Walmes Zeviani
Milson Evaldo Serafim
Materiais e métodos
O experimento avaliou 3 fatores:
Os níveis foram completamente cruzados perfazendo 2*2*7=28 combinações
experimentais. O experimento foi instalado em delineamento de blocos
casualizados com 3 blocos.
##-----------------------------------------------------------------------------
## Definições da sessão, pacotes a serem usados.
pkg <- c("lattice", "latticeExtra", "reshape",
"doBy", "multcomp", "nlme",
"plyr", "wzRfun")
sapply(pkg, library, character.only=TRUE, logical.return=TRUE)
## lattice latticeExtra reshape doBy multcomp nlme
## TRUE TRUE TRUE TRUE TRUE TRUE
## plyr wzRfun
## TRUE TRUE
source("lattice_setup.R")
##-----------------------------------------------------------------------------
## Informações sobre as versões dos pacotes.
sessionInfo()
## R version 3.1.1 (2014-07-10)
## Platform: i686-pc-linux-gnu (32-bit)
##
## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C LC_TIME=pt_BR.UTF-8
## [4] LC_COLLATE=en_US.UTF-8 LC_MONETARY=pt_BR.UTF-8 LC_MESSAGES=en_US.UTF-8
## [7] LC_PAPER=pt_BR.UTF-8 LC_NAME=C LC_ADDRESS=C
## [10] LC_TELEPHONE=C LC_MEASUREMENT=pt_BR.UTF-8 LC_IDENTIFICATION=C
##
## attached base packages:
## [1] splines stats graphics grDevices utils datasets base
##
## other attached packages:
## [1] wzRfun_0.1 plyr_1.8.1 nlme_3.1-117 multcomp_1.3-3
## [5] TH.data_1.0-3 mvtnorm_0.9-99992 doBy_4.5-10 MASS_7.3-33
## [9] survival_2.37-7 reshape_0.8.5 latticeExtra_0.6-26 RColorBrewer_1.0-5
## [13] lattice_0.20-29 knitr_1.5
##
## loaded via a namespace (and not attached):
## [1] evaluate_0.5.5 formatR_0.10 grid_3.1.1 lme4_1.1-6
## [5] Matrix_1.1-4 methods_3.1.1 minqa_1.2.3 Rcpp_0.11.1
## [9] RcppEigen_0.3.2.1.2 sandwich_2.3-0 stringr_0.6.2 tools_3.1.1
## [13] zoo_1.7-11
## obs: Para instalar um pacote faça:
## install.packages("nome_do_pacote", dependencies=TRUE)
Análise dos dados
##-----------------------------------------------------------------------------
## Ler.
url <- "http://www.leg.ufpr.br/~walmes/data/maracuja_altura.txt"
mara <- read.table(url, header=TRUE, sep="\t")
str(mara)
## 'data.frame': 1344 obs. of 7 variables:
## $ agregado: Factor w/ 2 levels "<2","4 a 10": 2 2 2 2 2 2 2 2 2 2 ...
## $ familia : Factor w/ 2 levels "F29","F48": 1 1 1 1 1 1 1 1 1 1 ...
## $ cinza : num 0 0 0 0 0 0 1.5 1.5 1.5 1.5 ...
## $ bloco : int 1 1 2 2 3 3 1 1 2 2 ...
## $ rept : int 1 2 1 2 1 2 1 2 1 2 ...
## $ data : Factor w/ 8 levels "2012/02/24","2012/03/01",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ altura : num 6 6.5 4.5 4 4.5 4.5 8 7.2 6 7.4 ...
mara <- transform(mara, fam=factor(familia), blc=factor(bloco),
agr=factor(agregado, labels=c("4-10 mm","0-2 mm")),
dta=as.Date(data))
mara$dias <- as.numeric(mara$dta-min(mara$dta))
str(mara)
## 'data.frame': 1344 obs. of 12 variables:
## $ agregado: Factor w/ 2 levels "<2","4 a 10": 2 2 2 2 2 2 2 2 2 2 ...
## $ familia : Factor w/ 2 levels "F29","F48": 1 1 1 1 1 1 1 1 1 1 ...
## $ cinza : num 0 0 0 0 0 0 1.5 1.5 1.5 1.5 ...
## $ bloco : int 1 1 2 2 3 3 1 1 2 2 ...
## $ rept : int 1 2 1 2 1 2 1 2 1 2 ...
## $ data : Factor w/ 8 levels "2012/02/24","2012/03/01",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ altura : num 6 6.5 4.5 4 4.5 4.5 8 7.2 6 7.4 ...
## $ fam : Factor w/ 2 levels "F29","F48": 1 1 1 1 1 1 1 1 1 1 ...
## $ blc : Factor w/ 3 levels "1","2","3": 1 1 2 2 3 3 1 1 2 2 ...
## $ agr : Factor w/ 2 levels "4-10 mm","0-2 mm": 2 2 2 2 2 2 2 2 2 2 ...
## $ dta : Date, format: "2012-02-24" "2012-02-24" ...
## $ dias : num 0 0 0 0 0 0 0 0 0 0 ...
mara$id <- with(mara, interaction(blc, fam, agr, cinza, dias))
nlevels(mara$id) # 3*2*2*7*
## [1] 672
nrow(mara)
## [1] 1344
mara <- ddply(mara, .(blc, fam, agr, cinza, dias), summarise, altura=mean(altura))
str(mara)
## 'data.frame': 672 obs. of 6 variables:
## $ blc : Factor w/ 3 levels "1","2","3": 1 1 1 1 1 1 1 1 1 1 ...
## $ fam : Factor w/ 2 levels "F29","F48": 1 1 1 1 1 1 1 1 1 1 ...
## $ agr : Factor w/ 2 levels "4-10 mm","0-2 mm": 1 1 1 1 1 1 1 1 1 1 ...
## $ cinza : num 0 0 0 0 0 0 0 0 1.5 1.5 ...
## $ dias : num 0 6 14 21 28 35 42 47 0 6 ...
## $ altura: num 6.65 7.3 12.25 40.25 62.75 ...
##------------------------------------------------------------------------------------------
## dados de experimento com 4 fatores:
## * fam: categórica a família do maracujá
## * agr: categórica a classe de agregado usado para encher os vasos de cultivo das plantas
## * cinza: métrica a dose de cinza aplicado ao solo
## * dias: métrica o dia de avaliação da planta
## deseja-se verificar o efeito de fam*agr*cinza no crescimento das plantas
##-----------------------------------------------------------------------------
## Ver.
## xyplot(altura~cinza|fam*agr, groups=dias, data=mara, type=c("p","a"))
xyplot(altura~dias|fam*agr, groups=cinza, data=mara, type=c("p","a"))
## xyplot(log(altura)~cinza|fam*agr, groups=dias, data=mara, type=c("p","a"))
## xyplot(log(altura)~dias|fam*agr, groups=cinza, data=mara, type=c("p","a"))
##-----------------------------------------------------------------------------
## Análise só com a última medida.
max(mara$dias)
## [1] 47
xyplot(altura~cinza|fam, groups=agr, data=subset(mara, dias==47),
type=c("p","a"))
xyplot(altura~cinza|fam, groups=agr,
data=subset(mara[-c(144,456,112,656),], dias==47),
type=c("p","a"))
##-----------------------------------------------------------------------------
## Modelo.
m0 <- lm(altura~blc+fam*agr*cinza,
data=subset(mara[-c(144,456,112,656),], dias==47))
## Resíduos.
par(mfrow=c(2,2)); plot(m0); layout(1)
## Quadro de anova.
anova(m0)
## Analysis of Variance Table
##
## Response: altura
## Df Sum Sq Mean Sq F value Pr(>F)
## blc 2 1009 505 5.93 0.0042 **
## fam 1 66 66 0.77 0.3824
## agr 1 230 230 2.70 0.1049
## cinza 1 82 82 0.97 0.3280
## fam:agr 1 9 9 0.10 0.7527
## fam:cinza 1 634 634 7.46 0.0080 **
## agr:cinza 1 670 670 7.88 0.0065 **
## fam:agr:cinza 1 756 756 8.89 0.0039 **
## Residuals 70 5953 85
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##-----------------------------------------------------------------------------
## Usando modelos não lineares mistos.
## Medidas repetidas nos indivíduos que são as parcelas.
mara$parcela <- with(mara, interaction(blc, fam, agr, cinza, sep="_"))
nlevels(mara$parcela) # 3*2*2*7
## [1] 84
marag <- groupedData(formula=altura~dias|parcela, data=mara, order=FALSE)
str(marag)
