icccal: Item Characteristic Curve Calculations

In birtr: The R Package for "The Basics of Item Response Theory Using R"

Description

Computes the logistic deviate L, the exponent of negative L, the denominator, and the value of probability of correct response for each of seven ability levels evenly spaced from -3 to +3 under the one-, two-, or three-parameter logistic item characteristic curve model.

Usage

icccal(b, a, c)

Arguments

b	a single number representing the value of item difficulty.
a	a single number representing the value of item discrimination.
c	a single number representing the value of lower asymptote.

Details

While the theoretical range of ability is from negative infinity to positive infinity, practical considerations usually limit the range of values from -3 to +3. Under the one-parameter logistic model, a = 1 and c = 0. Under the two-parameter logistic model, c = 0. The parameter c has a theoretical range from 0 to 1, but in practice values above .35 are not considered acceptable, hence use the range from 0 to .35 for c.

References

Baker, F. B., & Kim, S.-H. (2017). The basics of item response theory using R. New York, NY: Springer. ISBN-13: 978-3-319-54204-1

Examples

icccal(1.5, 1.3, .2)
icccal(a = 1.3, b = 1.5, c = .2)
icccal(1)      # icccal(1, 1, 0)
icccal(1, 0.5) # icccal(1, 0.5, 0)

Example output

  theta     L       expnl    opexpnl         P
1    -3 -5.85 347.2343805 348.234380 0.2022973
2    -2 -4.55  94.6324083  95.632408 0.2083654
3    -1 -3.25  25.7903399  26.790340 0.2298615
4     0 -1.95   7.0286876   8.028688 0.2996427
5     1 -0.65   1.9155408   2.915541 0.4743916
6     2  0.65   0.5220458   1.522046 0.7256084
7     3  1.95   0.1422741   1.142274 0.9003573
  theta     L       expnl    opexpnl         P
1    -3 -5.85 347.2343805 348.234380 0.2022973
2    -2 -4.55  94.6324083  95.632408 0.2083654
3    -1 -3.25  25.7903399  26.790340 0.2298615
4     0 -1.95   7.0286876   8.028688 0.2996427
5     1 -0.65   1.9155408   2.915541 0.4743916
6     2  0.65   0.5220458   1.522046 0.7256084
7     3  1.95   0.1422741   1.142274 0.9003573
  theta  L      expnl   opexpnl          P
1    -3 -4 54.5981500 55.598150 0.01798621
2    -2 -3 20.0855369 21.085537 0.04742587
3    -1 -2  7.3890561  8.389056 0.11920292
4     0 -1  2.7182818  3.718282 0.26894142
5     1  0  1.0000000  2.000000 0.50000000
6     2  1  0.3678794  1.367879 0.73105858
7     3  2  0.1353353  1.135335 0.88079708
  theta    L     expnl  opexpnl         P
1    -3 -2.0 7.3890561 8.389056 0.1192029
2    -2 -1.5 4.4816891 5.481689 0.1824255
3    -1 -1.0 2.7182818 3.718282 0.2689414
4     0 -0.5 1.6487213 2.648721 0.3775407
5     1  0.0 1.0000000 2.000000 0.5000000
6     2  0.5 0.6065307 1.606531 0.6224593
7     3  1.0 0.3678794 1.367879 0.7310586

birtr documentation built on May 2, 2019, 9:18 a.m.