for Percent Body Fat
> library(foreign)
> fat <- read.dta("c:/fat.dta")
> attach(fat)
> bf1 <- (time+3)*I(time > -3)
> bf2 <- (time+2)*I(time > -2)
> bf3 <- (time+1)*I(time > -1)
> bf4 <- (time)*I(time > 0)
> bf5 <- (time-1)*I(time > 1)
> bf6 <- (time-2)*I(time > 2)
> bf7 <- (time-3)*I(time > 3)
> Const <- factor(rep(1,length(pbf)))
> library(nlme)
> model <- lme(pbf ~ time + bf4,
+ random=list(Const=pdIdent(~bf1+bf2+bf3+bf5+bf6+bf7-1),
+ id=pdSymm(~time+bf4), id=pdIdent(~bf2+bf3+bf5+bf6-1)))
> summary(model)
Linear mixed-effects model fit by REML
Data: NULL
AIC BIC logLik
6009.233 6068.666 -2992.617
Random effects:
Formula: ~bf1 + bf2 + bf3 + bf5 + bf6 + bf7 - 1 | Const
Structure: Multiple of an Identity
bf1 bf2 bf3 bf5 bf6 bf7
StdDev: 1.435129 1.435129 1.435129 1.435129 1.435129 1.435129
Formula: ~time + bf4 | id %in% Const
Structure: General positive-definite
StdDev Corr
(Intercept) 6.771193 (Intr) time
time 1.356945 0.281
bf4 1.859846 -0.551 -0.956
Formula: ~bf2 + bf3 + bf5 + bf6 - 1 | id %in% id %in% Const
Structure: Multiple of an Identity
bf2 bf3 bf5 bf6 Residual
StdDev: 0.4617243 0.4617243 0.4617243 0.4617243 2.836783
Fixed effects: pbf ~ time + bf4
Value Std.Error DF t-value p-value
(Intercept) 21.941421 1.5477764 885 14.176092 0.0000
time 0.337703 0.4462351 885 0.756782 0.4494
bf4 3.322306 0.7515140 885 4.420817 0.0000
Correlation:
(Intr) time
time 0.907
bf4 -0.048 -0.055
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-3.30450306 -0.53850645 -0.02459064 0.52561260 3.56183467
Number of Observations: 1049
Number of Groups:
Const id %in% Const id.1 %in% id %in% Const
1 162 162
> ranef(model)
Level: Const
bf1 bf2 bf3 bf5 bf6 bf7
1 -0.6825784 -0.4113161 1.643085 -1.427715 -1.947879 0.3928926
Level: id %in% Const
(Intercept) time bf4
1/1 -4.1000344 1.026503309 -0.879386739
1/2 -3.1228883 0.550977653 -0.394535074
1/3 2.2061904 0.497112196 -0.778035740
1/4 -10.7044544 -1.876842588 3.137002477
1/5 -11.2312341 -0.363733684 1.377252711
1/6 10.2758141 3.358384272 -4.867361003
1/7 -3.3636550 0.933034404 -0.829815092
1/8 -1.2198284 -0.499569617 0.698096505
1/9 -3.0107118 0.407699927 -0.233136517
1/10 -5.8478766 -1.177780223 1.895519383
1/11 8.0251632 0.107080555 -0.801899890
1/12 -3.1634910 -0.247336550 0.560667832
1/13 -0.9483916 -0.078024829 0.172704220
1/14 -7.5031356 1.853797155 -1.579818517
1/15 -2.7966284 0.615266448 -0.498594353
1/16 7.4165424 -1.335711614 0.969404875
1/17 7.5090867 -0.895493335 0.436778784
1/18 -0.4256699 0.630701785 -0.716192926
1/19 3.3600312 0.379327661 -0.734546644
1/20 3.5598688 -1.394224195 1.363184568
1/21 -12.1112949 0.668662071 0.220314886
1/22 4.2596576 0.202173002 -0.598915682
1/23 5.4046396 -0.930152419 0.654905964
1/24 0.3608454 0.287359744 -0.372921551
1/25 2.8391330 1.257869632 -1.738226666
1/26 12.4752153 -0.237806178 -0.764578412
1/27 4.1548914 -0.109088586 -0.219011493
1/28 -2.4844702 -1.760895119 2.308162931
1/29 -1.5948603 -0.407182282 0.619455981
