07 Lecture 04 RandomCoeffReg

07 Lecture 04 RandomCoeffReg - EXST7025 Biological...

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Unformatted text preview: EXST7025 : Biological Population Statistics II Random coefficients regression Geaghan Page 1 Random coefficients model Yij = β0 + si + (β 1 + di)Xij + eij Note that the βk are fixed estimates of the population average the dependent variable is Yij Xij is the independent variable eij the residual term si is the random effect of subjects on the intercept di is the random effect of subjects on the slope The random components are assumed to be NIDrv(0, σ2) where the variances are σs2 for si, σd2 for di and σ2 for eij In a drug experiment where there are “i” subjects and “j” doses of a drug the new terms with the “i” subscript allow estimating the response for a particular patient. So there are two levels of interest β0 + β1Xij gives the population average slope and intercept β0 + si + (β 1 + di)Xij gives the values for a particular patient These are loosely related to the concepts of “broad inference space” and “narrow inference space”. Broad inference space refers to inference made about average performance made across many categories (e.g. all possible subjects under a wide range of conditions) while narrow inference space defines a smaller subset of conditions of interest. The original model Yij = β0 + si + (β 1 + di)Xij + eij Can also be expressed as a somewhat more familiar form Yij = β0 + β1Xij + e*ij where e*ij = si + di + eij Y Note: 1) raw data may appear to have nonhomogeneous variance is the lines diverge from a common origin. X EXST7025 : Biological Population Statistics II Random coefficients regression Geaghan Page 2 1 /*********************************************************************/ 2 /*** Geaghan MS Thesis Flier data ***/ 3 /*********************************************************************/ 4 dm'log;clear;output;clear'; 5 OPTIONS NOCENTER PS=512 LS=111 NODATE NONUMBER nolabel; 6 *ODS HTML style=minimal body='C:\Geaghan\Current\EXST7025\Spring2008\SAS\RandCoeff\FlierGrowth.html'; 7 8 ods graphics on; NOTE: ODS Statistical Graphics will require a SAS/GRAPH license when it is declared production. 9 10 LIBNAME SASDATA 'C:\Geaghan\Current\EXST7025\Spring2008\SAS\RandCoeff\'; NOTE: Libref SASDATA was successfully assigned as follows: Engine: V9 Physical Name: C:\Geaghan\Current\EXST7025\Spring2008\SAS\RandCoeff 11 FILENAME INPUT 'C:\Geaghan\Current\EXST7025\Spring2008\SAS\RandCoeff\ONEper.csv'; 12 TITLE1 'Growth Curves fitted to Flier sunfish'; 13 14 DATA Flier (keep=sasdate fno age time size lt ar st md sex Age_Days time scale) 15 Original (keep=sasdate fno age lt ar st md sex Age_Days tsl); 16 infile input missover delimiter="," firstobs=2; 17 input Mo Day Yr Ar St Md sx sex $ Sn Dayno Age Age_Days Lt Wt TSL 18 Size1 Size2 Size3 Size4 Size5 Size6 Edge EdgeGrow K FNO; 19 sasdate = mdy(mo,day,yr); format sasdate date7.; 20 if lt gt 14.0 and wt lt 20 then wt = .; 21 IF AGE EQ . THEN DELETE; 22 IF LT EQ . THEN DELETE; 23 IF LT EQ 0 THEN DELETE; 24 IF TSL EQ . THEN DELETE; 25 output original; 26 array sl [6] size1 - size6; 27 do Year = 1 to 6 by 1; 28 TIME = year; 29 if edge gt 0 then size = lt * sl(year) / edge; 30 else size = .; 31 scale = sl(year); 32 if scale eq . then delete; 33 if age ne 0 and year le age then output flier; 34 end; 35 RUN;e NOTE: The infile INPUT is: File Name=C:\Geaghan\Current\EXST7025\Spring2008\SAS\RandCoeff\ONEper.csv, RECFM=V,LRECL=256e NOTE: 664 records were read from the infile INPUT. The minimum record length was 66. The maximum record length was 114. NOTE: The data set WORK.FLIER has 1680 observations and 12 variables. NOTE: The data set WORK.ORIGINAL has 664 observations and 10 variables. NOTE: DATA statement used (Total process time): real time 0.17 seconds cpu time 0.03 secondse 36 37 proc freq data=original; table age*sex / norow nocol nopercent; run;e NOTE: There were 664 observations read from the data set WORK.ORIGINAL. NOTE: The PROCEDURE FREQ printed page 1. NOTE: PROCEDURE FREQ used (Total process time): real time 0.07 seconds cpu time 0.03 secondse 38 39 proc sort data=flier; by fno time; run;e NOTE: There were 1680 observations read from the data set WORK.FLIER. NOTE: The data set WORK.FLIER has 1680 observations and 12 variables. NOTE: PROCEDURE SORT used (Total process time): real time 0.01 seconds cpu time 0.01 secondse 40 proc sort data=original; by fno age; run;e NOTE: There were 664 observations read from the data set WORK.ORIGINAL. EXST7025 : Biological Population Statistics II Random coefficients regression Geaghan Page 3 NOTE: The data set WORK.ORIGINAL has 664 observations and 10 variables. NOTE: PROCEDURE SORT used (Total process time): real time 0.01 seconds cpu time 0.00 seconds 43 44 OPTIONS PS=52 LS=111; 45 proc plot data=original; plot lt*age_days; run;e NOTE: There were 664 observations read from the data set WORK.ORIGINAL. NOTE: The PROCEDURE PLOT printed page 2. NOTE: PROCEDURE PLOT used (Total process time): real time 0.06 seconds cpu time 0.03 secondse 46 proc plot data=original; plot tsl*age_days; run;e NOTE: There were 664 observations read from the data set WORK.ORIGINAL. NOTE: The PROCEDURE PLOT printed page 3. NOTE: PROCEDURE PLOT used (Total process time): real time 0.04 seconds cpu time 0.04 secondse 47 proc plot data=flier; plot size*time; run;e NOTE: There were 1680 observations read from the data set WORK.FLIER. NOTE: The PROCEDURE PLOT printed page 4. NOTE: PROCEDURE PLOT used (Total process time): real time 0.04 seconds cpu time 0.03 secondse 48 proc plot data=flier; plot scale*time; run;e 49 OPTIONS PS=512 LS=111; NOTE: There were 1680 observations read from the data set WORK.FLIER. NOTE: The PROCEDURE PLOT printed page 5. NOTE: PROCEDURE PLOT used (Total process time): real time 0.06 seconds cpu time 0.04 secondse Growth Curves fitted to Flier sunfish The FREQ Procedure Table of Age by sex Age sex Frequency|F |I |M | ---------+--------+--------+--------+ 