## Classes 'nfnGroupedData', 'nfGroupedData', 'groupedData' and 'data.frame': 672 obs. of 7 variables:
## $ blc : Factor w/ 3 levels "1","2","3": 1 1 1 1 1 1 1 1 1 1 ...
## $ fam : Factor w/ 2 levels "F29","F48": 1 1 1 1 1 1 1 1 1 1 ...
## $ agr : Factor w/ 2 levels "4-10 mm","0-2 mm": 1 1 1 1 1 1 1 1 1 1 ...
## $ cinza : num 0 0 0 0 0 0 0 0 1.5 1.5 ...
## $ dias : num 0 6 14 21 28 35 42 47 0 6 ...
## $ altura : num 6.65 7.3 12.25 40.25 62.75 ...
## $ parcela: Factor w/ 84 levels "1_F29_4-10 mm_0",..: 1 1 1 1 1 1 1 1 13 13 ...
## - attr(*, "formula")=Class 'formula' length 3 altura ~ dias | parcela
## .. ..- attr(*, ".Environment")=<environment: R_GlobalEnv>
## - attr(*, "FUN")=function (x)
## - attr(*, "order.groups")= logi FALSE
##-----------------------------------------------------------------------------
## Modelo sem efeito dos fatores experimentais.
nn0 <- nlme(altura~SSlogis(dias, A, B, C), fixed=A+B+C~1, random=A+B+C~1,
data=marag, start=list(fixed=c(148, 31, 6.8)))
## Quadro com as estimativas dos parâmetros.
summary(nn0)$tTable
## Value Std.Error DF t-value p-value
## A 148.854 0.9895 586 150.43 0.000e+00
## B 31.428 0.4684 586 67.10 3.282e-277
## C 6.813 0.1429 586 47.68 7.751e-204
VarCorr(nn0)
## parcela = pdLogChol(list(A ~ 1,B ~ 1,C ~ 1))
## Variance StdDev Corr
## A 11.810 3.437 A B
## B 16.925 4.114 0.585
## C 1.084 1.041 -0.098 0.750
## Residual 24.159 4.915
intervals(nn0)
## Approximate 95% confidence intervals
##
## Fixed effects:
## lower est. upper
## A 146.915 148.854 150.793
## B 30.510 31.428 32.345
## C 6.533 6.813 7.093
## attr(,"label")
## [1] "Fixed effects:"
##
## Random Effects:
## Level: parcela
## lower est. upper
## sd(A) 1.7289 3.43661 6.8311
## sd(B) 3.4726 4.11406 4.8740
## sd(C) 0.8136 1.04116 1.3324
## cor(A,B) -0.2932 0.58492 0.9277
## cor(A,C) -0.7802 -0.09762 0.6911
## cor(B,C) 0.5683 0.74992 0.8618
##
## Within-group standard error:
## lower est. upper
## 4.615 4.915 5.234
plot(nn0)
pairs(nn0)
par(mfrow=c(1,3)); apply(ranef(nn0), 2, qqnorm); layout(1)
## $A
## $A$x
## [1] -1.42291 -0.28740 1.34517 -0.99153 -2.51495 -0.81222 -0.73181 0.07467 0.69334
## [10] -0.65587 0.10463 -0.44716 -1.27480 -1.73166 -1.21023 0.54852 1.21023 2.51495
## [19] -0.89826 0.01492 -0.41441 0.99153 -0.54852 0.58355 0.94387 0.13469 0.73181
## [28] -1.15035 0.19520 -0.35020 0.44716 -0.22571 0.81222 -0.69334 -0.51416 -1.61117
## [37] -0.85445 -0.10463 0.38211 1.88430 2.10017 1.51036 -2.10017 0.04478 -0.16487
## [46] 0.51416 1.73166 0.35020 1.42291 0.85445 0.89826 1.15035 -0.13469 -1.09433
## [55] 0.28740 1.27480 1.04155 -1.51036 -0.01492 -0.04478 -1.34517 -1.88430 0.16487
## [64] 0.77139 0.41441 -1.04155 -0.25643 -0.07467 -0.38211 -0.94387 0.61931 1.09433
## [73] -0.61931 0.25643 1.61117 -0.19520 -0.77139 0.65587 0.22571 0.48039 0.31864
## [82] -0.31864 -0.48039 -0.58355
##
## $A$y
## 1_F29_4-10 mm_0 2_F29_4-10 mm_0 3_F29_4-10 mm_0 1_F48_4-10 mm_0 2_F48_4-10 mm_0
## -3.90436 -0.60330 4.28471 -3.14920 -8.64523
## 3_F48_4-10 mm_0 1_F29_0-2 mm_0 2_F29_0-2 mm_0 3_F29_0-2 mm_0 1_F48_0-2 mm_0
## -2.72745 -2.64657 0.22191 2.12549 -1.81075
## 2_F48_0-2 mm_0 3_F48_0-2 mm_0 1_F29_4-10 mm_1.5 2_F29_4-10 mm_1.5 3_F29_4-10 mm_1.5
## 0.22374 -1.46176 -3.47766 -5.41348 -3.32781
## 1_F48_4-10 mm_1.5 2_F48_4-10 mm_1.5 3_F48_4-10 mm_1.5 1_F29_0-2 mm_1.5 2_F29_0-2 mm_1.5
## 2.00319 3.91453 6.27303 -3.07687 0.09352
## 3_F29_0-2 mm_1.5 1_F48_0-2 mm_1.5 2_F48_0-2 mm_1.5 3_F48_0-2 mm_1.5 1_F29_4-10 mm_3
## -1.24235 3.15369 -1.62843 2.01045 3.12884
## 2_F29_4-10 mm_3 3_F29_4-10 mm_3 1_F48_4-10 mm_3 2_F48_4-10 mm_3 3_F48_4-10 mm_3
## 0.23350 2.44227 -3.26521 0.60646 -0.84790
## 1_F29_0-2 mm_3 2_F29_0-2 mm_3 3_F29_0-2 mm_3 1_F48_0-2 mm_3 2_F48_0-2 mm_3
## 1.39096 -0.57274 2.50222 -2.43466 -1.56316
## 3_F48_0-2 mm_3 1_F29_4-10 mm_6 2_F29_4-10 mm_6 3_F29_4-10 mm_6 1_F48_4-10 mm_6
## -5.08285 -3.00591 -0.34326 1.08796 5.80361
## 2_F48_4-10 mm_6 3_F48_4-10 mm_6 1_F29_0-2 mm_6 2_F29_0-2 mm_6 3_F29_0-2 mm_6
## 6.24376 4.56141 -6.85682 0.17435 -0.48299
## 1_F48_0-2 mm_6 2_F48_0-2 mm_6 3_F48_0-2 mm_6 1_F29_4-10 mm_12 2_F29_4-10 mm_12
## 1.86851 4.90295 1.05840 4.31443 2.73963
## 3_F29_4-10 mm_12 1_F48_4-10 mm_12 2_F48_4-10 mm_12 3_F48_4-10 mm_12 1_F29_0-2 mm_12
## 3.11953 3.47171 -0.45656 -3.22771 0.90584
## 2_F29_0-2 mm_12 3_F29_0-2 mm_12 1_F48_0-2 mm_12 2_F48_0-2 mm_12 3_F48_0-2 mm_12
## 4.12107 3.16761 -3.99713 -0.22235 -0.25856
## 1_F29_4-10 mm_24 2_F29_4-10 mm_24 3_F29_4-10 mm_24 1_F48_4-10 mm_24 2_F48_4-10 mm_24
## -3.82876 -5.65287 0.41990 2.50129 1.28819
## 3_F48_4-10 mm_24 1_F29_0-2 mm_24 2_F29_0-2 mm_24 3_F29_0-2 mm_24 1_F48_0-2 mm_24
## -3.20910 -0.58583 -0.31565 -1.20484 -3.12967
## 2_F48_0-2 mm_24 3_F48_0-2 mm_24 1_F29_4-10 mm_48 2_F29_4-10 mm_48 3_F29_4-10 mm_48
## 2.02474 3.25289 -1.70647 0.69544 4.70135
## 1_F48_4-10 mm_48 2_F48_4-10 mm_48 3_F48_4-10 mm_48 1_F29_0-2 mm_48 2_F29_0-2 mm_48
## -0.48322 -2.67413 2.10429 0.63960 1.63983
## 3_F29_0-2 mm_48 1_F48_0-2 mm_48 2_F48_0-2 mm_48 3_F48_0-2 mm_48
## 0.94070 -0.65622 -1.48553 -1.69225
##
##
## $B
## $B$x
## [1] -0.54852 0.41441 2.10017 -2.51495 -2.10017 0.73181 -1.21023 0.58355 0.07467
## [10] -1.27480 0.04478 0.13469 -0.99153 -1.73166 -1.61117 -0.38211 0.99153 1.42291
## [19] -0.16487 -0.58355 -0.31864 0.38211 1.04155 1.51036 1.27480 -0.04478 0.44716
## [28] -1.51036 -0.25643 -0.13469 0.19520 -0.19520 1.15035 -1.09433 -0.85445 0.77139
## [37] -0.94387 -0.69334 0.48039 2.51495 0.69334 0.28740 -1.34517 -0.41441 -0.48039
## [46] 0.94387 0.16487 0.81222 0.85445 0.25643 -0.07467 0.54852 -0.65587 1.09433
## [55] -0.44716 0.65587 0.89826 -0.51416 -0.28740 