1/30 -7.9088419 0.125781129 0.514497381
1/31 7.5317795 -0.089832559 -0.525678385
1/32 5.8051643 -1.089953600 0.811779062
1/33 19.0238103 0.871092050 -2.636843774
1/34 -8.9123912 -1.051255532 2.002134760
1/35 0.6273759 -0.661165319 0.735567022
1/36 -1.2916170 -0.109868505 0.239505688
1/37 2.9264405 -0.627067449 0.501757847
1/38 -3.3216001 0.918724121 -0.816286722
1/39 -3.0918638 0.404389888 -0.222372002
1/40 0.5735309 -0.429563451 0.463962619
1/41 3.8795114 0.810728715 -1.292529365
1/42 -7.7699548 -0.375236615 1.100168231
1/43 5.2075324 0.063252094 -0.512922614
1/44 -0.7268995 -0.134452702 0.221371828
1/45 3.2292025 0.293885100 -0.621685940
1/46 -6.7868007 0.243567066 0.279798760
1/47 -13.2900569 -0.884187008 2.170735726
1/48 -5.9503272 0.696104919 -0.330016666
1/49 1.1150732 0.151184403 -0.273932593
1/50 -1.5440024 -0.932230260 1.241172545
1/51 -5.1785470 -1.086259539 1.730169868
1/52 2.8532801 -0.298359151 0.116001402
1/53 -1.1881334 1.024697993 -1.121877394
1/54 0.2920906 0.108687527 -0.154122822
1/55 -4.1027367 0.697146561 -0.486483607
1/56 4.7212561 -0.348357686 0.018674580
1/57 6.3704136 0.404642916 -1.017645657
1/58 -1.2727263 -0.612400029 0.837062998
1/59 5.6434835 0.531829665 -1.108211280
1/60 6.0715562 -1.278928856 1.014704494
1/61 -12.1029892 -0.919245093 2.112802431
1/62 -8.5604969 -0.002631189 0.722345856
1/63 -2.2567062 1.493948210 -1.591565740
1/64 -0.7299606 -0.476261712 0.629151420
1/65 0.6693363 0.322673579 -0.440942419
1/66 -0.2745755 0.642139889 -0.742524222
1/67 5.0267065 0.656820340 -1.205413210
1/68 1.0315733 0.012448583 -0.101509533
1/69 -3.8284081 0.016975017 0.301404698
1/70 -2.0204798 -0.167294053 0.369206917
1/71 4.6444156 2.421585510 -3.277339797
1/72 -16.0755892 -0.915738217 2.442379031
1/73 -4.2827005 0.726036437 -0.505807901
1/74 3.2304380 0.479291681 -0.842841096
1/75 4.4251868 0.413158877 -0.864370923
1/76 -1.4061312 -1.575630396 1.996684171
1/77 7.6806470 1.059252348 -1.908184023
1/78 7.5655336 -1.748716152 1.449293009
1/79 3.8063562 -2.838408446 3.064307040
1/80 2.1654231 -0.093115117 -0.070910714
1/81 7.5574246 0.066125353 -0.713774049
1/82 -6.9478619 -0.548246356 1.237371587
1/83 9.5053432 0.960532597 -1.943786707
1/84 -1.9701959 -0.194423211 0.397327391
1/85 -2.7164603 -0.587060079 0.928146595
1/86 0.7929642 1.141803375 -1.427937941
1/87 18.8741157 -0.008119946 -1.576025048
1/88 -14.8919465 -0.318914122 1.631370435
1/89 -2.3596929 -0.081179267 0.295035268
1/90 -7.5925203 -0.917587757 1.731880208
1/91 4.8953770 0.559724046 -1.078616406
1/92 -0.8738582 -0.945958281 1.201237749
1/93 -6.0645870 -0.656754678 1.292532562
1/94 6.5664828 0.275522179 -0.880173947
1/95 5.6447391 -0.293544079 -0.124263235
1/96 -3.6035458 0.924126610 -0.799040597
1/97 1.5572670 2.279697341 -2.848806961
1/98 -1.4736193 -0.835535783 1.119975021
1/99 -1.4251633 1.312176684 -1.444710169
1/100 -1.9215219 1.059072714 -1.101245196
1/101 -5.0638797 0.336367243 0.024406699
1/102 -2.3360434 -0.239089898 0.481317692
