# gutt: Guttman's Lambda In LatentREGpp: Item Response Theory Implemented in R and Cpp

## Description

Six Lower limits of reliability coefficients are presented.

## Usage

 1 gutt(data) 

## Arguments

 data a matrix or a Dataframe that holds the test response data

## Details

Let

S_j^2

the variances over persons of the n items in the test, and S_t^2 the variance over persons of the sum of the items. The firt estimate λ_1 can be computed from L_1 = 1 - (sum{s_j^2}/S_t^2) Let C_2 the sum of squares of the covariances between items, therefore is the sum of n(n-1)/2 terms. The bound lambda_2 is computed by L_2 = L_1 + (√{n/n-1 C_2}/S_t^2) The third lower bound λ_3 is a modification of λ_1, it is computed from the L_3 = n/(n-1) L_1 Fourth lower bound λ_4 has been interpreted as the greatest split half reliability, and requires that the test be scored as twohalves. It is calculated from

L_4 = 2(1 - (s_a^2 + s_b^2)/s_t^2)

where S_a^2 and S_b^2 are the respectives variances of the two parts for the single trial. For the fifth lower bound lambda_5, let C_{2j} be the sum of the squares of the covariances of item j with the remaining n-1 items, and let \bar{C}_2 be the largest of the

C_{2j}

. Then the coefficient can be computed from L_5 = L_1 + (2√{bar{C}_2})/S_t^2 The final bound is based on multiple correlation, let e_j^2 be the variance of the errors of estimate of item j from its linear multiple regression on the remaining n-1 items. Then lambda_6 can be computed from L_6 = 1 - (∑{e_j^2})/S_t^2

## Value

The six coefficients Guttman for the test.

## References

Guttman, L. (1945). A basis for analyzing test-retest reliability. Psychometrika, 10(4), 255-282.

LatentREGpp documentation built on April 14, 2017, 11:55 a.m.