anchor trap! comparison of free and anchored results when using set constraint = default or none in conquest

anchor-trap-conquest.md

Free estimation (no anchors) using ConQuest gives the following item parameters for a 9 item test.

x <- c(0.39, -1.485, -1.138, -0.089, 0.901, 0.558, 0.225, -0.105, 0.743)

Next we add 3 logits to q1 through q5 and make q1 to q5 item anchors. q6 to q9 then still need to be calibrated. These are the results when:

anchored with set constraint = none;

y <- c(3.39, 1.515, 1.862, 2.911, 3.901, 3.559, 3.225, 2.895, 3.743)

anchored with constraint = DEFAULT;

z <- c(3.39, 1.515, 1.862, 2.911, 3.901, -2.994, -3.633, -4.281, -2.67)

That is, our results for q1 to q5 are identical to what values we anchored with

identical(x[1:5] + 3, y[1:5])
#> [1] TRUE
identical(x[1:5] + 3, z[1:5])
#> [1] TRUE

x correlates well with constraint = none results for all values including q6 to q9

cor(x, y)
#> [1] 0.9999999
plot(x, y)

x does not correlate well when constraint = DEFAULT!!

cor(x, z)
#> [1] -0.1744164
plot(x, z)

Created on 2018-05-29 by the reprex package (v0.2.0).