Description Usage Arguments Details Value References Examples
Link two sets of FMP item parameters using linear or nonlinear transformations of the latent trait.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 |
bmat1 |
FMP item parameters on an anchor test. |
bmat2 |
FMP item parameters to be rescaled. |
maxncat |
Maximum number of response categories (the first maxncat - 1 columns of bmat1 and bmat2 are intercepts) |
cvec1 |
Vector of lower asymptote parameters for the anchor test. |
cvec2 |
Vector of lower asymptote parameters corresponding to the rescaled item parameters. |
dvec1 |
Vector of upper asymptote parameters for the anchor test. |
dvec2 |
Vector of upper asymptote parameters corresponding to the rescaled item parameters. |
k_theta |
Complexity of the latent trait transformation (k_theta = 0 is linear, k_theta > 0 is nonlinear). |
int |
Matrix with two columns, used for numerical integration. Column 1 is a grid of theta values, column 2 are normalized densities associated with the column 1 values. |
... |
Additional arguments passed to optim. |
The goal of item parameter linking is to find a metric transformation such that the fitted parameters for one test can be transformed to the same metric as those for the other test. In the Haebara approach, the overall sum of squared differences between the original and transformed individual item response functions is minimized. In the Stocking-Lord approach, the sum of squared differences between the original and transformed test response functions is minimized. See Feuerstahler (2016, 2019) for details on linking with the FMP model.
par |
(Greek-letter) parameters estimated by optim. |
value |
Value of the minimized criterion function. |
counts |
Number of function counts in optim. |
convergence |
Convergence criterion given by optim. |
message |
Message given by optim. |
tvec |
Vector of theta transformation coefficients (t = t0,....,t(2k_θ+1)) |
bmat |
Transformed bmat2 item parameters. |
Feuerstahler, L. M. (2016). Exploring alternate latent trait metrics with the filtered monotonic polynomial IRT model (Unpublished dissertation). University of Minnesota, Minneapolis, MN. http://hdl.handle.net/11299/182267
Feuerstahler, L. M. (2019). Metric Transformations and the Filtered Monotonic Polynomial Item Response Model. Psychometrika, 84, 105–123. doi: 10.1007/s11336-018-9642-9
Haebara, T. (1980). Equating logistic ability scales by a weighted least squares method. Japanese Psychological Research, 22, 144–149. doi: 10.4992/psycholres1954.22.144
Stocking, M. L., & Lord, F. M. (1983). Developing a common metric in item response theory. Applied Psychological Measurement, 7, 201–210. doi: 10.1002/j.2333-8504.1982.tb01311.x
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | set.seed(2342)
bmat <- sim_bmat(n_items = 10, k = 2)$bmat
theta1 <- rnorm(100)
theta2 <- rnorm(100, mean = -1)
dat1 <- sim_data(bmat = bmat, theta = theta1)
dat2 <- sim_data(bmat = bmat, theta = theta2)
# estimate each model with fixed-effects and k = 0
fmp0_1 <- fmp(dat = dat1, k = 0, em = FALSE)
fmp0_2 <- fmp(dat = dat2, k = 0, em = FALSE)
# Stocking-Lord linking
sl_res <- sl_link(bmat1 = fmp0_1$bmat[1:5, ],
bmat2 = fmp0_2$bmat[1:5, ],
k_theta = 0)
hb_res <- hb_link(bmat1 = fmp0_1$bmat[1:5, ],
bmat2 = fmp0_2$bmat[1:5, ],
k_theta = 0)
|
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.