1/103 -8.7718153 -1.329481787 2.322039862
1/104 4.4463156 -0.194901045 -0.141185378
1/105 6.3530972 0.372571154 -0.977953010
1/106 8.9683809 0.021039380 -0.778561385
1/107 -1.7183314 -1.091541576 1.445757886
1/108 2.4832538 -0.745914677 0.680687959
1/109 1.3095623 -1.367697009 1.520616508
1/110 5.9943022 1.153711792 -1.879125569
1/111 -10.7286885 -0.263039569 1.214978615
1/112 11.0477906 -1.441734456 0.790732361
1/113 -3.1321421 -0.026843285 0.295150398
1/114 7.7547603 -0.476689751 -0.083180667
1/115 4.1046506 1.229375023 -1.810576145
1/116 0.6231078 0.998723991 -1.243080846
1/117 -11.9411684 0.042949396 0.952028875
1/118 -10.0780740 -0.554685490 1.508032648
1/119 0.2368285 -0.156537118 0.166734447
1/120 3.1489460 0.657311018 -1.048238453
1/121 8.2172311 -0.561140760 -0.021348249
1/122 -1.6212113 0.400784730 -0.341630570
1/123 11.2836453 0.946317131 -2.076242371
1/124 -3.6485972 0.656285953 -0.475921836
1/125 5.9968957 0.700885653 -1.339460671
1/126 -0.9893535 -0.339312205 0.487665697
1/127 11.5554329 0.045105227 -1.024604794
1/128 17.6140252 2.143504522 -4.035437422
1/129 1.0719011 -0.049051879 -0.031573417
1/130 -6.3297541 0.171283097 0.327580813
1/131 2.7228456 0.272741243 -0.553935680
1/132 -0.6083061 0.355785734 -0.373079442
1/133 -0.5497598 0.107101133 -0.081503531
1/134 3.5238802 -0.730565268 0.574959585
1/135 -3.3105561 -0.483180508 0.854208815
1/136 -2.1344181 -1.397706665 1.845741245
1/137 1.2882173 1.104973191 -1.425635676
1/138 -8.1727860 -1.220374224 2.141628691
1/139 -14.5267352 -0.716142451 2.074283714
1/140 6.0135381 1.393079208 -2.166127861
1/141 -6.0947972 -0.610999517 1.240518796
1/142 10.2548482 0.263262111 -1.175434486
1/143 0.6764810 0.021432586 -0.082387514
1/144 -1.4927620 -0.056284672 0.192519756
1/145 -0.9402461 -0.130929800 0.235095913
1/146 0.4109342 0.661771334 -0.823522780
1/147 -0.8570048 0.054178787 0.007406308
1/148 -1.3111137 -0.277472680 0.440970456
1/149 5.7314312 0.101671236 -0.602742950
1/150 7.5663243 -1.079396274 0.651228586
1/151 -16.6991773 -2.935256716 4.902544298
1/152 -2.4489477 1.452337267 -1.525803866
1/153 0.6870455 -0.326775792 0.331877233
1/154 1.6893630 0.889598218 -1.202556690
1/155 -6.4818005 0.914328619 -0.545542363
1/156 -8.4895489 -0.111017495 0.845608813
1/157 1.4827455 -0.097436399 -0.008403896
1/158 2.5519177 -0.093955619 -0.102380220
1/159 -1.4925212 -0.134511213 0.285765237
1/160 -1.8529972 -0.136302273 0.318185986
1/161 2.6846472 0.457884427 -0.771463878
1/162 -9.6855858 -0.047844254 0.870775353
Level: id %in% id %in% Const
bf2 bf3 bf5 bf6
1/1 -0.0974033170 -0.1666778915 -3.719207e-05 0.0000000000
1/2 0.2023022585 0.1703575303 7.088646e-02 0.0055930239
1/3 0.1104186820 0.0291854684 1.449175e-02 0.0139578487
1/4 0.1014544596 0.1971899290 2.428238e-01 0.1689964484
1/5 0.0362152587 0.0781900198 6.028693e-02 0.0375440037
1/6 0.4063232630 0.2107684940 -2.357578e-02 -0.0205505132
1/7 0.0127055369 -0.0091048192 -5.258333e-02 -0.0290874144