1.73166 -1.88430 -1.42291 -0.73181
## [64] 1.21023 -0.35020 -0.22571 -0.77139 -0.81222 -0.61931 -0.10463 0.51416 1.34517
## [73] 0.61931 0.35020 0.31864 -1.04155 -0.89826 0.22571 0.01492 1.88430 1.61117
## [82] -1.15035 0.10463 -0.01492
##
## $B$y
## 1_F29_4-10 mm_0 2_F29_4-10 mm_0 3_F29_4-10 mm_0 1_F48_4-10 mm_0 2_F48_4-10 mm_0
## -2.41136 1.27887 10.77028 -6.32303 -6.27413
## 3_F48_4-10 mm_0 1_F29_0-2 mm_0 2_F29_0-2 mm_0 3_F29_0-2 mm_0 1_F48_0-2 mm_0
## 2.66029 -5.04198 1.89235 -0.01366 -5.14724
## 2_F48_0-2 mm_0 3_F48_0-2 mm_0 1_F29_4-10 mm_1.5 2_F29_4-10 mm_1.5 3_F29_4-10 mm_1.5
## -0.51926 0.35884 -4.18285 -5.86831 -5.42311
## 1_F48_4-10 mm_1.5 2_F48_4-10 mm_1.5 3_F48_4-10 mm_1.5 1_F29_0-2 mm_1.5 2_F29_0-2 mm_1.5
## -2.01298 4.16480 5.94976 -1.16789 -2.42415
## 3_F29_0-2 mm_1.5 1_F48_0-2 mm_1.5 2_F48_0-2 mm_1.5 3_F48_0-2 mm_1.5 1_F29_4-10 mm_3
## -1.88333 1.19067 4.61395 5.99508 5.27968
## 2_F29_4-10 mm_3 3_F29_4-10 mm_3 1_F48_4-10 mm_3 2_F48_4-10 mm_3 3_F48_4-10 mm_3
## -0.83623 1.35864 -5.40428 -1.81809 -1.15210
## 1_F29_0-2 mm_3 2_F29_0-2 mm_3 3_F29_0-2 mm_3 1_F48_0-2 mm_3 2_F48_0-2 mm_3
## 0.53012 -1.56494 4.93885 -4.33927 -3.78233
## 3_F48_0-2 mm_3 1_F29_4-10 mm_6 2_F29_4-10 mm_6 3_F29_4-10 mm_6 1_F48_4-10 mm_6
## 2.80264 -4.11198 -2.69603 1.39014 12.12587
## 2_F48_4-10 mm_6 3_F48_4-10 mm_6 1_F29_0-2 mm_6 2_F29_0-2 mm_6 3_F29_0-2 mm_6
## 2.41718 0.86947 -5.18606 -2.02400 -2.31921
## 1_F48_0-2 mm_6 2_F48_0-2 mm_6 3_F48_0-2 mm_6 1_F29_4-10 mm_12 2_F29_4-10 mm_12
## 3.10781 0.46335 2.95269 3.03696 0.77510
## 3_F29_4-10 mm_12 1_F48_4-10 mm_12 2_F48_4-10 mm_12 3_F48_4-10 mm_12 1_F29_0-2 mm_12
## -0.98288 1.45935 -2.67019 4.76667 -2.26067
## 2_F29_0-2 mm_12 3_F29_0-2 mm_12 1_F48_0-2 mm_12 2_F48_0-2 mm_12 3_F48_0-2 mm_12
## 2.33714 3.05454 -2.38955 -1.86584 9.13446
## 1_F29_4-10 mm_24 2_F29_4-10 mm_24 3_F29_4-10 mm_24 1_F48_4-10 mm_24 2_F48_4-10 mm_24
## -5.98512 -5.31792 -2.85683 5.05512 -1.95922
## 3_F48_4-10 mm_24 1_F29_0-2 mm_24 2_F29_0-2 mm_24 3_F29_0-2 mm_24 1_F48_0-2 mm_24
## -1.64069 -3.26849 -3.68719 -2.47379 -1.13574
## 2_F48_0-2 mm_24 3_F48_0-2 mm_24 1_F29_4-10 mm_48 2_F29_4-10 mm_48 3_F29_4-10 mm_48
## 1.40800 5.44314 2.05145 1.15995 1.00223
## 1_F48_4-10 mm_48 2_F48_4-10 mm_48 3_F48_4-10 mm_48 1_F29_0-2 mm_48 2_F29_0-2 mm_48
## -4.31592 -3.91710 0.70557 -0.52018 9.52627
## 3_F29_0-2 mm_48 1_F48_0-2 mm_48 2_F48_0-2 mm_48 3_F48_0-2 mm_48
## 8.38211 -4.57924 0.08143 -0.73641
##
##
## $C
## $C$x
## [1] 0.44716 0.85445 1.61117 -1.88430 0.35020 1.27480 -1.04155 0.81222 -0.38211
## [10] -1.73166 0.07467 0.73181 -0.25643 -0.31864 -0.89826 -1.61117 0.58355 0.54852
## [19] 0.65587 -0.69334 0.01492 -0.19520 1.34517 1.21023 0.94387 -0.07467 0.10463
## [28] -0.99153 -0.54852 0.16487 0.13469 -0.13469 1.04155 -0.61931 -0.73181 1.42291
## [37] -0.41441 -0.65587 0.28740 1.73166 -0.77139 -0.85445 0.25643 -0.51416 -0.48039
## [46] 0.77139 -1.42291 0.89826 0.19520 -0.22571 -1.51036 -0.16487 -0.58355 1.51036
## [55] -1.15035 -0.01492 0.31864 0.48039 -0.35020 2.51495 -1.09433 0.04478 -1.27480
## [64] 1.09433 -1.21023 0.51416 -0.94387 -1.34517 -0.28740 0.69334 0.22571 0.99153
## [73] 1.15035 0.38211 -0.81222 -2.10017 -0.44716 -0.04478 -0.10463 2.10017 1.88430
## [82] -2.51495 0.61931 0.41441
##
## $C$y
## 1_F29_4-10 mm_0 2_F29_4-10 mm_0 3_F29_4-10 mm_0 1_F48_4-10 mm_0 2_F48_4-10 mm_0
## 0.21606 0.54599 2.28553 -1.18484 0.18849
## 3_F48_4-10 mm_0 1_F29_0-2 mm_0 2_F29_0-2 mm_0 3_F29_0-2 mm_0 1_F48_0-2 mm_0
## 1.50018 -0.91183 0.53273 -0.52966 -1.15097
## 2_F48_0-2 mm_0 3_F48_0-2 mm_0 1_F29_4-10 mm_1.5 2_F29_4-10 mm_1.5 3_F29_4-10 mm_1.5
## -0.21657 0.47273 -0.43945 -0.48436 -0.86130
## 1_F48_4-10 mm_1.5 2_F48_4-10 mm_1.5 3_F48_4-10 mm_1.5 1_F29_0-2 mm_1.5 2_F29_0-2 mm_1.5
## -1.12001 0.32566 0.29700 0.39808 -0.77596
## 3_F29_0-2 mm_1.5 1_F48_0-2 mm_1.5 2_F48_0-2 mm_1.5 3_F48_0-2 mm_1.5 1_F29_4-10 mm_3
## -0.27796 -0.40979 1.83539 1.36469 0.86662
## 2_F29_4-10 mm_3 3_F29_4-10 mm_3 1_F48_4-10 mm_3 2_F48_4-10 mm_3 3_F48_4-10 mm_3
## -0.31745 -0.18178 -0.87093 -0.71433 -0.14832
## 1_F29_0-2 mm_3 2_F29_0-2 mm_3 3_F29_0-2 mm_3 1_F48_0-2 mm_3 2_F48_0-2 mm_3
## -0.17921 -0.34421 0.91536 -0.74512 -0.78854
## 3_F48_0-2 mm_3 1_F29_4-10 mm_6 2_F29_4-10 mm_6 3_F29_4-10 mm_6 1_F48_4-10 mm_6
## 2.12675 -0.53411 -0.75260 0.16284 2.33101
## 2_F48_4-10 mm_6 3_F48_4-10 mm_6 1_F29_0-2 mm_6 2_F29_0-2 mm_6 3_F29_0-2 mm_6
## -0.79257 -0.85752 0.08444 -0.67193 -0.60078
## 1_F48_0-2 mm_6 2_F48_0-2 mm_6 3_F48_0-2 mm_6 1_F29_4-10 mm_12 2_F29_4-10 mm_12
## 0.50316 -1.06794 0.65524 -0.12335 -0.43654
## 3_F29_4-10 mm_12 1_F48_4-10 mm_12 2_F48_4-10 mm_12 3_F48_4-10 mm_12 1_F29_0-2 mm_12
## -1.07596 -0.40500 -0.71633 2.27805 -0.92579
## 2_F29_0-2 mm_12 3_F29_0-2 mm_12 1_F48_0-2 mm_12 2_F48_0-2 mm_12 3_F48_0-2 mm_12
## -0.29274 0.16564 0.24605 -0.52449 2.90060
## 1_F29_4-10 mm_24 2_F29_4-10 mm_24 3_F29_4-10 mm_24 1_F48_4-10 mm_24 2_F48_4-10 mm_24
## -0.91256 -0.25388 -0.99114 0.95164 -0.92627
## 3_F48_4-10 mm_24 1_F29_0-2 mm_24 2_F29_0-2 mm_24 3_F29_0-2 mm_24 1_F48_0-2 mm_24
## 0.28352 -0.87031 -1.06766 -0.47028 0.42115
## 2_F48_0-2 mm_24 3_F48_0-2 mm_24 1_F29_4-10 mm_48 2_F29_4-10 mm_48 3_F29_4-10 mm_48
## -0.06330 0.88627 1.05867 0.18852 -0.85092
## 1_F48_4-10 mm_48 2_F48_4-10 mm_48 3_F48_4-10 mm_48 1_F29_0-2 mm_48 2_F29_0-2 mm_48
## -1.22075 -0.55555 -0.30099 -0.31971 2.55299
## 3_F29_0-2 mm_48 1_F48_0-2 mm_48 2_F48_0-2 mm_48 3_F48_0-2 mm_48
## 2.37047 -1.25999 0.39241 0.18957
outl <- which(abs(residuals(nn0, type="pearson"))>3); outl
## 1_F29_4-10 mm_3 1_F29_4-10 mm_3 1_F29_4-10 mm_48 1_F29_4-10 mm_48
## 23 24 54 55
marag <- marag[-outl,]
