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## Applied Longitudianal Data Analysis

by: Jordane Kemmer

20

0

18

# Applied Longitudianal Data Analysis ST 732

Marketplace > North Carolina State University > Statistics > ST 732 > Applied Longitudianal Data Analysis
Jordane Kemmer
NCS
GPA 3.79

Staff

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COURSE
PROF.
Staff
TYPE
Class Notes
PAGES
18
WORDS
KARMA
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## Popular in Statistics

This 18 page Class Notes was uploaded by Jordane Kemmer on Thursday October 15, 2015. The Class Notes belongs to ST 732 at North Carolina State University taught by Staff in Fall. Since its upload, it has received 20 views. For similar materials see /class/223963/st-732-north-carolina-state-university in Statistics at North Carolina State University.

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Date Created: 10/15/15
Choice Among Models 0 Recall Yz Xz Zz bz 6239 with bi N MVNq0G and ei N MVNni0R 031 o How to choose which columns of X1 should be in Zi 0 Start with simplest effects intercept main effects of the different factors then consider interactions Decide on best fit by either 0 likelihood ratio test REML using tables and approxima tions from Fitzmaurice Laird and Ware a minimum AIC my recommendation Prediction of Random Effects o The fixed effects parameters in are almost always of inter est Statistical inferences are made about by estimation and testing 0 We may also be interested in the per subject random effects bi eg to forecast the future trajectory for a subject 0 These are random variables not parameters so we talk about predicting them either by point predictors or prediction in tervals Best Linear Unbiased Predictor BLUP c From general arguments best predictor is Easing 2222 1 lter X13 where 2 CovYZ ZZGZZZRZgt and B is the GLS estimator o This is a linear function of Y so it is also the BLUP c We don t know G and Bi and we can t calculate the GLS estimator of so we replace them all by REML estimates to get the empirical BLUP Case study Six Cities Study Response is FEVl 0 Data are a subset of 300 girls from Topeka Kansas Occasions are annual examinations 0 One outlier is excluded The SAS program title FEVl data from the Six Cities Study options linesize 80 pagesize 21 nodate data fevl infile fev1tXt firstobs 43 input ID Height Age InitialHeight InitialAge LogFEVl LogHeight logHeight InitialLogHeight logInitialHeight run proc mixed data fevl where ID 197 class ID model LogFEVl Age LogHeight InitialAge InitialLogHeight solution chisq random intercept age type un subject ID G V solution run SAS output FEV1 data from the Six Cities Study The Mixed Procedure Model Information Data Set WORKFEV1 Dependent Variable LogFEVl Covariance Structure Unstructured Subject Effect ID Estimation Method REML Residual Variance Method Profile Fixed Effects SE Method ModelBased Degrees of Freedom Method Containment Class ID FEV1 data from the Six Cities Class Level Information Levels 299 The Mixed Procedure Values 94 103 104 105 110 111 112 117 118 119 98 Study 10 20 30 40 50 60 70 80 90 100 101 102 106 107 108 109 113 114 115 116 120 121 122 123 FEV1 data from the Six Cities Study The Mixed Procedure 124 131 138 145 152 159 166 173 180 187 194 202 209 216 223 230 237 125 132 139 146 153 160 167 174 181 188 195 203 210 217 224 231 238 126 133 140 147 154 161 168 175 182 189 196 204 211 218 225 232 239 127 134 141 148 155 162 169 176 183 190 198 205 212 219 226 233 240 128 135 142 149 