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Ordinal Models

Ordinal Models. Ordinal Models. Estimating gender-specific LLCA with repeated ordinal data Examining the effect of time invariant covariates on class membership The effect of class membership on a later outcome. The data. 5 repeated measures of bedwetting 4½, 5½, 6½ ,7½ & 9½ yrs

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Ordinal Models

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  1. Ordinal Models

  2. Ordinal Models • Estimating gender-specific LLCA with repeated ordinal data • Examining the effect of time invariant covariates on class membership • The effect of class membership on a later outcome

  3. The data • 5 repeated measures of bedwetting • 4½, 5½, 6½ ,7½ & 9½ yrs • 3-level ordinal • Dry • Infrequent wetting (< 2 nights/week) • Frequent wetting (2+ nights/week)

  4. 4 time point ordinal LLCA (Boys) title: 4 time point LLCA of ordinal bedwetting; data: file is 'C:\Work\bedwet_dsm4_llca\spss\llca_dsm4.txt'; listwise is ON; variable: names ID sex nwet_kk2 nwet_kk3 nwet_kk4 nwet_kk5 nwet_km2 nwet_km3 nwet_km4 nwet_km5 nwet_kp2 nwet_kp3 nwet_kp4 nwet_kp5 nwet_kr2 nwet_kr3 nwet_kr4 nwet_kr5 nwet_ku2 nwet_ku3 nwet_ku4 nwet_ku5; categorical = nwet_kk3 nwet_km3 nwet_kp3 nwet_kr3 nwet_ku3; usevariables nwet_kk3 nwet_km3 nwet_kp3 nwet_kr3 nwet_ku3; missing are nwet_kk3 nwet_km3 nwet_kp3 nwet_kr3 nwet_ku3 (999); classes = c (4); useobservations (sex==1);

  5. RESULTS IN PROBABILITY SCALE Latent Class 1 NWET_KK3 Category 1 0.190 0.030 6.430 0.000 Category 2 0.672 0.033 20.134 0.000 Category 3 0.138 0.026 5.409 0.000 NWET_KM3 Category 1 0.224 0.038 5.929 0.000 Category 2 0.727 0.036 20.254 0.000 Category 3 0.048 0.019 2.533 0.011 NWET_KP3 Category 1 0.160 0.045 3.540 0.000 Category 2 0.823 0.044 18.613 0.000 Category 3 0.017 0.011 1.473 0.141 NWET_KR3 Category 1 0.075 0.064 1.178 0.239 Category 2 0.903 0.061 14.686 0.000 Category 3 0.022 0.011 1.929 0.054 NWET_KU3 Category 1 0.456 0.054 8.486 0.000 Category 2 0.532 0.052 10.269 0.000 Category 3 0.012 0.008 1.501 0.133

  6. RESULTS IN PROBABILITY SCALE Dry Latent Class 1 NWET_KK3 Category 1 0.190 0.030 6.430 0.000 Category 2 0.672 0.033 20.134 0.000 Category 3 0.138 0.026 5.409 0.000 NWET_KM3 Category 1 0.224 0.038 5.929 0.000 Category 2 0.727 0.036 20.254 0.000 Category 3 0.048 0.019 2.533 0.011 NWET_KP3 Category 1 0.160 0.045 3.540 0.000 Category 2 0.823 0.044 18.613 0.000 Category 3 0.017 0.011 1.473 0.141 NWET_KR3 Category 1 0.075 0.064 1.178 0.239 Category 2 0.903 0.061 14.686 0.000 Category 3 0.022 0.011 1.929 0.054 NWET_KU3 Category 1 0.456 0.054 8.486 0.000 Category 2 0.532 0.052 10.269 0.000 Category 3 0.012 0.008 1.501 0.133 Infrequent wetting Frequent wetting

