sirt (version 1.5-0)

prmse.subscores.scales: Proportional Reduction of Mean Squared Error (PRMSE) for Subscale Scores

Description

This function estimates the proportional reduction of mean squared error (PRMSE) according to Haberman (Haberman 2008; Haberman, Sinharay & Puhan, 2008).

Usage

prmse.subscores.scales(data, subscale)

Arguments

data

An $N \times I$ data frame of item responses

subscale

Vector of labels corresponding to subscales

Value

• Matrix with columns corresponding to subscales The symbol X denotes the subscale and Z the whole scale (see also in the Examples section for the structure of this matrix).

References

Haberman, S. J. (2008). When can subscores have value? Journal of Educational and Behavioral Statistics, 33, 204-229. Haberman, S., Sinharay, S., & Puhan, G. (2008). Reporting subscores for institutions. British Journal of Mathematical and Statistical Psychology, 62, 79-95.

Examples

#############################################################################
# EXAMPLE 1: PRMSE Reading data data.read
#############################################################################	

data( data.read )
p1 <- prmse.subscores.scales(data=data.read, 
         subscale = substring( colnames(data.read) , 1 ,1 ) )
print( p1 , digits= 3 )
  ##                 A       B       C
  ## N         328.000 328.000 328.000
  ## nX          4.000   4.000   4.000
  ## M.X         2.616   2.811   3.253
  ## Var.X       1.381   1.059   1.107
  ## SD.X        1.175   1.029   1.052
  ## alpha.X     0.545   0.381   0.640
  ## [...]
  ## nZ         12.000  12.000  12.000
  ## M.Z         8.680   8.680   8.680
  ## Var.Z       5.668   5.668   5.668
  ## SD.Z        2.381   2.381   2.381
  ## alpha.Z     0.677   0.677   0.677
  ## [...]
  ## cor.TX_Z    0.799   0.835   0.684
  ## rmse.X      0.585   0.500   0.505
  ## rmse.Z      0.522   0.350   0.614
  ## rmse.XZ     0.495   0.350   0.478
  ## prmse.X     0.545   0.381   0.640
  ## prmse.Z     0.638   0.697   0.468
  ## prmse.XZ    0.674   0.697   0.677
#-> Scales A and B do not have lower RMSEA,
#   but for scale C the RMSE is smaller than the RMSE of a
#   prediction based on a whole scale.