ipd: Item Parameter Drift
In irt: Item Response Theory and Computerized Adaptive Testing Functions

Description Usage Arguments Value Author(s) References Examples

This function detects the unstable (i.e. items whose item parameter values drifted) for a given two sets of items.

1	ipd(ip1, ip2, method = "robust-z", anchor_item_ids = NULL, alpha = 0.01)

`ip1`	Itempool object for the first calibration.
`ip2`	Itempool object for the second calibration.
`method`	The method of item parameter drift analysis.
`anchor_item_ids`	Anchor item ids. If `NULL`, all items are assumed to be anchor items.
`alpha`	Two tailed critical value to detect the unstable items. For example if alpha = 0.05 , the critical value is calculated using `qnorm(1-alpha/2)` (= 1.96). Items whose absolute robust z values are larger than this number will be flagged as unstable. "robust-z" Robust-Z method based on the Huynh and Meyer (2010).

Return a list depending on the method:

robust-z

output$a$cor: Correlation between two $a$ parameter sets.
output$a$sd_ratio: The ratio of the standard deviation of ip2 to the standard deviation of ip1.
output$a$robust_z: Robust-z statistic values for each item discrimination parameter.
output$a$unstable: Item ID's which were flagged if robust z statistic value for a parameters is larger than the absolute value of the critical value (i.e. qnorm(1-alphe/2)).
output$b$robust_z: Robust-z statistic values for each item difficulty or threshold parameter. If an item has threshold parameters, robust z statistic will be calculated for each threshold.
output$b$unstable: Item ID's which were flagged if robust z statistic for difficulty/threshold parameters are larger than the absolute value of the critical value (i.e. qnorm(1-alphe/2)).

Emre Gonulates

Huynh, Huynh and Meyer, Patrick (2010) "Use of Robust z in Detecting Unstable Items in Item Response Theory Models," Practical Assessment, Research, and Evaluation: Vol. 15 , Article 2. DOI: <doi:10.7275/ycx6-e864> Available at: https://scholarworks.umass.edu/pare/vol15/iss1/2/

# The example from Huynh and Meyer (2010)
ip1 <- c(itempool(
  a = c(0.729, 0.846, 0.909, 0.818, 0.742, 0.890, 1.741, 0.907, 1.487, 1.228,
        0.672, 1.007, 1.016, 0.776, 0.921, 0.550, 0.624, 0.984, 0.506, 0.594,
        0.687, 0.541, 0.691, 0.843, 0.530, 0.462, 1.007, 0.825, 0.608, 1.177,
        0.900, 0.861, 0.843, 1.404, 0.446, 1.014, 1.632, 0.831, 1.560, 0.798),
  b = c(1.585, 0.635, -0.378, -0.100, -0.195, 0.749, 1.246, 1.016, -0.234,
        0.537, 0.070, 1.985, 1.101, -0.742, 0.463, -0.060, 0.477, 1.084,
        -2.340, 1.068, -0.055, -1.045, 1.859, 0.645, -0.689, -2.583, 1.922,
        0.709, 0.499, 1.973, 0.104, 0.809, 0.640, 0.247, 0.820, 1.837,
        2.129, 1.012, 1.774, 0.095),
  c = c(0.134, 0.304, 0.267, 0.176, 0.215, 0.194, 0.267, 0.159, 0.095,
        0.197, 0.089, 0.272, 0.229, 0.159, 0.162, 0.100, 0.259, 0.167,
        0.000, 0.242, 0.323, 0.000, 0.196, 0.189, 0.000, 0.000, 0.334,
        0.538, 0.125, 0.511, 0.192, 0.353, 0.103, 0.241, 0.245, 0.118,
        0.155, 0.132, 0.215, 0.148),
  model = "3PL"),
  item(a = 0.561, b = c(0.784, -0.113, 1.166), model = "GPCM"),
  item(a = 0.745, b = c(3.687, 2.506, -0.001), model = "GPCM"))

ip2 <- c(itempool(
  a = c(0.650, 0.782, 0.816, 0.787, 0.611, 0.888, 1.192, 0.589, 1.211,
        0.742, 0.526, 0.690, 0.996, 0.816, 0.781, 0.507, 0.378, 0.976,
        0.473, 0.364, 0.585, 0.566, 0.511, 0.718, 0.354, 1.080, 0.840,
        0.865, 0.528, 0.814, 0.555, 0.701, 0.530, 1.220, 0.344, 0.966,
        1.044, 0.358, 1.192, 0.615),
  b = c(0.676, -0.525, -1.749, -1.092, -1.619, -0.406, -0.132, 0.006,
        -1.352, -0.872, -1.242, 0.873, 0.239, -2.038, -0.487, -1.372,
        -1.492, 0.214, -4.537, 0.220, -0.686, -2.394, 0.747, -0.467,
        -3.629, -5.000, 0.927, 0.305, -0.839, 1.270, -1.618, -0.091,
        -1.228, -1.019, -1.453, 1.090, 1.743, -1.436, 1.024, -1.358),
  c = c(0.110, 0.316, 0.161, 0.149, 0.145, 0.200, 0.243, 0.059, 0.081,
        0.075, 0.028, 0.267, 0.242, 0.189, 0.184, 0.121, 0.000, 0.170,
        0.000, 0.151, 0.383, 0.000, 0.195, 0.177, 0.000, 0.000, 0.352,
        0.647, 0.116, 0.501, 0.000, 0.286, 0.000, 0.248, 0.064, 0.150,
        0.126, 0.000, 0.187, 0.007),
  model = "3PL"),
  item(a = 0.486, b = c(-0.539, -1.489, -0.052), model = "GPCM"),
  item(a = 0.737, b = c(2.599, 1.250, -1.209), model = "GPCM"))
ipd(ip1, ip2)