0 | 3 | 2 | 15 | ---------+--------+--------+--------+ 1 | 42 | 7 | 45 | ---------+--------+--------+--------+ 2 | 104 | 2 | 90 | ---------+--------+--------+--------+ 3 | 144 | 5 | 97 | ---------+--------+--------+--------+ 4 | 39 | 1 | 49 | ---------+--------+--------+--------+ 5 | 5 | 1 | 8 | ---------+--------+--------+--------+ 6 | 3 | 0 | 2 | ---------+--------+--------+--------+ Total 340 18 306 Total 20 94 196 246 89 14 5 664 EXST7025 : Biological Population Statistics II Random coefficients regression Geaghan Page 4 Growth Curves fitted to Flier sunfish Plot of Lt*Age_Days. Legend: A = 1 obs, B = 2 obs, etc. Lt | 20 + | | | A 18 + A A | A AA | A AA A A | AC A A A A 16 + A CA AEAB A A A | A CA AB A B AAA A A B | B A BA BB C CAA F A AA B | A B B C C AB DCAA F A CB A 14 + B AA A AE D A F BE F F C A | A A C CA A A FADA B E GCC I D A | A CAF A A ABAH FA A H J A I B A | A DAFA AAAAB CAI EA A EA OAA D BA 12 + I H A AA AD E F C L A | A A C BC DB AADAG BA A B E | AA F AA C A AEAF D A | A AA AGAAB AAB AD G A 10 + B AA BAA O BA BCAA B A A | D DA B F A AAA | CAAA C B A F A A A A | EB C B A 8 + KA A BB | A L A A | B C D | A B C A 6 + B A D A | AA A | | 4 + | A | | 2 + | ---+------------+------------+------------+------------+------------+------------+------------+-0 1 2 3 4 5 6 7 Age_Days Growth Curves fitted to Flier sunfish Plot of TSL*Age_Days. Legend: A = 1 obs, B = 2 obs, etc. TSL | 450 + | | | A 400 + | | A A | A A 350 + A AB AG | A D DAA C B A A A A | A CDC BC A H A AA A | A A C ABD D CB A G A C A A A 300 + B B C AABD AAB DBCC J BBA AB | C EA A A F F C F AGAB C A FA A A | GAFA AAAAA M FA A L DBB C C A | CAB AAAA ABG FB FA O C A 250 + A G IC B B A BAF EA D Q A C | AA A FAD BBA BD J A A K A A | A E CA D A ABFAG B | AA AA H AD BAAA G F A A A 200 + A B D A AM A ACB A | A B CB A A K A AA A | A EC A D AAA B A A A | IAA A ABA A A 150 + N A | B A H A A | A A B D A | B B C 100 + A | A A | A | A 50 + | | | 0 + A A B | ---+------------+------------+------------+------------+------------+------------+------------+-0 1 2 3 4 5 6 7 Age_Days Growth Curves fitted to Flier sunfish EXST7025 : Biological Population Statistics II Random coefficients regression Geaghan Page 5 Plot of size*TIME. Legend: A = 1 obs, B = 2 obs, etc. size | 18 + A | | A | A A | B A B A 16 + C B | C B A | D F D A | A G D D A | K D A 14 + A L K A | B Q N A | H U P C | L Y J | Q Z Q A 12 + Y Z I | P Z H | Z Z B | Z Z A | Z T 10 + Z P | B Z L | F Z F | P Z A | Z Z 8 + Z Z | Z U | Z L | Z K | Z B 6 + Z | Z | Z | Z | Z 4 + T | H | I | G ---+----------------+----------------+----------------+----------------+----------------+-1 2 3 4 5 6 TIME NOTE: 542 obs hidden. Growth Curves fitted to Flier sunfish Plot of scale*TIME. Legend: A = 1 obs, B = 2 obs, etc. scale | 180 + A | | | A | A 160 + | A C A | G B A A | D E C | F I B A 140 + K I C | A N S D | B O R A | K Z N B | Q Z K A 120 + U Z K A | W Z D | Z Z B | Z Z | Z Y A 100 + Z M | Z C | C Z A | I Z A | X Z B 80 + Z Z | Z Q | Z L | Z C | Z B 60 + Z B | Z | Z | Z | X 40 + Q | L | G | E | A 20 + ---+----------------+----------------+----------------+----------------+----------------+-1 2 3 4 5 6 TIME NOTE: 608 obs hidden. EXST7025 : Biological Population Statistics II Random coefficients regression 51 52 53 54 55 NOTE: NOTE: NOTE: NOTE: NOTE: NOTE: NOTE: Geaghan Page 6 PROC NLIN DATA=original maxiter=1000; TITLE2 'TRADITIONAL vBert'; PARAMETERS LINF=300 K=-0.55 T0=-0.05; MODEL TSL = LINF*(1 - EXP(K*(Age_Days - T0))); RUN;e DER.LINF not initialized or missing. It will be computed automatically. DER.K not initialized or missing. It will be computed automatically. DER.T0 not initialized or missing. It will be computed automatically. PROC NLIN grid search time was 0: 0: 0. Convergence criterion met. The PROCEDURE NLIN printed page 6. PROCEDURE NLIN used (Total process time): real time 0.12 seconds cpu time 0.03 secondse Growth Curves fitted to Flier sunfish TRADITIONAL vBert The NLIN Procedure Dependent Variable TSL Method: Gauss-Newton Iterative Phase Iter LINF K T0 Sum of Squares 0 1 2 3 300.0 321.5 321.3 321.3 -0.5500 -0.5649 -0.5657 -0.5658 -0.0500 -0.0500 -0.0472 -0.0470 1035943 794199 794189 794189 NOTE: Convergence criterion met. Estimation Summary Method Iterations R PPC(T0) RPC(T0) Object Objective Observations Read Observations Used Observations Missing Source Model Error Corrected Total Parameter LINF K T0 Estimate 321.3 -0.5658 -0.0470 Gauss-Newton 3 7.046E-6 0.000298 0.002678 4.707E-9 794188.8 664 664 0 DF 2 661 663 Sum of Squares 1590409 794189 2384597 Approx Std Error 6.9895 0.0502 0.0865 1.0000000 0.9385081 -0.7336334 0.9385081 1.0000000 -0.8967642 F Value 661.85 Approx Pr > F <.0001 Approximate 95% Confidence Limits 307.6 335.0 -0.6643 -0.4673 -0.2169 0.1228 Approximate Correlation Matrix LINF K LINF K T0 Mean Square 795204 1201.5 T0 -0.7336334 -0.8967642 1.0000000 EXST7025 : Biological Population Statistics II Random coefficients regression 57 58 59 60 61 NOTE: NOTE: NOTE: NOTE: Geaghan Page 7 proc nlmixed data=original; PARAMETERS LINF=323.43 T0=-0.07202 K=-0.55; pred = Linf*(1 - exp(K*(age_days - T0))); MODEL TSL ~ normal(pred, S2); run; GCONV Convergence criterion satisfied. At least one element of the (projected) gradient is greater than 1e-3. The PROCEDURE NLMIXED printed page 7. PROCEDURE NLMIXED used (Total process time): real time 0.20 seconds cpu time 0.12 secondse Growth Curves fitted to Flier sunfish TRADITIONAL vBert The NLMIXED Procedure Specifications Data Set Dependent Variable Distribution for Dependent Variable Optimization Technique Integration Method Dimensions Observations Used Observations Not Used Total Observations Parameters Parameters LINF T0 323.43 -0.07202 WORK.ORIGINAL TSL Normal Dual Quasi-Newton None 664 0 664 4 K -0.55 S2 1 NegLogLike 397758.101 Iteration History Iter Calls NegLogLike Diff MaxGrad 1 8 62809.7143 334948.4 187787.2 2 15 49964.4458 12845.27 24296.68 3 19 49961.0891 3.356659 22196.56 4 21 48817.8901 1143.199 36352.15 5 24 27766.4292 21051.46 34454.47 . . . 