svdNorm {FMP}

Compute theta surrogates via normalized SVD scores

Description

Compute theta surrogates by calculating the normalized left singular vector of a (mean-centered) data matrix.

Usage

 svdNorm(data)

Arguments

data

N(subjects)-by-p(items) matrix of 0/1 item response data.

Value

the normalized left singular vector of the mean centered data matrix.

svdNorm will center the data automatically.

Author(s)

Niels Waller

Examples

NSubj <- 2000

## example item parameters for sample data: k=1 FMP 
b <- matrix(c(
    #b0    b1     b2    b3      b4   b5 b6 b7  k
  1.675, 1.974, -0.068, 0.053,  0,  0,  0,  0, 1,
  1.550, 1.805, -0.230, 0.032,  0,  0,  0,  0, 1,
  1.282, 1.063, -0.103, 0.003,  0,  0,  0,  0, 1,
  0.704, 1.376, -0.107, 0.040,  0,  0,  0,  0, 1,
  1.417, 1.413,  0.021, 0.000,  0,  0,  0,  0, 1,
 -0.008, 1.349, -0.195, 0.144,  0,  0,  0,  0, 1,
  0.512, 1.538, -0.089, 0.082,  0,  0,  0,  0, 1,
  0.122, 0.601, -0.082, 0.119,  0,  0,  0,  0, 1,
  1.801, 1.211,  0.015, 0.000,  0,  0,  0,  0, 1,
 -0.207, 1.191,  0.066, 0.033,  0,  0,  0,  0, 1,
 -0.215, 1.291, -0.087, 0.029,  0,  0,  0,  0, 1,
  0.259, 0.875,  0.177, 0.072,  0,  0,  0,  0, 1,
 -0.423, 0.942,  0.064, 0.094,  0,  0,  0,  0, 1,
  0.113, 0.795,  0.124, 0.110,  0,  0,  0,  0, 1,
  1.030, 1.525,  0.200, 0.076,  0,  0,  0,  0, 1,
  0.140, 1.209,  0.082, 0.148,  0,  0,  0,  0, 1,
  0.429, 1.480, -0.008, 0.061,  0,  0,  0,  0, 1,
  0.089, 0.785, -0.065, 0.018,  0,  0,  0,  0, 1,
 -0.516, 1.013,  0.016, 0.023,  0,  0,  0,  0, 1,
  0.143, 1.315, -0.011, 0.136,  0,  0,  0,  0, 1,
  0.347, 0.733, -0.121, 0.041,  0,  0,  0,  0, 1,
 -0.074, 0.869,  0.013, 0.026,  0,  0,  0,  0, 1,
  0.630, 1.484, -0.001, 0.000,  0,  0,  0,  0, 1), 
  nrow=23, ncol=9, byrow=TRUE)  
 
# generate data using the above item paramters
data<-genFMPData(NSubj=NSubj, bParam=b, seed=345)$data

# compute (initial) surrogate theta values from 
# the normed left singular vector of the centered 
# data matrix
thetaInit<-svdNorm(data)