##-----------------------------------------------------------------------------
## O intercepto não é zero, não sei porque, mas incorporar no modelo.
## modelo: Int+A/(1+exp(-(x-x0)/S)).
## modelo de efeitos aditivos, aleatório em A e B e modelagem da variância.
nn1 <- nlme(altura~int+A/(1+exp(-(dias-d50)/S)),
fixed=list(int~1,
A~blc+fam+agr+cinza,
d50~blc+fam+agr+cinza,
S~blc+fam+agr+cinza),
random=A+d50+S~1,
data=marag,
start=list(fixed=c(5,
120,0,0,0,0,0,
30,0,0,0,0,0,
4,0,0,0,0,0)))
## Quadro de testes de Wald para termos de efeito fixo.
anova(nn1, type="marginal")
## numDF denDF F-value p-value
## int 1 566 407.8 <.0001
## A.(Intercept) 1 566 2222.8 <.0001
## A.blc 2 566 2.1 0.1190
## A.fam 1 566 0.2 0.6833
## A.agr 1 566 0.8 0.3845
## A.cinza 1 566 0.0 0.8276
## d50.(Intercept) 1 566 1339.3 <.0001
## d50.blc 2 566 4.0 0.0186
## d50.fam 1 566 0.7 0.4012
## d50.agr 1 566 0.1 0.7521
## d50.cinza 1 566 0.0 0.8301
## S.(Intercept) 1 566 605.9 <.0001
## S.blc 2 566 0.9 0.4009
## S.fam 1 566 1.0 0.3130
## S.agr 1 566 0.5 0.4638
## S.cinza 1 566 0.6 0.4325
summary(nn1)$tTable
## Value Std.Error DF t-value p-value
## int 5.051035 0.250127 566 20.1939 1.058e-68
## A.(Intercept) 138.808393 2.944175 566 47.1468 3.694e-198
## A.blc2 -1.021472 2.930005 566 -0.3486 7.275e-01
## A.blc3 -5.823381 2.997077 566 -1.9430 5.251e-02
## A.famF48 -0.987887 2.420116 566 -0.4082 6.833e-01
## A.agr0-2 mm -2.106968 2.420894 566 -0.8703 3.845e-01
## A.cinza -0.016422 0.075380 566 -0.2179 8.276e-01
## d50.(Intercept) 29.508429 0.806308 566 36.5970 2.609e-151
## d50.blc2 0.487953 0.822423 566 0.5933 5.532e-01
## d50.blc3 2.233960 0.828153 566 2.6975 7.194e-03
## d50.famF48 0.566286 0.674037 566 0.8401 4.012e-01
## d50.agr0-2 mm 0.213052 0.674039 566 0.3161 7.521e-01
## d50.cinza 0.004527 0.021083 566 0.2147 8.301e-01
## S.(Intercept) 5.563479 0.226027 566 24.6142 1.672e-91
## S.blc2 -0.150342 0.225253 566 -0.6674 5.048e-01
## S.blc3 0.160759 0.230973 566 0.6960 4.867e-01
## S.famF48 0.188414 0.186587 566 1.0098 3.130e-01
## S.agr0-2 mm 0.136671 0.186444 566 0.7330 4.638e-01
## S.cinza -0.004616 0.005876 566 -0.7855 4.325e-01
VarCorr(nn1)
## parcela = pdLogChol(list(A ~ 1,d50 ~ 1,S ~ 1))
## Variance StdDev Corr
## A.(Intercept) 95.926 9.7942 A.(In) d50.(I
## d50.(Intercept) 8.767 2.9609 -0.308
## S.(Intercept) 0.480 0.6929 -0.436 0.338
## Residual 9.203 3.0337
plot(nn1)
par(mfrow=c(1,3)); apply(ranef(nn1), 2, qqnorm); layout(1)
## $`A.(Intercept)`
## $`A.(Intercept)`$x
## [1] -1.04155 -1.15035 -1.51036 0.61931 -0.99153 -1.21023 -0.28740 -0.94387 1.15035
## [10] 0.38211 0.25643 0.13469 -0.69334 -0.73181 1.04155 1.27480 -0.81222 0.04478
## [19] -0.13469 0.44716 0.28740 0.58355 -1.34517 -1.09433 -1.42291 -0.35020 0.77139
## [28] 0.35020 0.85445 0.19520 0.01492 0.73181 0.41441 1.51036 -0.19520 -1.27480
## [37] -0.61931 -0.48039 0.54852 -2.10017 1.61117 1.73166 -0.58355 -0.44716 1.21023
## [46] -0.89826 1.88430 -0.41441 -0.22571 -0.04478 2.51495 0.07467 0.31864 -1.61117
## [55] 0.89826 0.99153 0.94387 -0.31864 0.48039 -1.88430 -0.65587 -0.10463 0.81222
## [64] -0.85445 2.10017 -0.51416 0.22571 -0.54852 1.34517 0.16487 -0.01492 -0.38211
## [73] -0.16487 0.10463 1.42291 0.69334 -0.25643 1.09433 -0.07467 -2.51495 -1.73166
## [82] 0.65587 -0.77139 0.51416
##
## $`A.(Intercept)`$y
## 1_F29_4-10 mm_0 2_F29_4-10 mm_0 3_F29_4-10 mm_0 1_F48_4-10 mm_0 2_F48_4-10 mm_0
## -7.38246 -12.61424 -19.57036 5.02719 -5.57103
## 3_F48_4-10 mm_0 1_F29_0-2 mm_0 2_F29_0-2 mm_0 3_F29_0-2 mm_0 1_F48_0-2 mm_0
## -12.67929 0.32752 -5.00578 8.99623 3.94546
## 2_F48_0-2 mm_0 3_F48_0-2 mm_0 1_F29_4-10 mm_1.5 2_F29_4-10 mm_1.5 3_F29_4-10 mm_1.5
## 3.22650 2.63928 -2.80128 -2.82188 8.08369
## 1_F48_4-10 mm_1.5 2_F48_4-10 mm_1.5 3_F48_4-10 mm_1.5 1_F29_0-2 mm_1.5 2_F29_0-2 mm_1.5
## 9.30657 -3.93580 2.31755 0.69760 4.28765
## 3_F29_0-2 mm_1.5 1_F48_0-2 mm_1.5 2_F48_0-2 mm_1.5 3_F48_0-2 mm_1.5 1_F29_4-10 mm_3
## 3.52201 5.02535 -14.11475 -9.70453 -17.93561
## 2_F29_4-10 mm_3 3_F29_4-10 mm_3 1_F48_4-10 mm_3 2_F48_4-10 mm_3 3_F48_4-10 mm_3
## -0.06658 5.76933 3.88298 6.64436 2.91799
## 1_F29_0-2 mm_3 2_F29_0-2 mm_3 3_F29_0-2 mm_3 1_F48_0-2 mm_3 2_F48_0-2 mm_3
## 1.79343 5.72313 4.17991 11.11824 0.53872
## 3_F48_0-2 mm_3 1_F29_4-10 mm_6 2_F29_4-10 mm_6 3_F29_4-10 mm_6 1_F48_4-10 mm_6
## -12.85099 -2.60851 -0.52529 4.42380 -25.89911
## 2_F48_4-10 mm_6 3_F48_4-10 mm_6 1_F29_0-2 mm_6 2_F29_0-2 mm_6 3_F29_0-2 mm_6
## 11.19873 11.53821 -2.47411 -0.42292 9.15178
## 1_F48_0-2 mm_6 2_F48_0-2 mm_6 3_F48_0-2 mm_6 1_F29_4-10 mm_12 2_F29_4-10 mm_12
## -4.18185 11.97173 -0.33414 0.51876 1.34688
## 3_F29_4-10 mm_12 1_F48_4-10 mm_12 2_F48_4-10 mm_12 3_F48_4-10 mm_12 1_F29_0-2 mm_12
## 15.97173 2.48760 3.80883 -20.08940 7.34855
## 2_F29_0-2 mm_12 3_F29_0-2 mm_12 1_F48_0-2 mm_12 2_F48_0-2 mm_12 3_F48_0-2 mm_12
## 7.57522 7.45265 0.12709 4.34101 -25.68988
## 1_F29_4-10 mm_24 2_F29_4-10 mm_24 3_F29_4-10 mm_24 1_F48_4-10 mm_24 2_F48_4-10 mm_24
## -2.64109 0.74049 6.28745 -4.03358 13.65400
## 3_F48_4-10 mm_24 1_F29_0-2 mm_24 2_F29_0-2 mm_24 3_F29_0-2 mm_24 1_F48_0-2 mm_24
## -1.72850 2.91923 -1.84262 9.47553 2.81705
## 2_F48_0-2 mm_24 3_F48_0-2 mm_24 1_F29_4-10 mm_48 2_F29_4-10 mm_48 3_F29_4-10 mm_48
## 1.62975 -0.16973 0.63732 2.49311 9.52874
## 1_F48_4-10 mm_48 2_F48_4-10 mm_48 3_F48_4-10 mm_48 1_F29_0-2 mm_48 2_F29_0-2 mm_48
## 5.46906 0.35084 8.49880 1.22190 -29.45801
## 3_F29_0-2 mm_48 1_F48_0-2 mm_48 2_F48_0-2 mm_48 3_F48_0-2 mm_48
## -22.30289 5.28674 -3.15206 4.36504
##
##
## $`d50.(Intercept)`
## $`d50.