43 95 3294.99169 0.00098 2.605808 44 96 3294.99118 0.000513 1.840554 45 98 3294.9909 0.000276 0.008116 46 100 3294.9909 3.129E-7 0.001377 NOTE: GCONV Convergence criterion satisfied. Fit Statistics -2 Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) Slope -1.575E9 -3.999E8 -1559.89 -2511.48 -1746.1 -0.00094 -0.00065 -0.00054 -5.46E-7 6590.0 6598.0 6598.0 6616.0 Parameter Estimates Parameter LINF T0 K S2 Estimate 321.31 -0.04702 -0.5658 1196.07 Standard Error 7.3375 0.09044 0.05301 65.6427 DF 664 664 664 664 t Value 43.79 -0.52 -10.67 18.22 Pr > |t| <.0001 0.6033 <.0001 <.0001 Alpha 0.05 0.05 0.05 0.05 Lower 306.90 -0.2246 -0.6699 1067.17 Upper 335.71 0.1306 -0.4617 1324.96 Gradient 7.29E-6 -0.00002 -0.00138 -1.6E-7 EXST7025 : Biological Population Statistics II Random coefficients regression 63 64 65 66 67 NOTE: NOTE: NOTE: NOTE: NOTE: NOTE: NOTE: Geaghan Page 8 PROC NLIN DATA=flier maxiter=1000; TITLE2 'TRADITIONAL vBert'; PARAMETERS LINF=155 T0=-0.08 K=-0.47; MODEL scale = LINF*(1 - EXP(K*(TIME - T0))); RUN;e DER.LINF not initialized or missing. It will be computed automatically. DER.T0 not initialized or missing. It will be computed automatically. DER.K not initialized or missing. It will be computed automatically. PROC NLIN grid search time was 0: 0: 0. Convergence criterion met. The PROCEDURE NLIN printed page 8. PROCEDURE NLIN used (Total process time): real time 0.12 seconds cpu time 0.01 secondse Growth Curves fitted to Flier sunfish TRADITIONAL vBert The NLIN Procedure Dependent Variable scale Method: Gauss-Newton Iterative Phase Iter LINF T0 0 155.0 -0.0800 1 155.3 -0.0804 2 155.3 -0.0802 NOTE: Convergence criterion met. K -0.4700 -0.4736 -0.4737 Sum of Squares 275623 275026 275026 Estimation Summary Method Iterations R PPC(T0) RPC(T0) Object Objective Observations Read Observations Used Observations Missing Gauss-Newton 2 7.745E-7 0.000016 0.001288 7.927E-9 275025.5 1680 1680 0 NOTE: An intercept was not specified for this model. Source Model Error Uncorrected Total Parameter LINF T0 K Estimate 155.3 -0.0802 -0.4737 DF 3 1677 1680 Sum of Squares 15126125 275026 15401150 Approx Std Error 3.4534 0.0434 0.0295 Approximate Correlation Matrix LINF T0 LINF 1.0000000 -0.8321404 T0 -0.8321404 1.0000000 K 0.9696849 -0.9312146 Mean Square 5042042 164.0 F Value 30744.4 Approx Pr > F <.0001 Approximate 95% Confidence Limits 148.5 162.1 -0.1654 0.00489 -0.5315 -0.4159 K 0.9696849 -0.9312146 1.0000000 EXST7025 : Biological Population Statistics II Random coefficients regression Geaghan Page 9 69 proc nlmixed data=flier; 70 PARAMETERS LINF=155.73 T0=-0.08535 K=-0.47; 71 pred = Linf*(1 - exp(K*(time - T0))); 72 MODEL scale ~ normal(pred, S2); 73 run; NOTE: GCONV Convergence criterion satisfied. NOTE: The PROCEDURE NLMIXED printed page 9. NOTE: PROCEDURE NLMIXED used (Total process time): real time 0.26 seconds cpu time 0.18 secondse Growth Curves fitted to Flier sunfish TRADITIONAL vBert The NLMIXED Procedure Specifications Data Set Dependent Variable Distribution for Dependent Variable Optimization Technique Integration Method Dimensions Observations Used Observations Not Used Total Observations Parameters Parameters LINF T0 155.73 -0.08535 WORK.FLIER scale Normal Dual Quasi-Newton None 1680 0 1680 4 K -0.47 S2 1 NegLogLike 139057.865 Iteration History Iter Calls NegLogLike Diff MaxGrad 1 7 28495.0678 110562.8 130348 2 14 25355.7917 3139.276 20925.55 3 18 25341.9711 13.82051 18082.69 4 21 24260.7049 1081.266 54651.73 5 23 17096.3322 7164.373 10981.98 . . . 32 68 6666.19821 0.01533 6.492262 33 70 6666.19571 0.002503 3.747867 34 72 6666.19564 0.000063 0.00866 35 74 6666.19564 8.382E-8 0.000748 NOTE: GCONV Convergence criterion satisfied. Fit Statistics -2 Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) Slope -1.868E8 -1.937E8 -9792.26 -653.42 -1524.83 -0.0205 -0.00475 -0.00013 -1.61E-7 13332 13340 13340 13362 Parameter Estimates Parameter LINF T0 K S2 Estimate 155.31 -0.08025 -0.4737 163.71 Standard Error 3.4767 0.04367 0.02970 5.6484 DF 1680 1680 1680 1680 t Value 44.67 -1.84 -15.95 28.98 Pr > |t| <.0001 0.0663 <.0001 <.0001 Alpha 0.05 0.05 0.05 0.05 Lower 148.49 -0.1659 -0.5320 152.63 Upper 162.13 0.005414 -0.4154 174.78 Gradient -8.37E-6 -0.00075 -0.00029 4.299E-6 EXST7025 : Biological Population Statistics II Random coefficients regression Geaghan Page 10 75 proc sort data=flier; by fno; run;e NOTE: Input data set is already sorted, no sorting done. NOTE: PROCEDURE SORT used (Total process time): real time 0.00 seconds cpu time 0.00 secondse 76 data flier1; set flier; if age gt 2; run;e NOTE: There were 1680 observations read from the data set WORK.FLIER. NOTE: The data set WORK.FLIER1 has 1194 observations and 12 variables. NOTE: DATA statement used (Total process time): real time 0.00 seconds cpu time 0.00 secondse 77 PROC NLIN DATA=flier1 noprint maxiter=1000 outest=parmest; by fno; 78 TITLE2 'TRADITIONAL vBert'; 79 PARAMETERS LINF=155 T0=-0.08 K=-0.47; 80 MODEL scale = LINF*(1 - EXP(K*(TIME - T0))); 81 RUN;e NOTE: DER.LINF not initialized or missing. It will be computed automatically. NOTE: DER.T0 not initialized or missing. It will be computed automatically. NOTE: DER.K not initialized or missing. It will be computed automatically. NOTE: PROC NLIN grid search time was 0: 0: 0. NOTE: Convergence criterion met. NOTE: The above message was for the following by-group: FNO=313 NOTE: PROC NLIN grid search time was 0: 0: 0. WARNING: PROC NLIN failed to converge. NOTE: The above message was for the following by-group: FNO=314 . . . NOTE: PROC NLIN grid search time was 0: 0: 0. NOTE: Convergence criterion met. NOTE: The above message was for the following by-group: FNO=687 NOTE: PROC NLIN grid search time was 0: 0: 0. NOTE: Convergence criterion met. NOTE: The above message was for the following by-group: FNO=688 NOTE: The data set WORK.PARMEST has 47095 observations and 9 variables. NOTE: PROCEDURE NLIN used (Total process time): real time 