  7. Alternative 1 – three dimensions • A 3D plot… or something made out of plasticine

  8. Alternative 2 – two figures Infrequent bedwetting Frequent bedwetting

  9. Alternative 3 – two figures Any bedwetting Frequent bedwetting

  10. Alternative 3 – two figures Any bedwetting Frequent bedwetting (1) A persistent wetting group who mostly wet to a frequent level (2) A persistent wetting group who mostly wet to an infrequent level (3) A delayed group comprising mainly infrequent wetters (4) Normative group

  11. Fit statistics - Boys

  12. 5-class model (boys) Any bedwetting Frequent bedwetting

  13. 5-class model (boys) • Normative (63.8%) • Mild risk of infrequent wetting at start which soon disappears • Delayed-infrequent (18.2%) • Delayed attainment of nighttime bladder control but rarely attains frequent levels • Persistent-infrequent (11.4%) • Persistent throughout period but rarely attains frequent levels • Persistent-frequent (4.0%) • Persistently and frequently until late into period. Appears to be turning into lower frequency wetting however over 80% are still wetting to some degree at 9.5yr • Delayed-frequent (2.7%) • Frequent wetting until half-way through time period, reducing to a lower level of wetting which appears to be clearing up by 9.5yr

  14. Fit statistics – Girls – Oh!

  15. Fit statistics – Girls – Oh!

  16. 6-class model (girls) Any bedwetting Frequent bedwetting

  17. 6-class model (girls) • Normative (78.6%) • Delayed-infrequent (11.7%) • Persistent-infrequent (4.6%) • Persistent-frequent (1.6%) • Delayed-frequent (1.3%) • Relapse (2.0%) • Initial period of dryness followed by a return to infrequent wetting

  18. Incorporating covariates • 2-stage method • Export class probabilities to another package – Stata • Model class membership as a multinomial model with probability weighting • Using classes derived from repeated BW measures with partially missing data (gloss over)

  19. Multinomial models (boys) label values class class_label label define class_label /// 1 "Pers INF [1]" /// 2 "DelayFRQ [2]" /// 3 "Normal [3]" /// 4 "Pers FRQ [4]" /// 5 "DelayINF [5]", add tab class foreach var of varlist bedwet_m bedwet_p […] toilet { tab `var' if class==1 xi: mlogit class `var' [iw = boy_weights], rrr test `var' }

  20. Typical output Multinomial logistic regression Number of obs = 5004 LR chi2(4) = 85.09 Prob > chi2 = 0.0000 Log likelihood = -5256.9295 Pseudo R2 = 0.0080 ------------------------------------------------------------------------------ class | RRR Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- Pers INF [1] | bedwet_m | 2.456404 .3459902 6.38 0.000 1.863829 3.237378 -------------+---------------------------------------------------------------- DelayFRQ [2] | bedwet_m | 3.019243 .6958002 4.79 0.000 1.921915 4.743095 -------------+---------------------------------------------------------------- Pers FRQ [4] | bedwet_m | 3.795014 .6783016 7.46 0.000 2.673461 5.387073 -------------+---------------------------------------------------------------- DelayINF [5] | bedwet_m | 1.540813 .2046864 3.25 0.001 1.18761 1.999062 ------------------------------------------------------------------------------ (class==Normal [3] is the base outcome) ( 1) [Pers INF [1]]bedwet_m = 0 ( 2) [DelayDSM [2]]bedwet_m = 0 ( 3) [Pers DSM [4]]bedwet_m = 0 ( 4) [DelayINF [5]]bedwet_m = 0 chi2( 4) = 91.87, Prob > chi2 = 0.0000

  21. Selection of covariates (boys)

  22. What if we had used modal-class? • The further the posterior probabilities for class assignment are from 1 (i.e. the lower the entropy) the poorer the estimates from a model using the modal class • In this example (partial missing data) • entropy = 0.788 1 2 3 4 5 1 0.800 0.011 0.017 0.020 0.153 2 0.063 0.804 0.000 0.069 0.064 3 0.008 0.001 0.923 0.000 0.068 4 0.049 0.104 0.004 0.813 0.030 5 0.110 0.009 0.170 0.006 0.706