(Intercept)`$x
## [1] -0.22571 0.44716 2.10017 -1.73166 -2.51495 -0.19520 -1.04155 0.58355 -0.16487
## [10] -1.51036 0.10463 -0.41441 -0.61931 -1.88430 -2.10017 0.13469 1.34517 1.42291
## [19] 0.31864 -0.25643 -0.81222 0.73181 0.94387 0.69334 1.61117 0.25643 0.41441
## [28] -1.27480 -0.10463 -0.65587 0.61931 0.07467 1.27480 -0.54852 -1.15035 -0.28740
## [37] -0.58355 -0.44716 0.38211 2.51495 1.21023 0.16487 -1.09433 -0.38211 -0.73181
## [46] 1.09433 0.51416 0.28740 1.51036 0.54852 -0.13469 0.89826 -0.51416 0.04478
## [55] -0.01492 1.15035 0.65587 -0.35020 -0.31864 0.81222 -1.61117 -1.42291 -0.94387
## [64] 1.88430 0.01492 -1.34517 -0.48039 -0.89826 -0.85445 0.19520 0.48039 0.99153
## [73] 0.85445 0.77139 0.22571 -0.77139 -0.99153 -0.07467 0.35020 1.73166 1.04155
## [82] -1.21023 -0.04478 -0.69334
##
## $`d50.(Intercept)`$y
## 1_F29_4-10 mm_0 2_F29_4-10 mm_0 3_F29_4-10 mm_0 1_F48_4-10 mm_0 2_F48_4-10 mm_0
## -0.986652 1.005346 6.645373 -4.239215 -5.408564
## 3_F48_4-10 mm_0 1_F29_0-2 mm_0 2_F29_0-2 mm_0 3_F29_0-2 mm_0 1_F48_0-2 mm_0
## -0.735119 -3.234930 2.051388 -0.602557 -3.726676
## 2_F48_0-2 mm_0 3_F48_0-2 mm_0 1_F29_4-10 mm_1.5 2_F29_4-10 mm_1.5 3_F29_4-10 mm_1.5
## 0.008593 -1.369471 -2.230532 -4.322250 -5.141056
## 1_F48_4-10 mm_1.5 2_F48_4-10 mm_1.5 3_F48_4-10 mm_1.5 1_F29_0-2 mm_1.5 2_F29_0-2 mm_1.5
## 0.014241 3.984920 4.093410 0.703801 -1.070940
## 3_F29_0-2 mm_1.5 1_F48_0-2 mm_1.5 2_F48_0-2 mm_1.5 3_F48_0-2 mm_1.5 1_F29_4-10 mm_3
## -2.764842 2.230964 2.809369 2.184880 5.002192
## 2_F29_4-10 mm_3 3_F29_4-10 mm_3 1_F48_4-10 mm_3 2_F48_4-10 mm_3 3_F48_4-10 mm_3
## 0.460190 0.836014 -3.417222 -0.492346 -2.338628
## 1_F29_0-2 mm_3 2_F29_0-2 mm_3 3_F29_0-2 mm_3 1_F48_0-2 mm_3 2_F48_0-2 mm_3
## 2.084187 0.002665 3.777238 -2.070184 -3.359947
## 3_F48_0-2 mm_3 1_F29_4-10 mm_6 2_F29_4-10 mm_6 3_F29_4-10 mm_6 1_F48_4-10 mm_6
## -1.103152 -2.182573 -1.420397 0.824699 9.289791
## 2_F48_4-10 mm_6 3_F48_4-10 mm_6 1_F29_0-2 mm_6 2_F29_0-2 mm_6 3_F29_0-2 mm_6
## 3.702262 0.075332 -3.346712 -1.259868 -2.671593
## 1_F48_0-2 mm_6 2_F48_0-2 mm_6 3_F48_0-2 mm_6 1_F29_4-10 mm_12 2_F29_4-10 mm_12
## 3.142627 1.475688 0.558715 4.561532 1.919826
## 3_F29_4-10 mm_12 1_F48_4-10 mm_12 2_F48_4-10 mm_12 3_F48_4-10 mm_12 1_F29_0-2 mm_12
## -0.583576 2.604970 -1.598031 -0.074739 -0.140084
## 2_F29_0-2 mm_12 3_F29_0-2 mm_12 1_F48_0-2 mm_12 2_F48_0-2 mm_12 3_F48_0-2 mm_12
## 3.640484 2.156666 -1.247614 -1.204834 2.496125
## 1_F29_4-10 mm_24 2_F29_4-10 mm_24 3_F29_4-10 mm_24 1_F48_4-10 mm_24 2_F48_4-10 mm_24
## -4.065815 -3.463110 -3.218264 5.428834 -0.118511
## 3_F48_4-10 mm_24 1_F29_0-2 mm_24 2_F29_0-2 mm_24 3_F29_0-2 mm_24 1_F48_0-2 mm_24
## -3.428600 -1.509685 -2.989567 -2.805221 0.167230
## 2_F48_0-2 mm_24 3_F48_0-2 mm_24 1_F29_4-10 mm_48 2_F29_4-10 mm_48 3_F29_4-10 mm_48
## 1.455551 2.814519 2.532052 2.449775 0.396067
## 1_F48_4-10 mm_48 2_F48_4-10 mm_48 3_F48_4-10 mm_48 1_F29_0-2 mm_48 2_F29_0-2 mm_48
## -2.720956 -3.218490 -0.422179 0.743841 5.315618
## 3_F29_0-2 mm_48 1_F48_0-2 mm_48 2_F48_0-2 mm_48 3_F48_0-2 mm_48
## 2.901270 -3.387413 -0.354820 -2.501310
##
##
## $`S.(Intercept)`
## $`S.(Intercept)`$x
## [1] 0.73181 0.10463 1.34517 -0.38211 1.09433 0.77139 -1.15035 0.69334 -1.21023
## [10] -1.51036 -0.10463 0.44716 0.41441 0.58355 0.07467 -0.85445 -0.13469 -1.09433
## [19] 1.04155 -0.58355 -1.04155 -0.89826 1.61117 0.38211 2.10017 0.35020 -0.35020
## [28] 0.25643 0.01492 -0.81222 -0.19520 0.61931 0.81222 0.65587 -1.61117 1.73166
## [37] -0.04478 -0.65587 0.48039 1.15035 -0.77139 -2.10017 0.94387 -1.34517 -0.61931
## [46] 0.04478 -1.42291 -0.22571 -0.01492 -0.25643 -0.69334 -0.73181 -0.28740 1.51036
## [55] -0.54852 0.22571 0.13469 0.85445 -0.44716 1.88430 -0.51416 1.42291 -1.73166
## [64] 0.89826 0.51416 0.19520 -0.99153 -2.51495 -0.07467 1.21023 -0.31864 0.31864
## [73] -0.48039 0.99153 -1.27480 -0.94387 0.16487 -0.41441 -0.16487 2.51495 1.27480
## [82] -1.88430 0.54852 0.28740
##
## $`S.(Intercept)`$y
## 1_F29_4-10 mm_0 2_F29_4-10 mm_0 3_F29_4-10 mm_0 1_F48_4-10 mm_0 2_F48_4-10 mm_0
## 0.351932 -0.072971 0.953053 -0.245266 0.894671
## 3_F48_4-10 mm_0 1_F29_0-2 mm_0 2_F29_0-2 mm_0 3_F29_0-2 mm_0 1_F48_0-2 mm_0
## 0.393738 -0.580424 0.320429 -0.605999 -0.861277
## 2_F48_0-2 mm_0 3_F48_0-2 mm_0 1_F29_4-10 mm_1.5 2_F29_4-10 mm_1.5 3_F29_4-10 mm_1.5
## -0.117854 0.081493 0.029787 0.284954 -0.075017
## 1_F48_4-10 mm_1.5 2_F48_4-10 mm_1.5 3_F48_4-10 mm_1.5 1_F29_0-2 mm_1.5 2_F29_0-2 mm_1.5
## -0.500623 -0.126064 -0.577827 0.881780 -0.370251
## 3_F29_0-2 mm_1.5 1_F48_0-2 mm_1.5 2_F48_0-2 mm_1.5 3_F48_0-2 mm_1.5 1_F29_4-10 mm_3
## -0.535472 -0.504641 1.168511 0.025769 1.329837
## 2_F29_4-10 mm_3 3_F29_4-10 mm_3 1_F48_4-10 mm_3 2_F48_4-10 mm_3 3_F48_4-10 mm_3
## 0.018996 -0.240356 -0.020292 -0.107433 -0.485979
## 1_F29_0-2 mm_3 2_F29_0-2 mm_3 3_F29_0-2 mm_3 1_F48_0-2 mm_3 2_F48_0-2 mm_3
## -0.142120 0.292203 0.538241 0.303120 -0.885936
## 3_F48_0-2 mm_3 1_F29_4-10 mm_6 2_F29_4-10 mm_6 3_F29_4-10 mm_6 1_F48_4-10 mm_6
## 1.194143 -0.115072 -0.421674 0.125789 0.905169
## 2_F48_4-10 mm_6 3_F48_4-10 mm_6 1_F29_0-2 mm_6 2_F29_0-2 mm_6 3_F29_0-2 mm_6
## -0.482664 -0.935579 0.794217 -0.749670 -0.393922
## 1_F48_0-2 mm_6 2_F48_0-2 mm_6 3_F48_0-2 mm_6 1_F29_4-10 mm_12 2_F29_4-10 mm_12
## -0.102611 -0.786873 -0.150795 -0.113727 -0.186782
## 3_F29_4-10 mm_12 1_F48_4-10 mm_12 2_F48_4-10 mm_12 3_F48_4-10 mm_12 1_F29_0-2 mm_12
## -0.435675 -0.440637 -0.220816 1.017134 -0.363470
## 2_F29_0-2 mm_12 3_F29_0-2 mm_12 1_F48_0-2 mm_12 2_F48_0-2 mm_12 3_F48_0-2 mm_12
## -0.023846 -0.051997 0.557410 -0.320713 1.248255
## 1_F29_4-10 mm_24 2_F29_4-10 mm_24 3_F29_4-10 mm_24 1_F48_4-10 mm_24 2_F48_4-10 mm_24
## -0.356026 0.985115 -0.894365 0.702791 0.205437
## 3_F48_4-10 mm_24 1_F29_0-2 mm_24 2_F29_0-2 mm_24 3_F29_0-2 mm_24 1_F48_0-2 mm_24
## -0.030591 -0.531896 -1.416045 -0.117460 0.920581
## 2_F48_0-2 mm_24 3_F48_0-2 mm_24 1_F29_4-10 mm_48 2_F29_4-10 mm_48 3_F29_4-10 mm_48
## -0.234186 0.009793 -0.339237 0.802789 -0.715901
## 1_F48_4-10 mm_48 2_F48_4-10 mm_48 3_F48_4-10 mm_48 1_F29_0-2 mm_48 2_F29_0-2 mm_48
## -0.518866 -0.050196 -0.291555 -0.141071 1.334803
## 3_F29_0-2 mm_48 1_F48_0-2 mm_48 2_F48_0-2 mm_48 3_F48_0-2 mm_48
## 0.946523 -0.899367 0.266067 0.004559
intervals(nn1)
