Table I.

Ridge penalty: variations of β₁₁ and δ (N =5000).

β * 11	δ †	λ ‡	Bias§	Empirical precision¶	Accuracy of precision∥	MSE**
0.69	0	0.0	0.001	0.033	−0.004	0.033
		1	−0.036	0.030	−0.010	0.031
1.79	0	0.0	0.011	0.035	0.007	0.036
		0.2	−0.016	0.033	0.006	0.033
1.79	0.69	0.0	0.297	0.051	0.039	0.139
		0.1	0.279	0.048	0.038	0.126
1.79	1.79	0.0	1.146	0.056	0.041	1.369
		0.1	1.113	0.051	0.036	1.290
1.79	−1.79	0.0	−0.296	0.046	0.036	0.134
		0.2	−0.317	0.044	0.035	0.144

^*Simulated log odds ratio for association between x₁ and membership in class 1, relative to class 3.

^†Simulated log odds ratio for the independent association between covariate and the first of six latent class indicators.

^‡Candidate value for tuning parameter. Results are shown for λ=0 and the candidate λ value which minimized R, the cross-validated log-likelihood loss for the largest number of simulated data sets.

^§${\beta }_{11}-\left[\right(1∕\mathit{nsi}){\Sigma }_{\mathit{si}=1}^{\mathit{nsi}}{\widehat{\beta }}_{11,\mathit{si},\lambda },],$, where si are simulation iterations.

^¶${\Sigma }_{\mathit{si}=1}^{\mathit{nsi}}{({\widehat{\beta }}_{11,\mathit{si},\lambda }-{\beta }_{11,\lambda })}^2∕(n-1)$.

^∥$(1∕\mathit{nsi}){\Sigma }_{\mathit{si}=1}^{\mathit{nsi}}v\widehat{a}r\left({\widehat{\beta }}_{11,\mathit{si},\lambda }\right)$—empirical precision_λ.

^**Mean square error = empirical ${\text{precision}}_{\lambda }+{\text{bias}}_{\lambda }^2$.