  23. Estimates using mod class Bias depends on class and also covariate

  24. A later outcome • Boys’ data • Outcomes: • Key Stage 3 at 13-14 yrs • Achieved level 5 or greater in English/Sci/Maths • English failed = 1210 (27.9%) • Science failed = 895 (20.6%) • Maths failed = 845 (19.5%)

  25. 2 stage procedure - Stata label values class class_label label define class_label /// 1 "Pers INF [1]" /// 2 "DelayFRQ [2]" /// 3 "Normal [3]" /// 4 "Pers FRQ [4]" /// 5 "DelayINF [5]", add recode class 3=0 foreach var of varlist maths science english { tab `var' if class==1 xi: logit `var' i.class [iw = b_par_p], or test _Iclass_2 _Iclass_3 _Iclass_4 _Iclass_5 }

  26. KS3 - English Logistic regression Number of obs = 4341 LR chi2(4) = 7.73 Prob > chi2 = 0.1018 Log likelihood = -2564.536 Pseudo R2 = 0.0015 ------------------------------------------------------------------------------ k3_lev5e | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- Pers INF | .9896705 .1131557 -0.09 0.928 .7909827 1.238267 Delay FRQ | .8946308 .1964416 -0.51 0.612 .5817527 1.375781 Pers FRQ | 1.474409 .2323757 2.46 0.014 1.082589 2.008041 Delay INF | .9135896 .0852754 -0.97 0.333 .76085 1.096991 ------------------------------------------------------------------------------ ( 1) _Iclass_1 = 0 ( 2) _Iclass_2 = 0 ( 3) _Iclass_4 = 0 ( 4) _Iclass_5 = 0 chi2( 4) = 7.97 Prob > chi2 = 0.0926

  27. KS3 - Maths Logistic regression Number of obs = 4341 LR chi2(4) = 11.29 Prob > chi2 = 0.0235 Log likelihood = -2133.6412 Pseudo R2 = 0.0026 ------------------------------------------------------------------------------ k3_lev5m | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- Pers INF | .9460608 .1241854 -0.42 0.673 .7314512 1.223637 Delay FRQ | .9601245 .2358923 -0.17 0.868 .5931937 1.554027 Pers FRQ | 1.688991 .2836716 3.12 0.002 1.215249 2.347413 Delay INF | .8976914 .095965 -1.01 0.313 .7280008 1.106935 ------------------------------------------------------------------------------ ( 1) _Iclass_1 = 0 ( 2) _Iclass_2 = 0 ( 3) _Iclass_4 = 0 ( 4) _Iclass_5 = 0 chi2( 4) = 12.05 Prob > chi2 = 0.0170

  28. KS3 - Science Logistic regression Number of obs = 4341 LR chi2(4) = 8.94 Prob > chi2 = 0.0626 Log likelihood = -2203.9946 Pseudo R2 = 0.0020 ------------------------------------------------------------------------------ k3_lev5s | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- Pers INF | .8913295 .1159146 -0.88 0.376 .6907838 1.150097 Delay FRQ | 1.067237 .2482602 0.28 0.780 .6764799 1.683709 Pers FRQ | 1.525329 .2566845 2.51 0.012 1.096786 2.121314 Delay INF | .8888344 .092835 -1.13 0.259 .7242967 1.09075 ------------------------------------------------------------------------------ ( 1) _Iclass_1 = 0 ( 2) _Iclass_2 = 0 ( 3) _Iclass_4 = 0 ( 4) _Iclass_5 = 0 chi2( 4) = 9.34 Prob > chi2 = 0.0531

  29. Summary • Fitting ordinal models is similar to binary data however results (“trajectories”) are harder to interpret graphically • Resulting classes can be used either as outcomes or categorical predictors using weighted regression in Stata • Using variables derived from modal class assignment can often introduce very biased estimates

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