## Approximate 95% confidence intervals
##
## Fixed effects:
## lower est. upper
## int 4.56678 5.051035 5.53529
## A.(Intercept) 133.10838 138.808393 144.50840
## A.blc2 -6.69405 -1.021472 4.65110
## A.blc3 -11.62581 -5.823381 -0.02095
## A.famF48 -5.67330 -0.987887 3.69753
## A.agr0-2 mm -6.79389 -2.106968 2.57995
## A.cinza -0.16236 -0.016422 0.12952
## d50.(Intercept) 27.94739 29.508429 31.06946
## d50.blc2 -1.10428 0.487953 2.08019
## d50.blc3 0.63063 2.233960 3.83729
## d50.famF48 -0.73867 0.566286 1.87124
## d50.agr0-2 mm -1.09191 0.213052 1.51801
## d50.cinza -0.03629 0.004527 0.04534
## S.(Intercept) 5.12588 5.563479 6.00107
## S.blc2 -0.58644 -0.150342 0.28575
## S.blc3 -0.28641 0.160759 0.60793
## S.famF48 -0.17282 0.188414 0.54965
## S.agr0-2 mm -0.22429 0.136671 0.49763
## S.cinza -0.01599 -0.004616 0.00676
## attr(,"label")
## [1] "Fixed effects:"
##
## Random Effects:
## Level: parcela
## lower est. upper
## sd(A.(Intercept)) 7.71013 9.7942 12.44155
## sd(d50.(Intercept)) 2.50326 2.9609 3.50221
## sd(S.(Intercept)) 0.54527 0.6929 0.88038
## cor(A.(Intercept),d50.(Intercept)) -0.52675 -0.3077 -0.05031
## cor(A.(Intercept),S.(Intercept)) -0.68760 -0.4356 -0.08984
## cor(d50.(Intercept),S.(Intercept)) 0.06731 0.3380 0.56235
##
## Within-group standard error:
## lower est. upper
## 2.832 3.034 3.249
## Pelo modelo acima ninguém interfere no crescimento da planta.
##-----------------------------------------------------------------------------
## Modelo com interações.
nn2 <- nlme(altura~int+A/(1+exp(-(dias-d50)/S)),
fixed=list(int~1,
A~blc+fam*agr*cinza,
d50~blc+fam*agr*cinza,
S~blc+fam*agr*cinza),
random=A+d50+S~1,
data=marag,
start=list(fixed=c(5.2,
120,0,0,0,0,0,0,0,0,0,
30,0,0,0,0,0,0,0,0,0,
4,0,0,0,0,0,0,0,0,0)))
anova(nn2, type="marginal")
## numDF denDF F-value p-value
## int 1 554 402.4 <.0001
## A.(Intercept) 1 554 1535.3 <.0001
## A.blc 2 554 2.6 0.0777
## A.fam 1 554 0.3 0.5882
## A.agr 1 554 4.5 0.0340
## A.cinza 1 554 2.7 0.0984
## A.fam:agr 1 554 3.9 0.0489
## A.fam:cinza 1 554 0.5 0.4877
## A.agr:cinza 1 554 13.2 0.0003
## A.fam:agr:cinza 1 554 6.1 0.0141
## d50.(Intercept) 1 554 856.3 <.0001
## d50.blc 2 554 3.9 0.0201
## d50.fam 1 554 1.3 0.2503
## d50.agr 1 554 0.0 0.9590
## d50.cinza 1 554 0.4 0.5494
## d50.fam:agr 1 554 0.0 0.9844
## d50.fam:cinza 1 554 0.9 0.3517
## d50.agr:cinza 1 554 0.1 0.8176
## d50.fam:agr:cinza 1 554 0.0 0.9192
## S.(Intercept) 1 554 412.4 <.0001
## S.blc 2 554 0.9 0.3989
## S.fam 1 554 0.0 0.8967
## S.agr 1 554 0.0 0.8572
## S.cinza 1 554 0.4 0.5098
## S.fam:agr 1 554 0.4 0.5220
## S.fam:cinza 1 554 0.0 0.8462
## S.agr:cinza 1 554 0.1 0.7825
## S.fam:agr:cinza 1 554 0.1 0.7967
summary(nn2)$tTable
## Value Std.Error DF t-value p-value
## int 5.048608 0.25168 554 20.05965 1.080e-67
## A.(Intercept) 134.912429 3.44315 554 39.18289 8.103e-162
## A.blc2 -1.260908 2.74178 554 -0.45989 6.458e-01
## A.blc3 -6.066132 2.81438 554 -2.15540 3.156e-02
## A.famF48 2.286019 4.21985 554 0.54173 5.882e-01
## A.agr0-2 mm 8.925385 4.19889 554 2.12565 3.397e-02
## A.cinza 0.240671 0.14537 554 1.65555 9.838e-02
## A.famF48:agr0-2 mm -11.740518 5.94850 554 -1.97369 4.891e-02
## A.famF48:cinza -0.138770 0.19985 554 -0.69437 4.877e-01
## A.agr0-2 mm:cinza -0.745253 0.20495 554 -3.63621 3.025e-04
## A.famF48:agr0-2 mm:cinza 0.696205 0.28274 554 2.46233 1.411e-02
## d50.(Intercept) 29.218188 0.99846 554 29.26322 1.689e-114
## d50.blc2 0.442151 0.81869 554 0.54007 5.894e-01
## d50.blc3 2.190127 0.82465 554 2.65584 8.139e-03
## d50.famF48 1.428022 1.24085 554 1.15085 2.503e-01
## d50.agr0-2 mm 0.063752 1.23991 554 0.05142 9.590e-01
## d50.cinza 0.025324 0.04227 554 0.59906 5.494e-01
## d50.famF48:agr0-2 mm -0.034252 1.75564 554 -0.01951 9.844e-01
## d50.famF48:cinza -0.055236 0.05925 554 -0.93217 3.517e-01
## d50.agr0-2 mm:cinza 0.013827 0.05994 554 0.23068 8.176e-01
## d50.famF48:agr0-2 mm:cinza -0.008521 0.08400 554 -0.10144 9.192e-01
## S.(Intercept) 5.683723 0.27987 554 20.30839 5.940e-69
## S.blc2 -0.172300 0.22563 554 -0.76363 4.454e-01
## S.blc3 0.138910 0.23161 554 0.59975 5.489e-01
## S.famF48 0.044772 0.34467 554 0.12990 8.967e-01
## S.agr0-2 mm -0.061980 0.34440 554 -0.17996 8.572e-01
## S.cinza -0.007997 0.01212 554 -0.65961 5.098e-01
## S.famF48:agr0-2 mm 0.313526 0.48936 554 0.64069 5.220e-01
## S.famF48:cinza 0.003212 0.01655 554 0.19403 8.462e-01
## S.agr0-2 mm:cinza 0.004779 0.01730 554 0.27621 7.825e-01
## S.famF48:agr0-2 mm:cinza -0.006096 0.02365 554 -0.25780 7.967e-01
VarCorr(nn2)
## parcela = pdLogChol(list(A ~ 1,d50 ~ 1,S ~ 1))
## Variance StdDev Corr
## A.(Intercept) 79.7499 8.930 A.(In) d50.(I
## d50.(Intercept) 8.5178 2.919 -0.282
## S.(Intercept) 0.4706 0.686 -0.427 0.342
## Residual 9.1425 3.024
plot(nn2)
par(mfrow=c(1,3)); apply(ranef(nn2), 2, qqnorm); layout(1)
## $`A.(Intercept)`
## $`A.(Intercept)`$x
## [1] -0.58355 -1.09433 -1.61117 0.73181 -0.81222 -1.34517 -0.94387 -1.15035 0.35020
## [10] 0.69334 0.61931 0.48039 -0.19520 -0.16487 1.34517 1.21023 -0.48039 0.25643
## [19] -0.69334 -0.35020 -0.38211 0.85445 -1.42291 -1.04155 -1.51036 0.28740 1.15035
## [28] 0.51416 1.09433 0.41441 -0.41441 -0.04478 -0.22571 1.61117 0.07467 -1.27480
## [37] -0.28740 0.04478 0.94387 -2.10017 1.27480 1.42291 -0.99153 -0.61931 0.77139
## [46] -0.44716 1.73166 -0.10463 -0.01492 0.13469 2.51495 0.10463 0.38211 -1.88430
## [55] 0.81222 0.99153 0.89826 -0.13469 0.65587 -2.51495 -0.73181 -0.31864 0.58355
## [64] -0.89826 1.51036 -0.54852 1.04155 0.16487 1.88430 0.19520 0.01492 -0.25643
## [73] -0.85445 -0.51416 0.31864 -0.07467 -0.65587 0.54852 2.10017 -1.73166 -1.21023
## [82] 0.44716 -0.77139 0.22571
##
## $`A.