156 163 170 177 184 191 199 206 213 220 227 234 241 129 136 143 150 157 164 171 178 185 192 200 207 214 221 228 235 242 130 137 144 151 158 165 172 179 186 193 201 208 215 222 229 236 243 FEV1 data from the Six Cities Study The Mixed Procedure 244 245 246 247 248 249 251 252 253 254 255 256 258 259 260 261 262 263 265 266 267 268 269 270 272 273 274 275 276 277 279 280 281 282 283 284 286 287 288 289 290 291 293 294 295 296 297 298 300 Dimensions Covariance Parameters Columns in X Columns in Z Per Subject Subjects 2 LOMO1rlgt L0 250 257 264 271 278 285 292 299 10 Iteration DMD 0 FEV1 data from the Six Cities Study The Mixed Procedure Dimensions Max Obs Per Subject Observations Used Observations Not Used Total Observations Iteration History Evaluations 1 2 1 1 2 Res Log Like 296145030802 456761910964 456788023186 456788194328 12 1993 1993 Criterion 000006041 000000041 000000000 11 FEV1 data from the Six Cities Study The Mixed Procedure Convergence criteria met Estimated G Matrix Row Effect ID Coll 0012 1 Intercept 1 001221 000043 2 Age 1 000043 0000050 Estimated V Matrix for ID 1 Row Coll Col2 Col3 Col4 Col5 Col6 0017 1 001213 0008536 0008573 0008609 0008643 0008716 0008748 2 0008536 001226 0008722 0008811 0008895 0009076 0009156 12 FEV1 data from the Six Cities Study The Mixed Procedure Estimated V Matrix for ID 1 Row 0011 0012 0013 0014 0015 0016 0017 3 0008573 0008722 001250 0009014 0009149 0009440 0009567 4 0008609 0008811 0009014 001284 0009391 0009785 0009957 5 0008643 0008895 0009149 0009391 001325 001011 001033 6 0008716 0009076 0009440 0009785 001011 001445 001113 7 0008748 0009156 0009567 0009957 001033 001113 001510 00variance Parameter Estimates 00v Parm Subject Estimate UN11 ID 001221 UN21 ID 000043 13 FEVl data from the Six Cities Study The Mixed Procedure Covariance Parameter Estimates Cov Parm Subject Estimate UN22 ID 0000050 Residual 0003629 Fit Statistics 2 Res Log Likelihood 45679 AIC smaller is better 45599 AICC smaller is better 45599 BIC smaller is better 45451 Effect Intercept Age LogHeight InitialAge InitialLogHeight FEV1 data from the Six Cities Study The Mixed Procedure Null Model Likelihood Ratio Test DF ChiSquare Pr gt ChiSq 3 160643 lt0001 Solution for Fixed Effects Standard Estimate Error DF t Value 02883 003872 297 745 002353 0001395 251 1686 22372 004354 1440 5139 001651 0007458 1440 221 02182 01455 1440 150 Prgt t OOAAA 15 0001 0001 0001 0270 1340 Effect Intercept Age Intercept Age Intercept Age Intercept Age Intercept Age Intercept Age ID 03030101HgtAgtCDCDMMHH FEV1 data from the Six Cities Study The Mixed Procedure Solution for Random Effects Estimate 0004422 0000149 01820 000927 02440 001212 008905 0004137 004921 000746 003390 000262 Std Err Pred 007358 0005533 006033 0004318 005798 0004773 005540 0004497 006093 0004326 005558 0004393 DF 1440 1440 1440 1440 1440 1440 1440 1440 1440 1440 1440 1440 Value OOI OOI MFPMOOOO O39l 4s Prgt t 9521 9786 0026 0320 0001 0112 1082 3577 4194 0847 5419 5504 OOOOOOOAOOOO C71 10 Effect Age LogHeight InitialAge InitialLogHeight FEV1 data from the Six Cities Study The Mixed Procedure Type 3 Tests of Fixed Effects Num Den DF DF ChiSquare F Value 1 251 28434 28434 1 1440 264050 264050 1 1440 490 490 1 1440 225 225 Pr gt ChiSq lt0001 lt0001 00269 01337 17 Pr gt F lt0001 lt0001 00270 01340 Fit statistics Random effects 2 REML Log Likelihood AIC intercept age 45679 45599 intercept 44941 44901 intercept LogHeight 45895 45815 intercept Age LogHeight 45899 45759 18

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