﻿ CUTLO= cut off responses with low expectations

# CUTLO= cut off responses with low expectations = 0, no

Use this if guessing or response sets are evident. CUTLO= cuts off the bottom right-hand corner of the Scalogram in Table 22.

Eliminates (cuts off) observations where examinee measure is CUTLO= logits or more (user-rescaled by USCALE=) lower than item measure, so that the examinee has a low probability of success. The elimination of off-target responses takes place after PROX has converged. After elimination, PROX is restarted, followed by JMLE estimation and point-measure and fit calculation using only the reduced set of responses. This may mean that the original score-based ordering is changed.

For further discussion of tailoring the data to remove guessing situations, see  "Using a Theorem by Andersen and the Dichotomous Rasch Model to Assess the Presence of Random Guessing in Multiple Choice Items."  David Andrich, Ida Marais, and Stephen Humphry, Journal of Educational and Behavioral Statistics, October, 2011.

CUTLO= is equivalent to Waller's procedure in  Waller, M.I. (1976) "Estimating Parameters in the Rasch Model: Removing the Effects of Random Guessing", Report No. ETS-RB-76-0, Educational Testing Service, Princeton, N.J. http://files.eric.ed.gov/fulltext/ED120261.pdf

The CUTLO= value to USCALE=. So, if USCALE=10, then CUTLO=-1 means "omit responses where the person ability is 1 user-scaled unit or more lower than the item difficulty."

Usually with CUTLO= and CUTHI=, misfitting items aren't deleted - but miskeys etc. must be corrected first. Setting CUTLO= and CUTHI= is a compromise between fit and missing data. If you loose too much data, then increase the values. If there is still considerable misfit or skewing of equating, then decrease the values.

Here are the usual effects of CUTLO= and CUTHI=

1. Fit to the Rasch model improves.

2. The count of observations for each person and item decreases.

3. The variance in the data explained by the measures decreases.

CUTLO= is equivalent to the procedure outlined in Bruce Choppin. (1983). A two-parameter latent trait  model. (CSE Report No. 197). Los Angeles, CA: University of. California, Center for the Study of Evaluation, and the procedure in David Andrich, Ida Marais, and Stephen Humphry (2012) Using a Theorem by Andersen and the Dichotomous Rasch Model to Assess the Presence of Random Guessing in Multiple Choice Items Journal of Educational and Behavioral Statistics, 37, 417-442.

Polytomous items: CUTLO= and CUTHI= trim the data relative to the item difficulty, so they tend to remove data in high and low categories. You can adjust the item difficulty relative to the response structure using SAFILE=.

Example 1: Disregard responses where examinees are faced with too great a challenge, and so might guess wildly, i.e., where examinee measure is 2 or more logits lower than item measure:

CUTLO= -2  ; 12% success

This is equivalent to a "Optimum Appropriateness Measurement" (OAM) model in which it is assumed that persons might guess on all the items, so all responses in guessing situations are eliminated.

GUTTMAN SCALOGRAM OF RESPONSES:

PERSON |ITEM

| 12 22  1 3231311  1322112 2 113322

|62257012473946508491143795368350281

|-----------------------------------

147 +0001111110011010100111111000001000   154

130 +1100101111001110110101000000010100   135

93 +011110010100111010000001101000010    098

129 +111110111011011000000000000001010    134

134 +000110101110010001110010001000010    139

133 +100100111110000000101010011000000    138

137 +100000011110100101101000010000000    143

141 +110100010011100001100000000001010    147

138 +10100101011101000000000010010        144

113 +1011001000101111000000000000010      118

144 +10000010100010001000010001           151

114 +1000010010000100                     119

|-----------------------------------

| 12 22  1 3231311  1322112 2 113322

|62257012473946508491143795368350281

Example 2: Richard Gershon applied this technique in Guessing and Measurement with CUTLO=-1 ; 27% success

Example 3: We have some misbehaving children in our sample, but don't want their behavior to distort our final report.

An effective approach is in two stages:

Stage 1. calibrate the items using the good responses

Stage 2. anchor the items and measure the students using all the responses.

In Stage 1, we trim the test. We want to remove the responses by children that are so off-target that successes are probably due to chance or other off-dimensional behavior. These responses will contain most of the misfit. For this we analyze the data using

CUTLO= -2  (choose a suitable value by experimenting)

CUTLO= -1.39 ; 20% success

CUTLO= -1.10 ; 25% success

write an item file from this analysis:

IFILE=if.txt

In Stage 2. Anchor all the items at their good calibrations:

IAFILE=if.txt

Include all the responses (omit CUTLO=)

We can now report all the children without obvious child mis-behavior distorting the item measures.

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