(Intercept)`$y
## 1_F29_4-10 mm_0 2_F29_4-10 mm_0 3_F29_4-10 mm_0 1_F48_4-10 mm_0 2_F48_4-10 mm_0
## -3.8739 -8.8571 -16.1854 5.4864 -4.8571
## 3_F48_4-10 mm_0 1_F29_0-2 mm_0 2_F29_0-2 mm_0 3_F29_0-2 mm_0 1_F48_0-2 mm_0
## -11.6858 -6.0302 -10.0660 3.1603 5.2110
## 2_F48_0-2 mm_0 3_F48_0-2 mm_0 1_F29_4-10 mm_1.5 2_F29_4-10 mm_1.5 3_F29_4-10 mm_1.5
## 4.5732 3.9433 0.3603 0.5183 11.2246
## 1_F48_4-10 mm_1.5 2_F48_4-10 mm_1.5 3_F48_4-10 mm_1.5 1_F29_0-2 mm_1.5 2_F29_0-2 mm_1.5
## 9.4967 -3.2707 2.7453 -4.3436 -1.1114
## 3_F29_0-2 mm_1.5 1_F48_0-2 mm_1.5 2_F48_0-2 mm_1.5 3_F48_0-2 mm_1.5 1_F29_4-10 mm_3
## -1.8199 6.1365 -12.2765 -7.9481 -15.5047
## 2_F29_4-10 mm_3 3_F29_4-10 mm_3 1_F48_4-10 mm_3 2_F48_4-10 mm_3 3_F48_4-10 mm_3
## 2.7664 8.2941 4.0183 6.8517 3.2095
## 1_F29_0-2 mm_3 2_F29_0-2 mm_3 3_F29_0-2 mm_3 1_F48_0-2 mm_3 2_F48_0-2 mm_3
## -2.7221 1.0834 0.3251 11.9424 1.8378
## 3_F48_0-2 mm_3 1_F29_4-10 mm_6 2_F29_4-10 mm_6 3_F29_4-10 mm_6 1_F48_4-10 mm_6
## -11.2544 -0.4196 1.7987 6.3164 -23.6421
## 2_F48_4-10 mm_6 3_F48_4-10 mm_6 1_F29_0-2 mm_6 2_F29_0-2 mm_6 3_F29_0-2 mm_6
## 10.9493 11.3427 -6.0874 -3.8934 5.5090
## 1_F48_0-2 mm_6 2_F48_0-2 mm_6 3_F48_0-2 mm_6 1_F29_4-10 mm_12 2_F29_4-10 mm_12
## -3.0181 12.7811 0.7278 1.3723 2.2766
## 3_F29_4-10 mm_12 1_F48_4-10 mm_12 2_F48_4-10 mm_12 3_F48_4-10 mm_12 1_F29_0-2 mm_12
## 16.5352 1.8499 3.1886 -19.8181 6.0384
## 2_F29_0-2 mm_12 3_F29_0-2 mm_12 1_F48_0-2 mm_12 2_F48_0-2 mm_12 3_F48_0-2 mm_12
## 6.3701 6.2277 0.6440 4.9544 -23.7094
## 1_F29_4-10 mm_24 2_F29_4-10 mm_24 3_F29_4-10 mm_24 1_F48_4-10 mm_24 2_F48_4-10 mm_24
## -4.5618 -0.9594 4.4935 -5.2733 11.5773
## 3_F48_4-10 mm_24 1_F29_0-2 mm_24 2_F29_0-2 mm_24 3_F29_0-2 mm_24 1_F48_0-2 mm_24
## -3.4396 6.7584 2.4532 13.0897 2.4938
## 2_F48_0-2 mm_24 3_F48_0-2 mm_24 1_F29_4-10 mm_48 2_F29_4-10 mm_48 3_F29_4-10 mm_48
## 1.5783 -0.1598 -5.1374 -3.3661 2.9089
## 1_F48_4-10 mm_48 2_F48_4-10 mm_48 3_F48_4-10 mm_48 1_F29_0-2 mm_48 2_F29_0-2 mm_48
## 0.8990 -3.9497 4.3219 14.4724 -18.3643
## 3_F29_0-2 mm_48 1_F48_0-2 mm_48 2_F48_0-2 mm_48 3_F48_0-2 mm_48
## -11.0494 3.4344 -4.5867 2.6949
##
##
## $`d50.(Intercept)`
## $`d50.(Intercept)`$x
## [1] -0.16487 0.51416 2.10017 -1.88430 -2.51495 -0.31864 -0.89826 0.99153 0.10463
## [10] -1.61117 -0.04478 -0.54852 -0.61931 -1.51036 -2.10017 -0.07467 1.27480 1.34517
## [19] 0.48039 -0.13469 -0.73181 0.58355 0.89826 0.61931 1.73166 0.25643 0.41441
## [28] -1.42291 -0.25643 -0.94387 0.85445 0.22571 1.51036 -0.85445 -1.34517 -0.41441
## [37] -0.65587 -0.35020 0.38211 2.51495 1.21023 -0.01492 -0.99153 -0.22571 -0.77139
## [46] 1.04155 0.44716 0.16487 1.61117 0.65587 -0.10463 0.81222 -0.51416 0.07467
## [55] 0.01492 1.42291 0.73181 -0.38211 -0.28740 0.94387 -1.73166 -1.27480 -1.15035
## [64] 1.88430 0.13469 -1.04155 -0.58355 -1.21023 -1.09433 0.19520 0.54852 1.09433
## [73] 0.77139 0.69334 0.04478 -0.48039 -0.69334 0.31864 -0.19520 1.15035 0.35020
## [82] -0.81222 0.28740 -0.44716
##
## $`d50.(Intercept)`$y
## 1_F29_4-10 mm_0 2_F29_4-10 mm_0 3_F29_4-10 mm_0 1_F48_4-10 mm_0 2_F48_4-10 mm_0
## -0.758544 1.281239 6.852085 -4.819758 -5.944337
## 3_F48_4-10 mm_0 1_F29_0-2 mm_0 2_F29_0-2 mm_0 3_F29_0-2 mm_0 1_F48_0-2 mm_0
## -1.233598 -2.710972 2.774382 -0.002663 -4.119182
## 2_F48_0-2 mm_0 3_F48_0-2 mm_0 1_F29_4-10 mm_1.5 2_F29_4-10 mm_1.5 3_F29_4-10 mm_1.5
## -0.358101 -1.746362 -2.022693 -4.078396 -4.917265
## 1_F48_4-10 mm_1.5 2_F48_4-10 mm_1.5 3_F48_4-10 mm_1.5 1_F29_0-2 mm_1.5 2_F29_0-2 mm_1.5
## -0.525139 3.514448 3.595847 1.276706 -0.555306
## 3_F29_0-2 mm_1.5 1_F48_0-2 mm_1.5 2_F48_0-2 mm_1.5 3_F48_0-2 mm_1.5 1_F29_4-10 mm_3
## -2.239307 1.875190 2.571359 1.925827 5.159632
## 2_F29_4-10 mm_3 3_F29_4-10 mm_3 1_F48_4-10 mm_3 2_F48_4-10 mm_3 3_F48_4-10 mm_3
## 0.664657 1.004460 -3.893265 -0.941138 -2.780564
## 1_F29_0-2 mm_3 2_F29_0-2 mm_3 3_F29_0-2 mm_3 1_F48_0-2 mm_3 2_F48_0-2 mm_3
## 2.550024 0.480101 4.349488 -2.404246 -3.620689
## 3_F48_0-2 mm_3 1_F29_4-10 mm_6 2_F29_4-10 mm_6 3_F29_4-10 mm_6 1_F48_4-10 mm_6
## -1.316236 -2.042717 -1.244479 0.943177 9.256601
## 2_F48_4-10 mm_6 3_F48_4-10 mm_6 1_F29_0-2 mm_6 2_F29_0-2 mm_6 3_F29_0-2 mm_6
## 3.349274 -0.276935 -3.025928 -0.930022 -2.358522
## 1_F48_0-2 mm_6 2_F48_0-2 mm_6 3_F48_0-2 mm_6 1_F29_4-10 mm_12 2_F29_4-10 mm_12
## 2.959348 1.274649 0.376877 4.602514 1.989278
## 3_F29_4-10 mm_12 1_F48_4-10 mm_12 2_F48_4-10 mm_12 3_F48_4-10 mm_12 1_F29_0-2 mm_12
## -0.550541 2.465598 -1.714484 -0.042693 -0.118160
## 2_F29_0-2 mm_12 3_F29_0-2 mm_12 1_F48_0-2 mm_12 2_F48_0-2 mm_12 3_F48_0-2 mm_12
## 3.693464 2.203892 -1.284471 -1.213304 2.723426
## 1_F29_4-10 mm_24 2_F29_4-10 mm_24 3_F29_4-10 mm_24 1_F48_4-10 mm_24 2_F48_4-10 mm_24
## -4.233296 -3.573484 -3.358468 5.803099 0.170368
## 3_F48_4-10 mm_24 1_F29_0-2 mm_24 2_F29_0-2 mm_24 3_F29_0-2 mm_24 1_F48_0-2 mm_24
## -3.097033 -1.972352 -3.377239 -3.286198 0.474156
## 2_F48_0-2 mm_24 3_F48_0-2 mm_24 1_F29_4-10 mm_48 2_F29_4-10 mm_48 3_F29_4-10 mm_48
## 1.810302 3.173543 2.294239 2.086097 -0.097496
## 1_F48_4-10 mm_48 2_F48_4-10 mm_48 3_F48_4-10 mm_48 1_F29_0-2 mm_48 2_F29_0-2 mm_48
## -1.601764 -2.045516 0.760989 -0.808080 3.210222
## 3_F29_0-2 mm_48 1_F48_0-2 mm_48 2_F48_0-2 mm_48 3_F48_0-2 mm_48
## 0.846472 -2.376541 0.726657 -1.452201
##
##
## $`S.(Intercept)`
## $`S.(Intercept)`$x
## [1] 0.58355 -0.16487 0.99153 -0.38211 1.09433 0.69334 -0.77139 0.85445 -0.73181
## [10] -1.88430 -0.19520 0.22571 0.01492 0.51416 -0.28740 -0.94387 0.10463 -1.15035
## [19] 1.51036 -0.22571 -0.54852 -1.27480 1.73166 0.19520 2.10017 0.04478 -0.58355
## [28] 0.16487 0.07467 -0.89826 0.35020 0.73181 0.89826 0.54852 -2.10017 1.88430
## [37] -0.31864 -0.99153 0.31864 1.42291 -0.85445 -1.73166 1.15035 -1.34517 -0.44716
## [46] -0.01492 -1.42291 -0.25643 -0.07467 -0.35020 -1.04155 -0.69334 -0.13469 1.61117
## [55] -0.48039 0.44716 0.28740 0.77139 -0.61931 2.51495 -0.51416 1.27480 -1.51036
## [64] 0.94387 0.61931 0.41441 -1.21023 -2.51495 -0.04478 1.04155 -0.41441 0.25643
## [73] 0.13469 1.34517 -1.09433 -0.81222 0.48039 -0.10463 -0.65587 1.21023 0.81222
## [82] -1.61117 0.65587 0.38211
##
## $`S.