Latent variable mixture models to test for differential item functioning: a population-based analysis

Table 3 Likelihood ratio (LR) test statistics for differential item functioning on the SF-36 physical functioning and mental health sub-scale items

Item	LR Statistic	Δdf^*	p-value
Physical Functioning
PF1: Vigorous activities	99.63	4	<0.0001
PF2: Moderate activities	127.49	4	<0.0001
PF3: Lifting or carrying groceries	151.04	4	<0.0001
PF4: Climbing several flights of stairs	37.69	4	<0.0001
PF5: Climbing one flight of stairs	60.95	4	<0.0001
PF6: Bending, kneeling or stooping	141.85	4	<0.0001
PF7: Walking more than a mile	87.79	4	<0.0001
PF8: Walking several blocks	34.51	4	<0.0001
PF9: Walking one block	3.26	2	0.196
PF10: Bathing or dressing self	64.76	2	<0.0001
Mental Health
MH1: Been a very nervous person?	71.79	3	<0.0001
MH2: Felt so down in the dumps that nothing could cheer you up?	21.03	3	0.0001
MH3: Felt calm and peaceful?	234.43	3	<0.0001
MH4: Felt downhearted and blue?	52.27	3	<0.0001
MH5: Been a happy person?	198.28	3	<0.0001

LR statistics are for the comparison of nested models: (a) mixture IRT model with free thresholds across classes for each item, and (b) IRT model with constrained thresholds across classes for each item. The mixture IRT model accounted for local dependence. Note that the latent variable mixture model for the physical functioning sub-scale had 3 classes and the model for the mental health sub-scale had 2 classes. Δdf is the difference in degrees of freedom for models defined in (a) and (b)

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