1. 1 Binary models 2 LCGA model of frequent bedwetting + tests of gender invariance

2. 2 Latent Class Growth Analysis Alternative to LLCA More parsimonius than LLCA Unlikely to capture some shapes e.g. relapse Fits polynomials on logit scale, not in probability space (more flexible than one might think)

3. 3 The data – frequent wetting BoysGirls 4.5yr Dry62%77% “Infrequent”27% 38% 17% 23% “Frequent”11%6% 5.5yr Dry72%84% “Infrequent”21% 28% 13% 16% “Frequent”7%3% 6.5yr Dry76%87% “Infrequent”20% 24% 11% 14% “Frequent”5%2% 7.5yr Dry81%90% “Infrequent”16% 19% 9% 10% “Frequent”3%1% 9.5yr Dry87%94% “Infrequent”11% 13% 5% 6% “Frequent”2%1%

4. 4 The plan Fit LLCA and LCGA models of the following: 1.model frequent bedwetting on boys and girls separately 2.Combine dataset and fit variant model with KNOWNCLASS 3.Test for gender invariance by constraining parameters across gender groups

5. 5 Sex specific models Boys (n = 2956)Girls (n = 2887) # class# parmsBICBLRTEntropyBICBLRTEntropy LLCA 2114345.3< 0.0010.9662594.5< 0.0010.979 3174292.7< 0.0010.9692615.5< 0.0010.982 4234316.4< 0.0010.96926550.380.995 5294357.40.350.9662698.60.990.997 LCGA 274324.6< 0.0010.9632575.9< 0.0010.975 3114249.2< 0.0010.972574.2< 0.0010.979 4154262.90.010.9612600.30.350.857 5194289.50.370.9652628.30.590.877

6. 6 LLCA results

7. 7 Fitting LCGA model variable: classes = c (3) ; useobservations (sex == 1); analysis: model: %OVERALL% I S Q | nwet_1@0 nwet_2@1 nwet_3@2 nwet_4@3 nwet_5@5;

8. 8 Sex specific models Boys (n = 2956)Girls (n = 2887) # class# parmsBICBLRTEntropyBICBLRTEntropy LLCA 2114345.3< 0.0010.9662594.5< 0.0010.979 3174292.7< 0.0010.9692615.5< 0.0010.982 4234316.4< 0.0010.96926550.380.995 5294357.40.350.9662698.60.990.997 LCGA 274324.6< 0.0010.9632575.9< 0.0010.975 3114249.2< 0.0010.972574.2< 0.0010.979 4154262.90.010.9612600.30.350.857 5194289.50.370.9652628.30.590.877

9. 9 LCGA / LLCA comparison Shapes v similar Parameters: LLCA (17) versus LCGA (11) LCGA BICs lower than LLCA LLCALCGA

10. 10 Fitting LCGA KNOWNCLASS model variable: classes = sex (2) c (3) ; knownclass = sex (kz021 = 1 kz021 = 2); analysis: model: %OVERALL% I S Q | nwet_1@0 nwet_2@1 nwet_3@2 nwet_4@3 nwet_5@5;

11. 11 LCGA knownclass results VariantInvariant Free parameters 2314 BIC 14946.614884 Entropy 0.9840.983 Class sizes ‘Normative’ (b:g) 92.6% : 96.6%92.3% : 96.8% ‘Delayed’ (b:g) 3.8% : 1.8%4.1% : 1.7% ‘Persistent’ (b:g) 3.6% : 1.6%3.7% : 1.6% Class spec entropy ‘Normative’ (b:g) 0.995 : 0.9960.991 : 0.997 ‘Delayed’ (b:g) 0.889 : 0.8500.892 : 0.857 ‘Persistent’ (b:g) 0.981 : 0.9900.986 : 0.980

12. 12 LCGA Invariant model model: %OVERALL% I S Q | nwet_1@0 nwet_2@1 nwet_3@2 nwet_4@3 nwet_5@5; c on sex; %sex#1.c#1%sex#2.c#1% [i] (1);[i] (1); [s] (11);[s] (11); [q] (111);[q] (111); %sex#1.c#2%sex#2.c#2% [i] (2);[i] (2); [s] (22);[s] (22); [q] (222);[q] (222); %sex#1.c#3% %sex#2.c#3% [i] (3);[i] (3); [s] (33);[s] (33); [q] (333); [q] (333);

13. 13 LCGA knownclass results VariantInvariant Free parameters 2314 BIC 14946.614884 Entropy 0.9840.983 Class sizes ‘Normative’ (b:g) 92.6% : 96.6%92.3% : 96.8% ‘Delayed’ (b:g) 3.8% : 1.8%4.1% : 1.7% ‘Persistent’ (b:g) 3.6% : 1.6%3.7% : 1.6% Class spec entropy ‘Normative’ (b:g) 0.995 : 0.9960.991 : 0.997 ‘Delayed’ (b:g) 0.889 : 0.8500.892 : 0.857 ‘Persistent’ (b:g) 0.981 : 0.9900.986 : 0.980

14. 14 LCGA knownclass Invariant

15. 15 LLCA knownclass Invariant %OVERALL% c on sex; %sex#1.c#1% [NWET_KK4$1] (1); [NWET_KM4$1] (2); [NWET_KP4$1] (3); [NWET_KR4$1](4); [NWET_KU4$1] (5); %sex#2.c#1% [NWET_KK4$1] (1); [NWET_KM4$1] (2); [NWET_KP4$1] (3); [NWET_KR4$1] (4); [NWET_KU4$1] (5); %sex#1.c#2% [NWET_KK4$1] (11); [NWET_KM4$1] (12); [NWET_KP4$1] (13); [NWET_KR4$1] (14); [NWET_KU4$1] (15); %sex#2.c#2% [NWET_KK4$1] (11); [NWET_KM4$1] (12); [NWET_KP4$1] (13); [NWET_KR4$1] (14); [NWET_KU4$1] (15); %sex#1.c#3% [NWET_KK4$1] (21); [NWET_KM4$1] (22); [NWET_KP4$1] (23); [NWET_KR4$1] (24); [NWET_KU4$1] (25); %sex#2.c#3% [NWET_KK4$1] (21); [NWET_KM4$1] (22); [NWET_KP4$1] (23); [NWET_KR4$1] (24); [NWET_KU4$1] (25);

16. 16 LCGA/LLCA Invariant results Variant LCGAInvariant LCGAInvariant LLCA Free parameters231420 BIC14946.61488414933 Entropy0.9840.983 Class sizes ‘Normative’ (b:g)92.6% : 96.6%92.3% : 96.8%92.1%:96.7% ‘Delayed’ (b:g)3.8% : 1.8%4.1% : 1.7%4.2%:1.8% ‘Persistent’ (b:g)3.6% : 1.6%3.7% : 1.6%3.6%:1.5% Class spec entropy ‘Normative’ (b:g)0.995 : 0.9960.991 : 0.9970.990: 0.997 ‘Delayed’ (b:g)0.889 : 0.8500.892 : 0.8570.907: 0.882 ‘Persistent’ (b:g)0.981 : 0.9900.986 : 0.9800.993: 0.989

17. 17 Summary LCGA is a possible, more parsimonius alternative, to LLCA when trajectory shapes are well-behaved One should approach an invariant model via individual models before combining data within a parameter variant knownclass model