Group work - Rasch analysis

Background

You have decided to do a Rasch analysis of the Roland Morris Disability Index (RMDQ-23). The RMDQ measures functional deficits in low back pain patients with or without sciatica (pain in the leg). It has 23 items, each item has yes/no response options, and the scale range is 0-100 (high score equals high disability). The RMDQ-23 can be found in Appendix 1 at the end of the page.

full at the end of this document.

Your sample consists of 230 patients with low back pain. Approx. half have been seen by medical doctors, physiotherapists or chiropractors (primary sector patients) and the other half have consulted specialist spinal unit.

Question 1 - The gold standard

You test the Rasch model fit (1 PL model) and find the following: χ2 = 0.0000 (DF 69)

1.1 Explain what the χ2 probability means?

Hint

Keywords: invariance, hierarchical, significant test




1.2 Explain what a Guttman scale is?

Hint

Keywords: hierarchical ordering, misclassification




Question 2 – item fit

You also look at the individual item fit (Table 1) to see if any items are not fitting the Rasch model.

Table 1. Individual item fit

Item Location SE FitResid DF ChiSq DF Prob
1 1,929 0,18 -0,865 210,18 2,331 3 0,506543
2 -2,334 0,227 0,624 218,74 3,892 3 0,273388
3 -0,847 0,167 -2,49 217,79 21,902 3 0,000069
4 0,101 0,157 0,668 210,18 1,135 3 0,768548
5 0,288 0,154 -3,074 216,84 11,165 3 0,010865
6 -0,173 0,158 -1,852 213,99 7,254 3 0,064239
7 -0,93 0,169 -2,112 215,89 5,436 3 0,142496
8 1,163 0,16 0,593 214,94 2,138 3 0,544282
9 -0,364 0,16 -0,458 213,04 1,51 3 0,68
10 -0,44 0,161 -1,76 214,94 3,889 3 0,273741
11 -0,956 0,169 -0,084 215,89 1,007 3 0,799527
12 -0,487 0,16 -1,659 218,74 7,184 3 0,066248
13 -0,17 0,159 -0,865 210,18 3,637 3 0,303395
14 0,399 0,156 -0,572 213,04 3,922 3 0,270056
15 -0,071 0,158 -0,273 212,09 1,645 3 0,649332
16 -1,975 0,209 -1,229 213,04 6,361 3 0,095318
17 0,231 0,157 3,162 209,23 21,339 3 0,000091
18 -0,625 0,164 -3,921 212,09 26,458 3 0,000008
19 3,813 0,31 0,472 209,23 2,689 3 0,442093
20 0,779 0,162 -0,849 201,62 2,569 3 0,462998
21 0,231 0,156 4,282 211,14 24,54 3 0,00002
22 -0,872 0,169 -2,041 212,09 6,545 3 0,087919
23 1,312 0,163 3,951 212,09 51,127 3 0

NB: The Bonferroni-corrected p-value for a questionnaire of 23-items is 0.0022.

2.1 What can you learn about the items in the RMDQ-23?

Hint

Look at the χ2 probability test results and the fit residuals (<-2.5). What do you see?




Question 3 – item difficulty

Next you turn to item difficulty. To do that you have produced a threshold map which is shown in Figure 1 (the specific item location can be found in the table on the right).

Figure 1. Threshold map

Item Location
1 1,928736
2 -2,33421
3 -0,84736
4 0,101178
5 0,287807
6 -0,17272
7 -0,93037
8 1,16251
9 -0,36365
10 -0,44025
11 -0,95604
12 -0,48699
13 -0,16972
14 0,399037
15 -0,07076
16 -1,97513
17 0,230672
18 -0,62511
19 3,812741
20 0,778695
21 0,230737
22 -0,87177
23 1,312


3.1 Find the most difficult item, the item closest to the average and easiest items and specify the content of them.


3.2 Considering the population we are looking at, does this make sense?


Question 4 – local dependence

As part of analyzing the RMDQ-23, you turn to local dependence. You have produced a person – item residual correlation matrix in Table 2 and need to consider the results.

Table 2. Person – item residual correlations

Pink = Mean residual correlation + 0.2; Yellow = Mean residual correlation + 0.3

4.1 Please explain what local dependence is?


4.2 Please describe the 3 most important item pairs showing local dependence. What do you want to do about it?

Hint

Find the three item pairs with highest mean residual correlation above + 0.3




Question 5 – Differential Item Functioning

When looking at DIF, you want to know if DIF is present in the RMDQ-23 in terms of where the patients are seen. You find the following for items 12 and 13:

Figure 2. ICC of item 12 (turning over in bed) stratified according to sector

Figure 3. ICC of item 13 (trouble putting on socks) stratified according to sector



5.1 Please explain what you see in Figure 2 and 3?

Hint

What types of DIF do you see?




Question 6 – targeting

Lastly, you decide to look at the person-item distribution. This is what you find:

Figure 4. Person-item threshold distribution

6.1 Please put the following labels on the x-axis: Easy items, difficult items, more able persons, less able persons.

Hint

Where are the ‘more and less able persons’ and the ‘easy and difficult items’?




6.2 Please explain what you see in Figure 4?

Hint

Keywords: Targeting of item thresholds and persons




Appendix 1. The Roland Morris Disability Questionnaire