Subject-specific observed profiles of log(fev1) vs age First 50 subjects in Six Cities Study
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1 Subject-specific observed profiles of log(fev1) vs age First 50 subjects in Six Cities Study age
2 Model 1: A simple broken stick model with knot at 14 fit with ML 1 With random subject-specific intercepts Model Information Data Set Dependent Variable Covariance Structure Subject Effect Estimation Method Residual Variance Method Fixed Effects SE Method Degrees of Freedom Method WORK.FEV Unstructured id ML Profile Model-Based Containment Class Level Information Class Levels Values id 299 not printed Dimensions Covariance Parameters 2 Columns in X 3 Columns in Z Per Subject 1 Subjects 299 Max Obs Per Subject 12 Number of Observations Number of Observations Read 1993 Number of Observations Used 1993 Number of Observations Not Used 0 Iteration History Iteration Evaluations -2 Log Like Criterion Convergence criteria met.
3 Model 1: A simple broken stick model with knot at 14 fit with ML 2 With random subject-specific intercepts Covariance Parameter Estimates Z Cov Parm Subject Estimate Error Value Pr > Z UN(1,1) id <.0001 Residual <.0001 Fit Statistics -2 Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) Null Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq <.0001 Solution for Fixed Effects Effect Estimate Error DF t Value Pr > t Intercept <.0001 age <.0001 age140plus <.0001 Type 3 Tests of Fixed Effects Num Den Effect DF DF Chi-Square F Value Pr > ChiSq Pr > F age <.0001 <.0001 age140plus <.0001 <.0001
4 Plot of observed and predicted vs age curve - model 1 Subject number Plot of observed and predicted vs age curve - model 1 Subject number age age
5 Plot of observed and predicted vs age curve - model 1 Subject number Plot of observed and predicted vs age curve - model 1 Subject numbers 16, 18, 35 age Predicted age id id
6 Model 2: A simple broken stick model with knot at 14 fit with ML 3 With random intercepts and slopes before and after knot Model Information Data Set Dependent Variable Covariance Structure Subject Effect Estimation Method Residual Variance Method Fixed Effects SE Method Degrees of Freedom Method WORK.FEV Unstructured id ML Profile Model-Based Containment Class Level Information Class Levels Values id 299 not printed Dimensions Covariance Parameters 7 Columns in X 3 Columns in Z Per Subject 3 Subjects 299 Max Obs Per Subject 12 Number of Observations Number of Observations Read 1993 Number of Observations Used 1993 Number of Observations Not Used 0 Iteration History Iteration Evaluations -2 Log Like Criterion Convergence criteria met.
7 Model 2: A simple broken stick model with knot at 14 fit with ML 4 With random intercepts and slopes before and after knot Covariance Parameter Estimates Z Cov Parm Subject Estimate Error Value Pr Z UN(1,1) id <.0001 UN(2,1) id <.0001 UN(2,2) id <.0001 UN(3,1) id UN(3,2) id <.0001 UN(3,3) id <.0001 Residual <.0001 Fit Statistics -2 Log Likelihood -421 AIC (smaller is better) -419 AICC (smaller is better) -419 BIC (smaller is better) Null Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq <.0001 Solution for Fixed Effects Effect Estimate Error DF t Value Pr > t Intercept <.0001 age <.0001 age140plus <.0001 Type 3 Tests of Fixed Effects Num Den Effect DF DF Chi-Square F Value Pr > ChiSq Pr > F age <.0001 <.0001 age140plus <.0001 <.0001
8 Plot of observed and predicted vs age curve - model 2 Subject numbers 16, 18, Predicted age id id Fit statistics for different knot locations based on model 2 5 Obs Descr value130 value135 value140 value145 value Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better)
9 Model 3: Broken stick model with knot at 14 & covariates 6 With random intercepts and slopes before and after knot Model Information Data Set Dependent Variable Covariance Structure Subject Effect Estimation Method Residual Variance Method Fixed Effects SE Method Degrees of Freedom Method WORK.FEV Unstructured id ML Profile Model-Based Containment Class Level Information Class Levels Values id 299 not printed Dimensions Covariance Parameters 7 Columns in X 6 Columns in Z Per Subject 3 Subjects 299 Max Obs Per Subject 12 Number of Observations Number of Observations Read 1993 Number of Observations Used 1993 Number of Observations Not Used 0 Iteration History Iteration Evaluations -2 Log Like Criterion Convergence criteria met.
10 Model 3: Broken stick model with knot at 14 & covariates 7 With random intercepts and slopes before and after knot Covariance Parameter Estimates Z Cov Parm Subject Estimate Error Value Pr Z UN(1,1) id <.0001 UN(2,1) id <.0001 UN(2,2) id <.0001 UN(3,1) id UN(3,2) id <.0001 UN(3,3) id <.0001 Residual <.0001 Fit Statistics -2 Log Likelihood -466 AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) Null Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq <.0001 Solution for Fixed Effects Effect Estimate Error DF t Value Pr > t Intercept <.0001 age <.0001 age140plus <.0001 baseage loght <.0001 logbht Type 3 Tests of Fixed Effects Num Den Effect DF DF Chi-Square F Value Pr > ChiSq Pr > F age <.0001 <.0001 age140plus <.0001 <.0001 baseage loght <.0001 <.0001
11 Model 3: Broken stick model with knot at 14 & covariates 8 With random intercepts and slopes before and after knot Type 3 Tests of Fixed Effects Num Den Effect DF DF Chi-Square F Value Pr > ChiSq Pr > F logbht Model 4: Broken stick model with knot at 14 & covariates 9 With random intercepts and slopes and residual spatial covariance Model Information Data Set Dependent Variable Covariance Structures Subject Effects Estimation Method Residual Variance Method Fixed Effects SE Method Degrees of Freedom Method WORK.FEV Unstructured, Spatial Gaussian id, id ML Profile Model-Based Containment Class Level Information Class Levels Values id 299 not printed Dimensions Covariance Parameters 8 Columns in X 6 Columns in Z Per Subject 3 Subjects 299 Max Obs Per Subject 12 Number of Observations Number of Observations Read 1993 Number of Observations Used 1993 Number of Observations Not Used 0 Convergence criteria met.
12 Model 4: Broken stick model with knot at 14 & covariates 10 With random intercepts and slopes and residual spatial covariance Covariance Parameter Estimates Z Cov Parm Subject Estimate Error Value Pr Z UN(1,1) id <.0001 UN(2,1) id UN(2,2) id UN(3,1) id UN(3,2) id UN(3,3) id SP(GAU) id <.0001 Residual <.0001 Fit Statistics -2 Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) Null Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq <.0001 Solution for Fixed Effects Effect Estimate Error DF t Value Pr > t Intercept <.0001 age <.0001 age140plus <.0001 baseage loght <.0001 logbht Type 3 Tests of Fixed Effects Num Den Effect DF DF Chi-Square F Value Pr > ChiSq Pr > F age <.0001 <.0001 age140plus <.0001 <.0001 baseage
13 Model 4: Broken stick model with knot at 14 & covariates 11 With random intercepts and slopes and residual spatial covariance Type 3 Tests of Fixed Effects Num Den Effect DF DF Chi-Square F Value Pr > ChiSq Pr > F loght <.0001 <.0001 logbht
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