Partial credit model category probabilities

plink Eq. 4 with the first step parameter dropped: P(X = k | theta) proportional to exp(sum_{v<=k} D a (theta - b_v)), empty sum = 0 for the lowest category. a = 1 gives the Masters (1982) partial credit model; one step reduces to the dichotomous 2PL.

Usage

morie_pcm(theta, steps, a = 1, D = 1)

Arguments

theta: Ability value.
steps: Numeric vector of step parameters b_2, ..., b_K.
a: Common discrimination (1 = Masters PCM).
D: Scaling constant (1 or 1.7).

Value

A list with elements probabilities, expected_score, n_categories, theta, a, D, method.

References

Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149-174. Muraki, E. (1992). Applied Psychological Measurement, 16, 159-176. Weeks, J. P. (2010). Journal of Statistical Software, 35(12).

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
morie_pcm(V, V)
#> $probabilities
#> [1] 0.1111111 0.1111111 0.1111111 0.1111111 0.1111111 0.1111111 0.1111111
#> [8] 0.1111111 0.1111111
#> 
#> $expected_score
#> [1] 4
#> 
#> $n_categories
#> [1] 9
#> 
#> $theta
#> [1] 1 2 3 4 5 6 7 8
#> 
#> $a
#> [1] 1
#> 
#> $D
#> [1] 1
#> 
#> $method
#> [1] "partial credit model (Masters 1982; plink Eq. 4)"
#>