0.98 seconds cpu time 0.98 secondse 82 83 data ParmestIter; set parmest; if _ITER_ = 1000; keep fno _SSE_ LINF T0 K; run;e NOTE: There were 47095 observations read from the data set WORK.PARMEST. NOTE: The data set WORK.PARMESTITER has 86 observations and 5 variables. NOTE: DATA statement used (Total process time): real time 0.13 seconds cpu time 0.01 secondse 84 data ParmestFinal; set parmest; if _TYPE_ = "FINAL"; keep fno _SSE_ LINF T0 K; run;e NOTE: There were 47095 observations read from the data set WORK.PARMEST. NOTE: The data set WORK.PARMESTFINAL has 311 observations and 5 variables. NOTE: DATA statement used (Total process time): real time 0.00 seconds cpu time 0.00 secondse 85 proc sort data=ParmestIter nodupkey; by fno; run;e NOTE: There were 86 observations read from the data set WORK.PARMESTITER. NOTE: 43 observations with duplicate key values were deleted. NOTE: The data set WORK.PARMESTITER has 43 observations and 5 variables. NOTE: PROCEDURE SORT used (Total process time): real time 0.01 seconds cpu time 0.01 secondse 86 proc sort data=ParmestFinal nodupkey; by fno; run;e NOTE: There were 311 observations read from the data set WORK.PARMESTFINAL. NOTE: 0 observations with duplicate key values were deleted. NOTE: The data set WORK.PARMESTFINAL has 311 observations and 5 variables. NOTE: PROCEDURE SORT used (Total process time): EXST7025 : Biological Population Statistics II Random coefficients regression Geaghan Page 11 real time 0.01 seconds cpu time 0.01 secondse 87 proc print data=parmestIter; run;e NOTE: There were 43 observations read from the data set WORK.PARMESTITER. NOTE: The PROCEDURE PRINT printed page 10. NOTE: PROCEDURE PRINT used (Total process time): real time 0.03 seconds cpu time 0.01 secondse Growth Curves fitted to Flier sunfish TRADITIONAL vBert Obs FNO _SSE_ LINF 1 314 58.816 9609.51 2 326 210.537 9056.06 3 327 166.258 3573.75 4 338 70.151 17037.64 5 340 4.338 7418.54 6 342 76.297 5975.70 7 352 96.273 13842.37 8 354 7.284 4656.91 9 363 225.175 3702.72 10 364 87.583 3464.37 11 368 21.978 5128.44 12 369 83.085 3247.46 13 374 80.613 3546.43 14 401 75.224 3262.11 15 402 57.246 4414.74 16 404 135.462 4592.32 17 408 236.029 6663.90 18 416 73.731 3640.02 19 417 23.672 5233.71 20 418 112.028 3932.18 T0 -1.48980 -0.43065 -1.49559 -0.38990 -1.19073 -2.36235 -2.50201 -1.27031 -1.22052 -1.52257 -1.02826 -1.34399 -1.00399 -1.12125 -1.47158 -0.97075 -0.64840 -1.51707 -1.32127 -0.94144 K -.002255962 -.002765282 -.006186791 -.001773594 -.003639755 -.003023430 -.001509885 -.005581207 -.006407866 -.007142377 -.005504725 -.008120780 -.007916186 -.008540746 -.005663943 -.005778114 -.004295876 -.007006898 -.005270784 -.007218558 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 426 430 438 444 459 463 466 469 478 479 481 491 497 499 514 515 531 538 541 576 581 664 666 146.132 228.107 183.276 57.259 9.368 20.473 211.665 5.870 99.591 151.521 142.772 232.650 91.540 67.973 300.784 54.641 355.009 309.430 11.493 567.893 287.876 356.904 465.508 7075.10 6826.59 4592.16 3443.56 4066.65 3958.27 13809.11 14640.79 13286.89 5681.50 19527.35 18435.85 7575.79 4015.27 3571.73 9485.46 195358.38 8128.64 9542.90 9911.31 27769.73 47744.61 12642.51 -0.66323 -2.04940 -0.84830 -1.15979 -1.05495 -1.27664 -0.40142 -1.02250 -0.38633 -0.73416 -1.67732 -1.73015 -0.66413 -1.07341 -1.13634 -0.68734 0.38446 -1.61927 -1.46141 -1.27475 -1.33948 -1.27687 -0.94090 -.004030741 -.003391993 -.006068193 -.008208733 -.006726858 -.006975778 -.002250357 -.002035305 -.002331414 -.005046036 -.001339232 -.001414945 -.004161155 -.007387342 -.008206217 -.003355263 -.000210764 -.003243058 -.002790989 -.002953046 -.000762774 -.000577540 -.002217360 88 proc print data=parmestFinal; run;e NOTE: There were 311 observations read from the data set WORK.PARMESTFINAL. NOTE: The PROCEDURE PRINT printed page 11. NOTE: PROCEDURE PRINT used (Total process time): real time 0.03 seconds cpu time 0.01 secondse Growth Curves fitted to Flier sunfish TRADITIONAL vBert Obs FNO _SSE_ LINF T0 1 313 0.000 124.06 -0.76249 2 315 0.000 339.27 -0.26493 3 316 0.000 138.25 0.37761 4 317 0.000 120.97 0.11313 5 318 0.000 123.48 0.22580 6 319 0.000 363.59 -0.26553 7 320 0.000 144.33 -0.60498 8 321 0.000 131.37 0.37194 9 322 0.000 168.03 0.20515 10 323 0.000 124.49 0.24029 11 324 0.000 120.70 0.26429 12 325 0.000 135.16 0.45765 13 328 0.000 115.23 -0.12683 14 329 0.000 141.59 -0.17782 15 330 0.000 163.73 0.09951 16 331 0.000 159.09 0.18587 17 332 0.000 1626.88 -0.33441 18 333 0.000 171.13 -0.36884 19 334 0.000 114.53 0.43751 20 335 0.000 221.04 -0.93855 21 336 0.000 144.46 0.22122 22 337 0.000 137.78 0.18562 23 339 0.000 120.57 0.14211 24 341 0.000 132.91 0.46389 25 343 0.000 128.19 0.37772 26 344 0.000 142.04 0.19134 27 345 0.000 390.55 -1.84242 28 346 0.000 280.29 -0.57165 29 347 0.000 121.31 0.44407 30 348 0.000 142.03 0.38803 31 349 0.000 175.00 -0.39674 32 350 0.000 140.60 0.16479 33 351 0.000 138.37 -0.34978 34 353 0.000 144.99 -0.14305 35 355 0.000 127.65 0.14949 36 356 0.000 118.29 0.49871 37 357 0.000 481.06 -0.58690 K -0.30095 -0.10047 -0.47916 -0.56984 -0.49331 -0.10017 -0.34270 -0.80609 -0.35986 -0.74736 -0.67090 -0.61227 -0.61505 -0.39793 -0.38145 -0.40678 -0.02063 -0.26522 -1.15406 -0.17881 -0.49539 -0.61543 -0.84880 -0.79389 -0.81407 -0.48818 -0.07102 -0.14443 -1.05981 -0.67531 -0.27000 -0.65029 -0.47306 -0.39672 -0.79664 -1.12741 -0.07388 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 358 359 360 361 362 365 366 367 370 371 372 375 376 377 378 379 403 405 406 407 409 410 411 412 413 414 415 419 420 421 422 423 424 425 427 428 429 431 432 433 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1129.98 182.89 142.23 142.92 156.60 1178.86 1004.72 146.59 362.89 115.88 143.23 136.74 124.99 152.22 271.66 517.82 151.34 142.03 142.63 146.28 141.94 217.05 124.60 152.39 143.65 140.40 179.39 256.45 234.66 193.51 128.38 127.79 144.29 259.20 466.58 151.38 147.11 124.74 166.34 182.01 -1.10551 -0.62819 -0.28869 -0.03004 -0.18693 -1.35204 -1.06094 -0.05108 -0.81591 0.35854 -0.01919 0.13569 0.18260 0.06720 0.16547 -0.57155 0.22568 0.50226 0.13560 0.19586 -0.69742 -0.79634 0.47496 -0.15391 -0.16205 0.35222 0.10915 -0.28835 -1.09921 -0.43662 0.15311 0.62309 0.30194 -0.34606 -0.26375 0.03158 0.29376 -0.07948 -0.30377 -0.40429 -0.02686 -0.24485 -0.42337 -0.48615 -0.40174 -0.02367 -0.03047 -0.49935 -0.10356 -0.90304 -0.49741 -0.66205 -0.77767 -0.57054 -0.19506 -0.06686 -0.57405 -1.34247 -0.56512 -0.42746 -0.41410 -0.21110 -0.95538 -0.38278 -0.49092 -0.72977 -0.38983 -0.19057 -0.17017 -0.27241 -0.79354 -0.81787 -0.70238 -0.17399 -0.09720 -0.44586 -0.66666 -0.90070 -0.40026 -0.27100 EXST7025 : Biological Population Statistics II Random coefficients regression 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 434 435 436 437 439 440 441 442 443 445 446 447 448 449 450 451 452 453 454 455 456 457 458 460 461 462 464 465 467 468 470 471 472 473 474 475 476 477 480 482 483 484 485 486 487 488 489 490 492 493 494 495 496 498 500 501 502 503 504 505 506 507 508 509 510 511 512 513 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 532 533 534 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 198.73 141.87 117.67 324.06 152.88 150.95 130.47 142.34 179.75 180.33 132.45 153.51 145.52 210.34 140.21 171.37 135.44 175.77 129.09 175.09 181.95 123.68 284.42 143.22 222.34 135.31 126.18 171.15 165.70 1023.41 149.88 166.87 137.70 139.46 150.92 250.77 199.28 161.58 140.26 169.03 128.50 358.78 133.23 146.31 184.28 142.65 221.13 169.15 268.28 130.79 169.93 210.70 375.67 6809.31 264.29 154.77 157.28 355.06 165.31 143.86 400.56 254.28 154.96 174.23 149.11 1244.39 187.37 263.03 169.43 133.83 156.74 170.88 181.05 362.33 182.35 142.08 291.12 211.10 156.08 156.07 187.76 178.88 135.75 196.52 302.29 153.57 -0.33554 0.13338 0.14186 -1.42800 -0.50636 -0.08946 -0.04924 0.35187 -1.07399 -0.24207 0.11135 0.19494 0.19270 -0.34813 -0.16320 -0.25671 0.18547 0.07818 -0.04986 -0.44206 -0.15363 0.15692 0.14847 0.21202 -0.55223 0.15697 0.23386 -0.11080 0.55676 -0.00345 -0.29576 -0.87832 -0.17833 0.08541 0.29266 -0.48470 -0.25279 -0.53011 0.35698 -1.17670 0.37509 -1.00314 0.03539 0.32715 -0.31464 0.26897 -0.15438 -0.26206 -0.89039 0.08729 0.02476 -0.29606 -0.42033 -2.43976 -0.01927 0.09253 0.46845 -0.40828 0.14620 -0.50393 -0.77158 -1.00122 -0.04653 0.05765 0.48285 -1.26052 0.18722 -0.59459 0.34204 -0.10490 -0.03641 -0.05207 0.09114 -1.67771 0.02489 0.31724 -0.29396 -0.04584 0.00953 0.10608 -0.17006 0.11117 0.14895 0.11672 -1.08055 0.20498 Geaghan Page 12 -0.24941 -0.62315 -1.06058 -0.10099 -0.42356 -0.47772 -0.47335 -0.69227 -0.27685 -0.34357 -0.66382 -0.48735 -0.52291 -0.21885 -0.55269 -0.32673 -0.87852 -0.42523 -0.53960 -0.35367 -0.37302 -0.99287 -0.20979 -0.59298 -0.18629 -0.65800 -1.46570 -0.35249 -0.56380 -0.04432 -0.52828 -0.36924 -0.75724 -0.87110 -0.65723 -0.17289 -0.28778 -0.43805 -1.04070 -0.32323 -1.04496 -0.11924 -0.69784 -0.62023 -0.30560 -0.74990 -0.29153 -0.37270 -0.16847 -1.04498 -0.41265 -0.26455 -0.11929 -0.00367 -0.24780 -0.58486 -0.60762 -0.12818 -0.53548 -0.42352 -0.09907 -0.17327 -0.51413 -0.52723 -1.20017 -0.02487 -0.39932 -0.15534 -0.67012 -0.84797 -0.47249 -0.43236 -0.43380 -0.08874 -0.45306 -0.70084 -0.16685 -0.27059 -0.69825 -0.56837 -0.38397 -0.42956 -0.69341 -0.42747 -0.15378 -0.66556 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 535 536 537 539 540 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 577 578 579 580 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.020 19.526 7.338 0.876 10.927 0.107 0.068 1.253 5.167 5.778 2.234 0.003 2.334 0.011 3.566 0.015 1.365 10.718 1.807 1.144 6.090 3.349 19.435 5.966 1.908 3.230 4.358 32.390 36.384 1.384 0.052 1.727 5.896 0.026 3.628 0.115 0.686 0.217 0.343 4.438 0.200 0.390 0.035 169.86 147.63 144.25 170.05 159.00 168.36 170.04 169.99 139.63 169.12 1095.89 164.22 155.17 158.04 149.71 161.79 229.99 166.49 144.13 179.28 182.52 164.72 177.54 155.73 151.46 174.00 148.29 198.54 492.59 132.04 205.02 170.40 204.05 240.48 184.86 198.53 187.84 179.12 163.52 169.01 160.30 127.63 200.14 148.52 232.84 136.84 165.22 234.72 184.26 159.25 184.72 186.21 150.36 180.14 167.48 139.94 186.90 171.13 150.49 156.22 115.51 193.79 268.40 163.09 191.91 134.76 136.73 164.67 168.83 185.24 220.82 128.57 164.71 157.08 170.25 165.17 135.69 158.89 150.02 163.58 146.61 342.46 152.65 180.10 172.06 173.49 -0.06739 0.00080 0.06514 -0.06256 0.15169 0.37538 0.15077 -0.06238 0.08946 -0.62389 -1.04690 0.14462 0.21517 0.28902 0.34438 0.43151 -0.31612 0.17130 0.35223 0.19437 0.19391 0.24576 0.01502 0.47683 -0.32123 -0.01279 -0.02489 -0.34603 -0.63275 0.39453 -0.43333 -0.33297 -0.35668 -0.68027 0.04408 -0.70090 -0.15186 -0.05522 -0.00150 0.08504 0.40270 0.48985 -0.35951 -0.03523 -0.16293 0.09977 -0.16444 -0.19985 -1.14230 -0.06643 0.07966 0.11907 0.24637 -0.11417 -0.10086 -0.18737 -0.39723 0.07760 0.11206 0.07911 0.56210 0.05188 -1.34325 0.31928 -0.49866 -0.04808 0.56903 -0.29342 -0.01055 -0.05377 -0.57652 0.70819 0.08602 0.01982 -0.69781 -0.03315 0.31597 -0.05205 -0.08138 -0.36418 -0.30129 -2.13528 0.09584 -0.00966 -0.32944 0.28494 -0.66520 -0.45499 -0.55696 -0.42593 -0.56457 -0.86405 -0.48819 -0.44154 -1.12957 -0.35673 -0.03236 -0.56260 -0.86226 -0.54894 -0.84608 -0.82394 -0.25629 -0.82399 -1.09039 -0.62521 -0.57382 -0.91337 -0.63656 -0.84631 -0.47145 -0.47823 -0.79700 -0.42525 -0.09367 -1.17415 -0.40978 -0.54272 -0.31787 -0.24878 -0.45028 -0.31714 -0.50835 -0.49217 -0.64734 -0.70571 -1.18787 -0.97334 -0.35637 -0.38800 -0.19024 -0.49740 -0.31786 -0.19961 -0.20468 -0.36459 -0.31062 -0.27711 -0.52769 -0.28498 -0.30952 -0.44794 -0.26490 -0.37484 -0.54793 -0.37475 -0.95019 -0.30203 -0.12347 -0.43066 -0.22818 -0.50373 -0.79428 -0.35842 -0.35633 -0.32068 -0.21548 -0.93330 -0.50442 -0.50483 -0.32896 -0.38949 -0.62540 -0.51480 -0.40974 -0.33330 -0.52136 -0.07237 -0.65346 -0.33420 -0.34485 -0.46882 EXST7025 : Biological Population Statistics II Random coefficients regression 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 