MEASURE OF FIT IN UDERREPORTED SAMPLE WITH CORRECTION
Injury categories/Measures of fit
Actual shares
MIXGOL predictions
MIXMNL predictions
No injury
66.4311
69.4232
69.4094
C.I.
-
69.3574/69.4889
69.3349/69.4839
Possible injury
15.0667
13.7549
13.8957
C.I.
-
13.7262/13.7835
13.8526/13.9389
Non-incapacitating injury
11.3647
10.9293
10.8844
C.I.
-
10.8999/10.9586
10.8553/10.9135
Incapacitating/Fatal injury
7.1375
5.8926
5.8105
C.I.
-
5.8599/5.9253
5.7786/5.8423
RMSE
-
1.7944
1.7827
C.I.
-
1.7256/1.8633
1.7119/1.8536
MAPE
-
8.6295
8.7599
C.I.
-
8.6266/8.6325
8.7569/8.7629
Predictive Log-likelihood
-
-3853.4807
-3881.9877
C.I.
-
-3869.9209/-3837.0405
-3898.5934/-3865.3820
AICc
-
7810.3072
7879.6556
C.I.
-
7777.4290/7843.1853
7846.4471/7912.8641
BIC
-
8129.8764
8236.6451
C.I.
-
8096.9087/8162.8441
8203.3327/8269.9575
1
To be sure, the logistic regression with two alternatives can be regarded as an ordered logit model with two alternatives.
2 To be sure, Ye and Lord (2011) have compared the ordered probit, multinomial logit and mixed logit model in terms of underreported data. The authors conclude that all the three models considered in the study perform poorly in the presence of underreported data. The exact impact of underreporting on these model frameworks needs further investigation. The study employs data simulation; however, the models are estimated with just one parameter and for a particular aggregate sample share.
3 AICc is a more stringent version of the AIC [AIC = 2K− 2ln(L)] in penalizing for additional parameters