Table 7.

Working recommendations for estimator choice when fitting multilevel cumulative logit models in practice

		Small VC (e.g. ICC=.13)		Large VC (e.g. ICC=.71)
		DV has many categories (5+)	DV has few categories (2)	DV has many categories (5+)	DV has few categories (2)
Many clusters (e.g. 100-200)	Large clusters (e.g. 20)	PQL, ML-AQ	PQL, ML-AQ	PQL, ML-AQ	ML-AQ
	Small clusters (e.g. 5)	PQL, ML-AQ	PQL, ML-AQ	ML-AQ	ML-AQ
Few clusters (e.g. 25-50)	Large clusters (e.g. 20)	PQL, ML-AQ	PQL, ML-AQ	PQL, ML-AQ	PQL, ML-AQ
	Small clusters (e.g. 5)	PQL, ML-AQ	PQL	PQL, ML-AQ

Notes. PQL=Penalized Quasi-Likelihood; ML-AQ= Maximum Likelihood with Adaptive Quadrature. Situations under which ML with adaptive quadrature or PQL perform similarly are denoted “PQL, MLAQ.” The selection of an estimator in these conditions should depend on the investigator's focus (fixed effects versus variance components) or other factors (such as computational speed or the desire to perform nested model comparisons). Situations under which PQL performs consistently better are denoted “PQL” and situations under which ML-AQ performs consistently better are denoted “ML-AQ.” Even in these conditions, however, the magnitude of performance differences is not always large. Consult Figures 2-7 and Tables 3-6 for more detailed information on estimator differences.