1/8 -0.0977188028 -0.0883217557 0.000000e+00 0.0000000000
1/9 -0.1076424917 -0.0558697468 -1.394151e-02 0.0000000000
1/10 0.2055089777 0.2399740978 2.412725e-01 0.1588324944
1/11 0.0550442479 0.0546296765 -3.926339e-02 -0.0602026624
1/12 0.2137435075 0.2064489914 1.235120e-01 0.0563841368
1/13 -0.0342841659 -0.0286446014 3.737036e-02 0.0805672536
1/14 -0.1378221317 -0.1631898316 -2.179079e-01 -0.1796197354
1/15 -0.0199657916 -0.0831149829 -1.023385e-01 -0.0495065750
1/16 -0.3559318647 -0.2869511633 -3.492278e-02 0.0297262136
1/17 -0.1308767326 -0.1098080265 -3.296709e-02 -0.0289546828
1/18 -0.1517007472 -0.1474471128 -1.237699e-01 -0.0741990182
1/19 0.1499333688 0.0613966018 -3.736631e-02 -0.0046915939
1/20 -0.1442764961 -0.0780552902 -6.463966e-03 0.0150048251
1/21 -0.1862667579 -0.2151217919 -1.035904e-01 -0.0276036018
1/22 -0.0159027639 -0.0300746397 -4.531610e-02 -0.0539140252
1/23 -0.0968566720 -0.0618559010 1.130224e-03 0.0159968713
1/24 0.0989403744 0.0970426323 2.939023e-02 0.0714194708
1/25 0.3825138548 0.2987269170 9.079848e-02 0.0395241458
1/26 0.2042089335 0.1693357374 7.036574e-02 0.0002611184
1/27 0.0448739449 0.0383653050 4.511073e-02 0.0486370644
1/28 -0.1590036155 -0.0631630551 -2.165921e-02 -0.0016010281
1/29 0.2814382054 0.2661199516 1.917076e-01 0.0997764254
1/30 -0.1328612932 -0.0862924046 0.000000e+00 0.0000000000
1/31 -0.1401221486 -0.1693589789 -1.419565e-02 0.0207429698
1/32 -0.4077643246 -0.3579919696 -6.389520e-02 0.0000000000
1/33 0.0536645315 0.0262458918 0.000000e+00 0.0000000000
1/34 0.0878011905 0.1156919634 2.605636e-01 0.1743793237
1/35 0.5161318705 0.4814199810 3.191694e-01 0.1586918224
1/36 -0.4628747406 -0.4123659868 -3.363557e-01 -0.2285435106
1/37 -0.1120355682 -0.0556553652 -5.155381e-02 -0.0346509193
1/38 0.2660398828 0.2054004186 2.075160e-01 0.2264087176
1/39 0.2733476561 0.2393465051 1.024367e-01 0.0419993754
1/40 -0.2519288132 -0.2451649540 -9.395726e-02 -0.0588713334
1/41 0.2738921519 0.1952314900 3.301409e-02 0.0000000000
1/42 0.1780015967 0.1585942556 2.614969e-02 0.0106549392
1/43 -0.1940097898 -0.1965376245 -1.153106e-01 -0.0259026496
1/44 -0.0380472572 -0.0272948010 -6.517677e-03 0.0000000000
1/45 0.2277148067 0.1917551292 4.427643e-02 -0.0135053329
1/46 0.0085968478 0.0256057925 -3.232512e-02 -0.1049638895
1/47 -0.3069511093 -0.2357121313 -8.249055e-02 -0.0899847001
1/48 -0.1809812212 -0.1725074433 -1.107957e-01 -0.0550022621
1/49 0.1020732517 0.1215691032 -5.618385e-02 -0.0209295928
1/50 0.0940806916 0.1183655358 1.943052e-01 0.0908927560
1/51 -0.0828128400 0.0256966437 -5.366783e-02 -0.0036197194
1/52 0.0658458511 0.0691349055 5.514186e-02 -0.0026018519
1/53 -0.0827729051 -0.1016913109 -1.311005e-01 -0.0636666522
1/54 0.0887471742 0.0824400353 -5.206794e-03 -0.0381894399
1/55 -0.0800236432 -0.0517233963 -2.014966e-01 -0.1350152913
1/56 0.1841039506 0.1857798123 8.807281e-02 0.0463064967
1/57 0.0389792908 0.0176101002 -5.384090e-02 -0.0083984258
1/58 -0.0829267310 -0.0284578987 -5.151031e-03 -0.0255631877