665 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 0.077 1.905 0.813 0.001 2.344 1.799 6.555 7.167 0.698 4.339 3.809 2.143 0.196 17.638 0.558 0.524 1.004 0.051 0.552 0.148 34.570 24.856 6.417 0.039 6.308 3.124 1.947 11.658 3.096 0.420 1.202 0.709 2.039 6.894 11.676 16.230 2.359 26.906 2.486 34.016 9.979 0.519 10.250 102.635 47.687 19.686 4.343 9.368 19.966 8.400 53.583 276.801 190.994 5.484 13.880 157.405 10.020 10.415 1.802 23.457 52.038 105.652 136.00 163.96 161.01 141.57 155.23 3217.00 344.00 224.37 179.65 165.81 202.10 145.37 215.58 145.38 645.29 309.00 192.81 347.61 411.95 191.82 120.69 287.92 163.54 149.65 197.68 200.03 163.26 203.68 155.00 230.77 183.44 186.72 150.22 142.66 741.25 181.24 162.08 213.86 158.82 158.94 183.46 243.31 189.43 204.47 182.43 187.93 174.50 159.06 173.72 198.90 179.22 205.32 201.24 221.30 214.22 234.84 300.23 151.56 222.86 217.05 209.70 504.19 -0.11674 -0.37015 0.08594 0.43732 -0.14192 -1.49362 -0.62944 0.41542 -0.13061 0.04733 0.09189 0.27140 0.01380 0.14116 -1.53102 -0.79213 0.11677 -0.55096 -0.81295 -0.13044 0.20915 -1.40690 -0.72147 0.29364 -0.15038 0.01117 0.00649 -0.12770 -0.06944 -0.19314 0.12091 -1.28271 -0.10989 0.33935 -1.30220 -0.10623 0.49893 -0.19099 0.10072 -0.10748 -0.07832 -1.22875 -0.17618 -0.15502 0.05817 -0.05474 -1.04074 -0.29341 0.39007 -0.03279 0.47597 0.05718 0.38133 -0.08007 -0.34354 -0.67723 -0.90557 0.30761 -0.31920 -0.03339 0.48958 -0.81571 Geaghan Page 13 -0.72526 -0.37261 -0.41579 -0.95649 -0.41913 -0.00811 -0.09996 -0.24483 -0.31601 -0.42192 -0.28793 -0.76655 -0.29568 -0.64172 -0.04206 -0.11692 -0.32057 -0.11069 -0.07951 -0.32736 -0.90631 -0.13851 -0.29257 -0.68567 -0.32399 -0.35066 -0.51233 -0.32190 -0.50047 -0.22302 -0.38334 -0.24295 -0.78488 -0.81371 -0.04005 -0.34611 -0.60576 -0.26493 -0.71685 -0.58239 -0.47699 -0.17057 -0.36302 -0.22823 -0.25117 -0.21199 -0.22809 -0.41108 -0.35243 -0.22880 -0.36448 -0.26591 -0.29796 -0.20591 -0.19210 -0.17989 -0.12190 -0.54276 -0.14373 -0.20340 -0.28191 -0.06611 EXST7025 : Biological Population Statistics II Random coefficients regression Geaghan Page 14 90 proc univariate data=ParmestFinal plot normal; var linf t0 k; run;e NOTE: The PROCEDURE UNIVARIATE printed pages 12-14. NOTE: PROCEDURE UNIVARIATE used (Total process time): real time 0.12 seconds cpu time 0.03 secondse Growth Curves fitted to Flier sunfish TRADITIONAL vBert The UNIVARIATE Procedure Variable: LINF Moments N Mean Std Deviation Skewness Uncorrected SS Coeff Variation 311 241.57709 444.603569 11.6925145 79428224.9 184.042108 Sum Weights Sum Observations Variance Kurtosis Corrected SS Std Error Mean Basic Statistical Measures Location Variability Mean 241.5771 Std Deviation Median 166.8741 Variance Mode . Range Interquartile Range Tests for Location: Mu0=0 Test -StatisticStudent's t t 9.582151 Sign M 155.5 Signed Rank S 24258 -----p Value-----Pr < W <0.0001 Pr > D <0.0100 Pr > W-Sq <0.0050 Pr > A-Sq <0.0050 -----Highest----Value Obs 1178.86 43 1244.39 143 1626.88 17 3217.00 255 6809.31 131 Histogram 444.60357 197672 6695 55.81139 -----p Value-----Pr > |t| <.0001 Pr >= |M| <.0001 Pr >= |S| <.0001 Tests for Normality Test --Statistic--Shapiro-Wilk W 0.192596 Kolmogorov-Smirnov D 0.387534 Cramer-von Mises W-Sq 16.7108 Anderson-Darling A-Sq 80.44013 Quantiles (Definition 5) Quantile Estimate 100% Max 6809.310 99% 1244.392 95% 466.576 90% 302.291 75% Q3 200.139 50% Median 166.874 25% Q1 144.328 10% 132.445 5% 124.605 1% 115.877 0% Min 114.531 Extreme Observations ------Lowest----Value Obs 114.531 19 115.230 13 115.514 224 115.877 47 117.668 80 311 75130.4751 197672.333 160.804147 61278423.3 25.2111554 Boxplot EXST7025 : Biological Population Statistics II Random coefficients regression Geaghan Page 15 6750+* . . . . . . .* . . .* .* .* 250+******************************************* ----+----+----+----+----+----+----+----+--* may represent up to 7 counts 1 * 1 * 1 6 4 298 * * * +--0--+ Normal Probability Plot 6750+ * | | | | | | | * | | | * | +*****++ | +++++++++++*** 250+******************************************* +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 Variable: T0 Moments N Mean Std Deviation Skewness Uncorrected SS Coeff Variation 311 -0.142686 0.49022664 -1.4031301 80.8316111 -343.57017 Sum Weights Sum Observations Variance Kurtosis Corrected SS Std Error Mean Basic Statistical Measures Location Variability Mean -0.14269 Std Deviation Median -0.03641 Variance Mode . Range Interquartile Range Tests for Location: Mu0=0 Test -StatisticStudent's t t -5.13292 Sign M -13.5 Signed Rank S -4996 311 -44.375355 0.24032215 2.62048169 74.4998679 0.0277982 0.49023 0.24032 3.14796 0.50684 -----p Value-----Pr > |t| <.0001 Pr >= |M| 0.1403 Pr >= |S| 0.0015 Tests for Normality Test --Statistic--Shapiro-Wilk W 0.899707 Kolmogorov-Smirnov D 0.13104 Cramer-von Mises W-Sq 1.464799 Anderson-Darling A-Sq 8.426367 Quantiles (Definition 5) Quantile Estimate 100% Max 0.7081938 99% 0.5620960 -----p Value-----Pr < W <0.0001 Pr > D <0.0100 Pr > W-Sq <0.0050 Pr > A-Sq <0.0050 EXST7025 : Biological Population Statistics II Random coefficients regression 95% 90% 75% Q3 50% Median 25% Q1 10% 5% 1% 0% Min Geaghan Page 16 0.4638905 0.3719356 0.1713011 -0.0364118 -0.3355385 -0.8129538 -1.1423009 -1.6777118 -2.4397637 Extreme Observations ------Lowest----Value Obs -2.43976 131 -2.13528 245 -1.84242 27 -1.67771 151 -1.53102 264 ------Highest----Value Obs 0.556761 106 0.562096 224 0.569035 230 0.623090 69 0.708194 235 Histogram Boxplot 0.7+* .*********** .********************** .************************************** .********************************** .****************** .********* .******** -0.9+**** .****** .*** .** .* .* .