gutt: Guttman's Lambda

In SICSresearch/IRTpp: Estimating IRT Parameters using the IRT Methodology

Description

Six Lower limits of reliability coefficients are presented.

Usage

gutt(test)

Arguments

test	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 $lambda_1$ can be computed from $L_1 = 1 - (sums_j^2/S_t^2)$ 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 $L_2 = L_1 + (sqrtn/n-1 C_2/S_t^2)$ The third lower bound $lambda_3$ is a modification of $lambda_1$, it is computed from the $L_3 = n/(n-1) L_1$ Fourth lower bound $lamda_4$ 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 $barC_2$ be the largest of the $C_2j$. Then the coefficient can be computed from $L_5 = L_1 + (2sqrtbarC_2)/S_t^2$ 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 $L_6 = 1 - (sume_j^2)/S_t^2$

Value

The six coefficients Guttman for the test.

References

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

Examples

#data <- simulateTest(model="2PL",items=10,individuals=1000)
#gutt(data$test) 

SICSresearch/IRTpp documentation built on May 9, 2019, 11:11 a.m.