1/59 0.2144352276 0.1698422415 5.876385e-02 0.0158837286
1/60 0.0413213171 0.0609115708 3.863587e-02 0.0274980161
1/61 -0.3632120051 -0.2547535946 -1.727819e-01 -0.1320074030
1/62 -0.1703780325 -0.1339509008 -1.940036e-04 0.0037708822
1/63 0.1266582720 0.0757918187 -3.060562e-02 -0.0183204037
1/64 -0.1278278123 -0.0634147915 -9.113623e-02 -0.0573182573
1/65 0.0211688864 -0.0308658287 0.000000e+00 0.0000000000
1/66 -0.1911777321 -0.1891894793 -1.878491e-01 -0.1170993962
1/67 0.2771251287 0.2219405107 4.881911e-02 0.0033265748
1/68 -0.3831822913 -0.3268364688 -2.376792e-01 -0.1145605116
1/69 0.1983898917 0.1736111112 -2.164882e-02 -0.0131516232
1/70 -0.1143143569 -0.0933689317 -5.147808e-02 -0.0305326563
1/71 0.2524613947 0.1250081455 2.782867e-03 0.0124458920
1/72 0.1276189343 0.1851254997 2.005781e-01 0.1526583595
1/73 -0.2225127302 -0.1460331828 3.335288e-02 0.0000000000
1/74 0.2151315975 0.0699421424 1.062200e-01 0.0210279268
1/75 -0.1355665571 -0.1025393251 -3.647927e-02 -0.0082492101
1/76 -0.3032537141 -0.2199935494 1.627721e-02 0.0943451819
1/77 0.1900521944 0.1136259223 0.000000e+00 0.0000000000
1/78 -0.0114026581 -0.0123843934 3.321364e-02 0.0304657219
1/79 -0.9985596692 -0.8381791183 -1.967833e-01 0.0076849854
1/80 0.6235438578 0.5490347911 2.830942e-01 0.1520870827
1/81 -0.0680639901 -0.0649979704 -8.291448e-02 -0.0566339753
1/82 0.3331637357 0.3138047667 2.309737e-01 0.1219985799
1/83 0.3507019379 0.2799380644 3.240813e-02 -0.0224319007
1/84 0.4035345013 0.3854757535 1.383326e-01 0.0064528916
1/85 0.0924406855 0.1077910424 1.013461e-01 0.0521897990
1/86 0.2407812341 0.1768744518 2.554809e-02 -0.0237950369
1/87 -0.0321991737 -0.0724147863 -5.458753e-03 0.0055452149
1/88 -0.4963480539 -0.3977158649 -2.294526e-01 -0.1249074266
1/89 -0.2327190513 -0.2080030225 -6.475113e-02 0.0000000000
1/90 -0.1424678424 -0.0727514749 0.000000e+00 0.0000000000
1/91 0.1570232960 0.1235881984 6.090783e-03 0.0000000000
1/92 0.1641673289 0.1827970551 1.233129e-01 0.0623956341
1/93 0.2235855665 0.2477655158 1.993014e-01 0.0534115409
1/94 0.0149652650 -0.0175123626 -2.369431e-02 -0.0178767772
1/95 0.3625277980 0.3422317088 1.539337e-01 0.0174164477
1/96 -0.4191009468 -0.4103451680 -2.309690e-01 -0.0470905616
1/97 0.3209263042 0.1581053599 0.000000e+00 0.0000000000
1/98 -0.1944050199 -0.1183325545 3.378276e-03 -0.0155304681
1/99 0.2820392142 0.2032552347 9.515184e-02 0.0849250492
1/100 -0.1886892970 -0.1853277805 -1.296789e-01 -0.0926229569
1/101 0.1391804159 0.1368297928 5.407527e-02 0.0275392496
1/102 -0.2356047181 -0.1797964412 0.000000e+00 0.0000000000
1/103 -0.3431637199 -0.2941518029 4.811204e-02 0.1601801332
1/104 0.0438156974 0.0167571586 1.924386e-02 -0.0051153577
1/105 0.3948718081 0.3447908935 1.350499e-01 0.0146681131
1/106 0.1363505018 0.0945656628 5.736583e-02 0.0216735198
1/107 -0.0563678252 -0.0062284833 2.012726e-02 0.0000000000
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