* . -2.5+* ----+----+----+----+----+----+----+--* may represent up to 2 counts 2 21 43 76 68 36 18 15 7 11 6 4 1 1 1 1 | | | +-----+ *--+--* +-----+ | | | 0 0 0 0 0 * * EXST7025 : Biological Population Statistics II Random coefficients regression Geaghan Page 17 Normal Probability Plot 0.7+ ++++ * | +++********** | +******* | ******** | ******+ | ****+++ | ***++ | **** -0.9+ +++** | ++++**** |++++ *** | *** | * | * |* | -2.5+* +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 Variable: K Moments N Mean Std Deviation Skewness Uncorrected SS Coeff Variation 311 -0.4606164 0.27333033 -0.7506885 89.1440254 -59.340117 Sum Weights Sum Observations Variance Kurtosis Corrected SS Std Error Mean Basic Statistical Measures Location Variability Mean -0.46062 Std Deviation Median -0.42337 Variance Mode . Range Interquartile Range Tests for Location: Mu0=0 Test -StatisticStudent's t t -29.7188 Sign M -155.5 Signed Rank S -24258 Tests for Normality Test Shapiro-Wilk Kolmogorov-Smirnov Cramer-von Mises Anderson-Darling 0.27333 0.07471 1.46204 0.35793 -----p Value-----Pr > |t| <.0001 Pr >= |M| <.0001 Pr >= |S| <.0001 --Statistic--W 0.961582 D 0.076061 W-Sq 0.437811 A-Sq 2.745223 Quantiles (Definition 5) Quantile Estimate 100% Max -0.00366525 99% -0.02366745 95% -0.07388079 90% -0.12347218 75% Q3 -0.26521723 50% Median -0.42337498 25% Q1 -0.62314630 10% -0.84607611 5% -0.97333961 1% -1.18786532 0% Min -1.46570376 311 -143.25171 0.07470947 0.43904079 23.1599348 0.01549914 -----p Value-----Pr < W <0.0001 Pr > D <0.0100 Pr > W-Sq <0.0050 Pr > A-Sq <0.0050 EXST7025 : Biological Population Statistics II Random coefficients regression Geaghan Page 18 Extreme Observations ------Lowest----- -------Highest------ Value -1.46570 -1.34247 -1.20017 -1.18787 -1.17415 Value -0.02487429 -0.02366745 -0.02063218 -0.00811033 -0.00366525 Obs 104 55 142 204 193 Histogram Boxplot -0.05+*********** 22 .**************** 31 .******************** 40 .************************** 51 .************************* 50 .***************** 33 .*************** 29 -0.75+********* 17 .******* 14 .***** 10 .*** 6 .*** 5 .* 1 .* 1 -1.45+* 1 ----+----+----+----+----+* may represent up to 2 counts | | +-----+ | | *--+--* | | +-----+ | | | | 0 0 0 0 Obs 143 43 17 255 131 Normal Probability Plot -0.05+ +*********** | ****** | ***** | ***** | *****+ | ****+ | **** -0.75+ **** | ++*** | ++**** | ++++*** |++**** | * |* -1.45+* +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 92 data flier1; set flier; if age gt 2; run;e NOTE: There were 1680 observations read from the data set WORK.FLIER. NOTE: The data set WORK.FLIER1 has 1194 observations and 12 variables. NOTE: DATA statement used (Total process time): real time 0.00 seconds cpu time 0.00 secondse 93 proc nlmixed data=flier1; 94 *PARAMETERS LINF=161 T0=-0.001 K=-0.47; 95 PARAMETERS LINF=181 T0=-0.176 K=-0.345 s2=40 s2k=0.004; 96 KK = K + B2; 97 pred = Linf*(1 - exp(Kk*(time - T0))); 98 MODEL scale ~ normal(pred, S2); 99 random b2 ~ normal([0],[s2k]) subject=FNO; 100 run; NOTE: GCONV Convergence criterion satisfied. NOTE: At least one element of the (projected) gradient is greater than 1e-3. NOTE: The PROCEDURE NLMIXED printed page 15. NOTE: PROCEDURE NLMIXED used (Total process time): real time 0.90 seconds cpu time 0.64 secondse Growth Curves fitted to Flier sunfish TRADITIONAL vBert The NLMIXED Procedure Specifications Data Set Dependent Variable Distribution for Dependent Variable Random Effects Distribution for Random Effects Subject Variable Optimization Technique Integration Method Dimensions WORK.FLIER1 scale Normal B2 Normal FNO Dual Quasi-Newton Adaptive Gaussian Quadrature EXST7025 : Biological Population Statistics II Random coefficients regression Observations Used Observations Not Used Total Observations Subjects Max Obs Per Subject Parameters Quadrature Points Parameters LINF 181 Geaghan Page 19 1194 0 1194 354 6 5 1 T0 -0.176 K -0.345 s2 40 s2k 0.004 Iteration History Iter Calls NegLogLike Diff MaxGrad 1 6 4322.05895 0.064117 154.4978 2 9 4322.05613 0.002826 153.9559 3 11 4322.05498 0.001149 149.1363 4 12 4322.05374 0.00124 13.49042 5 14 4322.05371 0.000028 12.07701 NOTE: GCONV Convergence criterion satisfied. Fit Statistics -2 Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) NegLogLike 4322.12307 Slope -11046.2 -4.66427 -0.09804 -0.0027 -0.00003 8644.1 8654.1 8654.2 8673.5 Parameter Estimates Parameter LINF T0 K s2 s2k 102 103 104 105 106 107 108 109 NOTE: NOTE: NOTE: NOTE: Estimate 181.00 -0.1767 -0.3446 39.9990 0.003874 Standard Error 3.6465 0.03003 0.01619 1.9795 0.000586 DF 353 353 353 353 353 t Value 49.64 -5.88 -21.28 20.21 6.61 Pr > |t| <.0001 <.0001 <.0001 <.0001 <.0001 Alpha 0.05 0.05 0.05 0.05 0.05 Lower 173.83 -0.2357 -0.3765 36.1059 0.002722 proc nlmixed data=flier1; *PARAMETERS LINF=161 T0=-0.001 K=-0.47; PARAMETERS LINF=194 T0=-0.28 K=-0.29 s2l=415 s2=48; LL = LInf + B1; pred = LL*(1 - exp(K*(time - T0))); MODEL scale ~ normal(pred, S2); random b1 ~ normal([0],[s2L]) subject=FNO; run; GCONV Convergence criterion satisfied. At least one element of the (projected) gradient is greater than 1e-3. The PROCEDURE NLMIXED printed page 16. PROCEDURE NLMIXED used (Total process time): real time 0.56 seconds cpu time 0.43 secondse Growth Curves fitted to Flier sunfish TRADITIONAL vBert The NLMIXED Procedure Specifications Data Set Dependent Variable Distribution for Dependent Variable Random Effects Distribution for Random Effects Subject Variable Optimization Technique Integration Method WORK.FLIER1 scale Normal B1 Normal FNO Dual Quasi-Newton Adaptive Gaussian Quadrature Upper 188.17 -0.1176 -0.3128 43.8920 0.005027 Gradient 0.012536 -0.06228 0.015469 0.035627 12.07701 EXST7025 : Biological Population Statistics II Random coefficients regression Dimensions Observations Used Observations Not Used Total Observations Subjects Max Obs Per Subject Parameters Quadrature Points Parameters LINF 194 T0 -0.28 Geaghan Page 20 1194 0 1194 354 6 5 1 K -0.29 s2l 415 s2 48 Iteration History Iter Calls NegLogLike Diff MaxGrad 1 5 4383.83517 0.259873 6.119456 2 8 4383.82651 0.008655 4.240364 3 9 4383.82645 0.000055 0.043476 4 12 4383.82645 3.256E-6 1.109234 NOTE: GCONV Convergence criterion satisfied. Fit Statistics -2 Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) NegLogLike 4384.09504 