A Machine Learning Approach to Assess Differential Item Functioning in Psychometric Questionnaires Using the Elastic Net Regularized Ordinal Logistic Regression in Small Sample Size Groups
Table 5
The results of the DIF analysis for the PedsQLTM 4.0 across children with ADHD and their parents based on the regularized (elastic net) and non-regularized OLR models.
OLR
Ridge
Elastic net OLR
LASSO
w=0
w=0.01
w=0.02
w=0.03
w=0.04
w=0.05
w=0.06
w=0.07
w=0.1
w=0.5
w=1
Physical Functioning
-value
1. Hard to walk more than a block
0.453
1.000
1.000
1.000
1.000
0.791
0.714
0.663
0.628
0.566
0.467
0.459
2. Hard to run
0.553
1.000
1.000
1.000
1.000
0.838
0.772
0.729
0.699
0.649
0.567
0.560
3. Hard to do sports or exercises
0.929
0.543
0.551
0.723
0.844
1.000
1.000
1.000
1.000
1.000
1.000
1.000
4. Hard to lift something heavy
0.007
0.146
0.154
0.059
0.035
0.024
0.019
0.016
0.014
0.011
0.007
0.007
5. Hard to take a bath or shower
0.001
0.006
0.007
0.003
0.002
0.002
0.001
0.001
0.001
0.001
0.001
0.001
6. Hard to do chores around house
0.070
0.276
0.290
0.169
0.130
0.108
0.098
0.091
0.087
0.080
0.071
0.070
7. Hurt or ache
0.572
0.442
0.452
0.494
0.519
0.536
0.546
0.552
0.557
0.564
0.575
0.575
8. Low energy
0.129
0.114
0.118
0.112
0.114
0.118
0.120
0.122
0.123
0.126
0.129
0.129
Emotional Functioning
1. Feel afraid or scared
0.160
0.514
0.537
0.367
0.299
0.257
0.234
0.218
0.208
0.189
0.163
0.161
2. Feel sad or blue
0.012
0.037
0.039
0.023
0.019
0.017
0.015
0.015
0.014
0.013
0.012
0.012
3. Feel angry
0.003
0.014
0.014
0.007
0.005
0.004
0.004
0.004
0.003
0.003
0.003
0.003
4. Trouble sleeping
0.909
0.820
0.823
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
0.963
5. Worry about what will happen
0.003
0.074
0.078
0.027
0.015
0.010
0.008
0.006
0.006
0.004
0.003
0.003
Social Functioning
1. Trouble getting along with peers
0.024
0.074
0.077
0.047
0.038
0.033
0.031
0.029
0.028
0.026
0.024
0.024
2. Other kids not wanting to be friends
0.985
0.925
0.928
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
3. Teased
0.167
0.298
0.309
0.250
0.226
0.210
0.201
0.195
0.190
0.182
0.169
0.168
4. Doing things other peers do
0.226
0.442
0.459
0.357
0.316
0.289
0.275
0.264
0.258
0.246
0.229
0.227
5. Hard to keep up when play with others
0.002
0.041
0.043
0.016
0.010
0.007
0.005
0.005
0.004
0.003
0.002
0.002
School Functioning
1. Hard to concentrate
0.576
0.644
0.648
1.000
1.000
1.000
1.000
1.000
1.000
0.889
0.605
0.587
2. Forget things
0.301
1.000
1.000
1.000
0.813
0.644
0.562
0.507
0.469
0.405
0.311
0.304
3. Trouble keeping up with schoolwork
0.773
0.510
0.517
0.758
1.000
1.000
1.000
1.000
1.000
1.000
0.830
0.795
4. Miss school – not well
0.550
0.261
0.267
0.376
0.436
0.476
0.497
0.511
0.519
0.533
0.553
0.554
5. Miss school – doctor appointment
0.935
0.445
0.452
0.645
0.762
0.847
0.898
0.931
0.950
0.957
0.942
0.973
Total number of uniform DIF items
7
4
4
6
7
7
7
7
7
7
7
7
Note: DIF: differential item functioning; LASSO: least absolute shrinkage and selection operator; OLR: ordinal logistic regression; w: weighting parameter; the bold numbers show the -values for items that demonstrate a uniform DIF.
