232143     9.7 2
3 Residual 0.2142857     9.3 2



$between
$between$var.obs
         1         2         3
1 1.857143 1.4821429 0.5000000
2 1.482143 3.0535714 0.9464286
3 0.500000 0.9464286 2.0714286
attr(,"colname.objects")
[1] "Person"

$between$var.universe
         1         2         3
1 1.571428 1.4821429 0.5000000
2 1.482143 2.7857142 0.9464286
3 0.500000 0.9464286 1.8571429
attr(,"colname.objects")
[1] "Person"

$between$generalizability
          1         2         3
1 0.8461538 0.0000000 0.0000000
2 0.0000000 0.9122807 0.0000000
3 0.0000000 0.0000000 0.8965517

$between$var.error.rel
          1         2         3
1 0.2857143 0.0000000 0.0000000
2 0.0000000 0.2678571 0.0000000
3 0.0000000 0.0000000 0.2142857

$between$sem.rel
          1         2       3
1 0.5345225 0.0000000 0.00000
2 0.0000000 0.5175492 0.00000
3 0.0000000 0.0000000 0.46291

$between$see.rel
          1         2         3
1 0.4916892 0.0000000 0.0000000
2 0.0000000 0.4943287 0.0000000
3 0.0000000 0.0000000 0.4383129

$between$dependability
          1         2         3
1 0.7586207 0.0000000 0.0000000
2 0.0000000 0.8976265 0.0000000
3 0.0000000 0.0000000 0.8093385

$between$var.error.abs
    1         2      3
1 0.5 0.0000000 0.0000
2 0.0 0.3177083 0.0000
3 0.0 0.0000000 0.4375

$between$sem.abs
          1         2         3
1 0.7071068 0.0000000 0.0000000
2 0.0000000 0.5636562 0.0000000
3 0.0000000 0.0000000 0.6614378

$between$see.abs
          1         2         3
1 0.6158818 0.0000000 0.0000000
2 0.0000000 0.5340257 0.0000000
3 0.0000000 0.0000000 0.5950509


$composite
$composite$var.universe
         [,1]
[1,] 1.580357

$composite$generalizability
          [,1]
[1,] 0.9414894

$composite$var.error.rel
[1] 0.09821429

$composite$sem.rel
[1] 0.3133916

$composite$see.rel
         [,1]
[1,] 0.304085

$composite$dependability
          [,1]
[1,] 0.9196796

$composite$var.error.abs
[1] 0.1380208

$composite$sem.abs
[1] 0.3715116

$composite$see.abs
          [,1]
[1,] 0.3562793


attr(,"class")
[1] "dstudy" "list"  

gtheory documentation built on May 2, 2019, 6:59 a.m.