Slope -1520.55 -0.81488 -0.00011 -3.87E-7 8767.7 8777.7 8777.7 8797.0 Parameter Estimates Parameter LINF T0 K s2l s2 110 111 112 113 114 115 116 117 118 119 120 NOTE: NOTE: NOTE: NOTE: Estimate 194.00 -0.2828 -0.2913 415.00 47.9984 Standard Error 5.9055 0.03816 0.01777 45.3096 2.3515 DF 353 353 353 353 353 t Value 32.85 -7.41 -16.39 9.16 20.41 Pr > |t| <.0001 <.0001 <.0001 <.0001 <.0001 Alpha 0.05 0.05 0.05 0.05 0.05 Lower 182.39 -0.3578 -0.3262 325.89 43.3737 Upper 205.61 -0.2077 -0.2563 504.11 52.6231 Gradient -0.00072 0.220002 1.109234 -0.00035 0.004147 proc nlmixed data=flier1; *PARAMETERS LINF=161 T0=-0.001 K=-0.47; PARAMETERS LINF=189.76 K=-0.3182 s2=33.23 s2k=0.005588 s2L=400.07 clk=1.05; LL = LInf + B1; KK = K + B2; *TT = T0 + B3; pred = LL*(1 - exp(Kk*(time - T0))); MODEL scale ~ normal(pred, S2); random b1 b2 ~ normal([0, 0],[s2L, clk, s2K]) subject=FNO; run; GCONV Convergence criterion satisfied. At least one element of the (projected) gradient is greater than 1e-3. The PROCEDURE NLMIXED printed page 17. PROCEDURE NLMIXED used (Total process time): real time 49.34 seconds cpu time 48.70 secondse Growth Curves fitted to Flier sunfish TRADITIONAL vBert The NLMIXED Procedure Specifications Data Set Dependent Variable Distribution for Dependent Variable Random Effects WORK.FLIER1 scale Normal B1 B2 T0=-0.25; EXST7025 : Biological Population Statistics II Random coefficients regression Geaghan Page 21 Distribution for Random Effects Subject Variable Optimization Technique Integration Method Dimensions Observations Used Observations Not Used Total Observations Subjects Max Obs Per Subject Parameters Quadrature Points Parameters LINF K 189.76 -0.3182 Normal FNO Dual Quasi-Newton Adaptive Gaussian Quadrature 1194 0 1194 354 6 6 21 s2 33.23 s2k 0.005588 s2L 400.07 Iteration History Iter Calls NegLogLike Diff MaxGrad 1 7 4300.36492 0.000316 7.607489 2 11 4300.36465 0.000273 1.523191 3 13 4300.36462 0.000036 1.237986 4 16 4300.36381 0.00081 111.4241 NOTE: GCONV Convergence criterion satisfied. Fit Statistics -2 Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) clk 1.05 NegLogLike 4300.36524 Slope -488.014 -3.01137 -0.00037 -0.00002 8600.7 8612.7 8612.8 8635.9 Parameter Estimates Parameter LINF K s2 s2k s2L clk 121 122 127 130 131 132 133 134 135 136 NOTE: NOTE: NOTE: NOTE: Estimate 189.70 -0.3183 33.2511 0.005586 400.13 1.0496 Standard Error 2.3736 0.006823 1.9185 0.000789 75.6318 0.2196 DF 352 352 352 352 352 352 t Value 79.92 -46.65 17.33 7.08 5.29 4.78 Pr > |t| <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 Alpha 0.05 0.05 0.05 0.05 0.05 0.05 Lower 185.03 -0.3317 29.4780 0.004034 251.38 0.6177 Upper 194.37 -0.3048 37.0242 0.007139 548.88 1.4816 Gradient -0.003 -0.25657 0.000558 -111.424 -0.01406 0.621108 proc nlmixed data=flier1; PARAMETERS LINF=189.73 K=-0.3494 s2=33.1989 s2k=0.02583 s2L=400.04 clk=1.018 T0=-0.2763; LL = LInf + B1; KK = K + B2; *TT = T0 + B3; pred = LL*(1 - exp(Kk*(time - T0))); MODEL scale ~ normal(pred, S2); random b1 b2 ~ normal([0, 0],[s2L, clk, s2K]) subject=FNO; run; GCONV Convergence criterion satisfied. At least one element of the (projected) gradient is greater than 1e-3. The PROCEDURE NLMIXED printed page 18. PROCEDURE NLMIXED used (Total process time): real time 3:14.04 cpu time 3:13.28e Growth Curves fitted to Flier sunfish TRADITIONAL vBert The NLMIXED Procedure Specifications EXST7025 : Biological Population Statistics II Random coefficients regression Geaghan Page 22 Data Set Dependent Variable Distribution for Dependent Variable Random Effects Distribution for Random Effects Subject Variable Optimization Technique Integration Method Dimensions Observations Used Observations Not Used Total Observations Subjects Max Obs Per Subject Parameters Quadrature Points Parameters LINF 189.73 K -0.3494 WORK.FLIER1 scale Normal B1 B2 Normal FNO Dual Quasi-Newton Adaptive Gaussian Quadrature 1194 0 1194 354 6 7 21 s2 33.1989 s2k 0.02583 s2L 400.04 Iteration History Iter Calls NegLogLike Diff MaxGrad 1 10 4359.75792 144.9635 10577.27 2 15 4356.18394 3.573972 24294.65 3 18 4336.60212 19.58183 14010.57 4 19 4312.55318 24.04894 21287.26 5 23 4297.92031 14.63287 4736.427 6 25 4296.88133 1.03898 918.3171 7 27 4296.67805 0.203283 414.7094 8 29 4296.62175 0.056298 15.39494 9 31 4296.58495 0.036797 682.3764 10 34 4293.986 2.598953 1531.729 11 35 4289.56223 4.423775 290.9723 12 45 4287.12183 2.440394 645.5522 13 49 4285.70373 1.418105 653.1032 14 51 4285.455 0.24873 812.5422 15 54 4285.34416 0.110842 607.7148 16 56 4285.29432 0.049839 458.2928 17 58 4285.26566 0.028659 21.90831 18 60 4285.26115 0.004503 7.617416 19 61 4285.26083 0.000325 5.420842 20 63 4285.25837 0.002456 8.670658 21 65 4285.23236 0.026012 5.659431 22 67 4285.23172 0.000637 1.292237 23 69 4285.23172 2.367E-6 0.135319 NOTE: GCONV Convergence criterion satisfied. Fit Statistics -2 Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) clk 1.018 T0 -0.2763 NegLogLike 4504.72141 Slope -352136 -26184.5 -4092.13 -204.91 -59.5968 -1.82698 -0.32074 -0.04381 -0.02535 -0.04565 -4.27503 -4.79565 -2.21927 -0.40731 -0.17947 -0.08614 -0.05824 -0.00743 -0.00026 -0.00214 -0.00268 -0.00118 -4.4E-6 8570.5 8584.5 8584.6 8611.5 Parameter Estimates Parameter LINF K s2 s2k s2L clk T0 Estimate 172.59 -0.4046 29.3867 0.01115 400.37 1.5246 -0.09182 Standard Error 3.1056 0.01705 1.7003 0.001635 49.0996 0.2153 0.02490 DF 352 352 352 352 352 352 352 t Value 55.57 -23.73 17.28 6.82 8.15 7.08 -3.69 Pr > |t| <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.0003 Alpha 0.05 0.05 0.05 0.05 0.05 0.05 0.05 Lower 166.48 -0.4381 26.0428 0.007933 303.80 1.1011 -0.1408 Upper 178.70 -0.3710 32.7306 0.01436 496.93 1.9481 -0.04285 Gradient -0.00011 -0.00126 0.000327 0.135319 -0.00595 0.000088 -0.00612 ...
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This note was uploaded on 12/29/2011 for the course EXST 7025 taught by Professor Geaghan,j during the Spring '08 term at LSU.

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