(Intercept)`$y
## 1_F29_4-10 mm_0 2_F29_4-10 mm_0 3_F29_4-10 mm_0 1_F48_4-10 mm_0 2_F48_4-10 mm_0
## 0.214498 -0.189135 0.849425 -0.249323 0.901912
## 3_F48_4-10 mm_0 1_F29_0-2 mm_0 2_F29_0-2 mm_0 3_F29_0-2 mm_0 1_F48_0-2 mm_0
## 0.425484 -0.428192 0.549220 -0.427437 -0.953356
## 2_F48_0-2 mm_0 3_F48_0-2 mm_0 1_F29_4-10 mm_1.5 2_F29_4-10 mm_1.5 3_F29_4-10 mm_1.5
## -0.200076 -0.004877 -0.103298 0.161839 -0.213396
## 1_F48_4-10 mm_1.5 2_F48_4-10 mm_1.5 3_F48_4-10 mm_1.5 1_F29_0-2 mm_1.5 2_F29_0-2 mm_1.5
## -0.504608 -0.094345 -0.558349 1.057928 -0.208962
## 3_F29_0-2 mm_1.5 1_F48_0-2 mm_1.5 2_F48_0-2 mm_1.5 3_F48_0-2 mm_1.5 1_F29_4-10 mm_3
## -0.366407 -0.592706 1.129149 -0.016920 1.250606
## 2_F29_4-10 mm_3 3_F29_4-10 mm_3 1_F48_4-10 mm_3 2_F48_4-10 mm_3 3_F48_4-10 mm_3
## -0.098155 -0.371389 -0.019706 -0.096032 -0.475006
## 1_F29_0-2 mm_3 2_F29_0-2 mm_3 3_F29_0-2 mm_3 1_F48_0-2 mm_3 2_F48_0-2 mm_3
## 0.017351 0.445640 0.708152 0.199414 -0.953650
## 3_F48_0-2 mm_3 1_F29_4-10 mm_6 2_F29_4-10 mm_6 3_F29_4-10 mm_6 1_F48_4-10 mm_6
## 1.147919 -0.217213 -0.513521 0.012961 1.012064
## 2_F48_4-10 mm_6 3_F48_4-10 mm_6 1_F29_0-2 mm_6 2_F29_0-2 mm_6 3_F29_0-2 mm_6
## -0.465467 -0.920397 0.912425 -0.616177 -0.280563
## 1_F48_0-2 mm_6 2_F48_0-2 mm_6 3_F48_0-2 mm_6 1_F29_4-10 mm_12 2_F29_4-10 mm_12
## -0.156708 -0.863206 -0.211441 -0.176520 -0.243961
## 3_F29_4-10 mm_12 1_F48_4-10 mm_12 2_F48_4-10 mm_12 3_F48_4-10 mm_12 1_F29_0-2 mm_12
## -0.518769 -0.406604 -0.186600 1.110789 -0.310033
## 2_F29_0-2 mm_12 3_F29_0-2 mm_12 1_F48_0-2 mm_12 2_F48_0-2 mm_12 3_F48_0-2 mm_12
## 0.043148 0.012450 0.494550 -0.375915 1.284886
## 1_F29_4-10 mm_24 2_F29_4-10 mm_24 3_F29_4-10 mm_24 1_F48_4-10 mm_24 2_F48_4-10 mm_24
## -0.358239 0.996621 -0.887437 0.784403 0.248374
## 3_F48_4-10 mm_24 1_F29_0-2 mm_24 2_F29_0-2 mm_24 3_F29_0-2 mm_24 1_F48_0-2 mm_24
## 0.038765 -0.569843 -1.423394 -0.170595 0.878569
## 2_F48_0-2 mm_24 3_F48_0-2 mm_24 1_F29_4-10 mm_48 2_F29_4-10 mm_48 3_F29_4-10 mm_48
## -0.253429 -0.003664 -0.051167 1.006069 -0.549818
## 1_F48_4-10 mm_48 2_F48_4-10 mm_48 3_F48_4-10 mm_48 1_F29_0-2 mm_48 2_F29_0-2 mm_48
## -0.429154 0.063045 -0.179246 -0.406255 0.925903
## 3_F29_0-2 mm_48 1_F48_0-2 mm_48 2_F48_0-2 mm_48 3_F48_0-2 mm_48
## 0.535640 -0.888882 0.311105 0.029237
intervals(nn2)
## Approximate 95% confidence intervals
##
## Fixed effects:
## lower est. upper
## int 4.56585 5.048608 5.53136
## A.(Intercept) 128.30800 134.912429 141.51685
## A.blc2 -6.52002 -1.260908 3.99820
## A.blc3 -11.46450 -6.066132 -0.66776
## A.famF48 -5.80823 2.286019 10.38027
## A.agr0-2 mm 0.87133 8.925385 16.97944
## A.cinza -0.03817 0.240671 0.51952
## A.famF48:agr0-2 mm -23.15055 -11.740518 -0.33049
## A.famF48:cinza -0.52211 -0.138770 0.24457
## A.agr0-2 mm:cinza -1.13838 -0.745253 -0.35212
## A.famF48:agr0-2 mm:cinza 0.15387 0.696205 1.23854
## d50.(Intercept) 27.30300 29.218188 31.13337
## d50.blc2 -1.12820 0.442151 2.01250
## d50.blc3 0.60834 2.190127 3.77191
## d50.famF48 -0.95209 1.428022 3.80813
## d50.agr0-2 mm -2.31456 0.063752 2.44207
## d50.cinza -0.05576 0.025324 0.10641
## d50.famF48:agr0-2 mm -3.40181 -0.034252 3.33331
## d50.famF48:cinza -0.16889 -0.055236 0.05842
## d50.agr0-2 mm:cinza -0.10115 0.013827 0.12880
## d50.famF48:agr0-2 mm:cinza -0.16965 -0.008521 0.15261
## S.(Intercept) 5.14689 5.683723 6.22055
## S.blc2 -0.60510 -0.172300 0.26050
## S.blc3 -0.30536 0.138910 0.58318
## S.famF48 -0.61635 0.044772 0.70590
## S.agr0-2 mm -0.72259 -0.061980 0.59863
## S.cinza -0.03125 -0.007997 0.01526
## S.famF48:agr0-2 mm -0.62513 0.313526 1.25218
## S.famF48:cinza -0.02854 0.003212 0.03496
## S.agr0-2 mm:cinza -0.02841 0.004779 0.03796
## S.famF48:agr0-2 mm:cinza -0.05145 -0.006096 0.03926
## attr(,"label")
## [1] "Fixed effects:"
##
## Random Effects:
## Level: parcela
## lower est. upper
## sd(A.(Intercept)) 7.03564 8.9303 11.33513
## sd(d50.(Intercept)) 2.46885 2.9185 3.45010
## sd(S.(Intercept)) 0.54065 0.6860 0.87042
## cor(A.(Intercept),d50.(Intercept)) -0.51060 -0.2822 -0.01652
## cor(A.(Intercept),S.(Intercept)) -0.68015 -0.4266 -0.08198
## cor(d50.(Intercept),S.(Intercept)) 0.07352 0.3418 0.56400
##
## Within-group standard error:
## lower est. upper
## 2.824 3.024 3.237
pairs(nn2)
## Esse parece ser um bom modelo, existe interação tripla apenas para A,
## o resto não muda.
##-----------------------------------------------------------------------------
## Modelo que é uma redução do nn2.
nn3 <- nlme(altura~int+A/(1+exp(-(dias-d50)/S)),
fixed=list(int~1,
A~blc+fam*agr*cinza,
d50~blc,
S~blc),
random=A+d50+S~1,
data=marag,
start=list(fixed=c(5.2,
120,0,0,0,0,0,0,0,0,0,
30,0,0,
4,0,0)))
anova(nn3, type="marginal")
## numDF denDF F-value p-value
## int 1 568 412.3 <.0001
## A.(Intercept) 1 568 1560.5 <.0001
## A.blc 2 568 2.8 0.0627
## A.fam 1 568 0.5 0.4791
## A.agr 1 568 4.6 0.0318
## A.cinza 1 568 3.0 0.0845
## A.fam:agr 1 568 4.0 0.0456
## A.fam:cinza 1 568 0.7 0.3922
## A.agr:cinza 1 568 13.1 0.0003
## A.fam:agr:cinza 1 568 6.3 0.0125
## d50.(Intercept) 1 568 2629.2 <.0001
## d50.blc 2 568 3.7 0.0244
## S.(Intercept) 1 568 1189.7 <.0001
## S.blc 2 568 0.8 0.4355
anova(nn3, nn2) # ótimo!!
## Model df AIC BIC logLik Test L.Ratio p-value
## nn3 1 24 4077 4185 -2015
## nn2 2 38 4099 4270 -2012 1 vs 2 6.153 0.9625
summary(nn3)$tTable
## Value Std.Error DF t-value p-value
## int 5.0501 0.2487 568 20.3059 2.494e-69
## A.(Intercept) 134.6841 3.4094 568 39.5034 4.492e-165
## A.blc2 -1.3152 2.7302 568 -0.4817 6.302e-01
## A.blc3 -6.2798 2.7980 568 -2.2444 2.519e-02
## A.famF48 2.9420 4.1540 568 0.7082 4.791e-01
## A.agr0-2 mm 8.8981 4.1339 568 2.1525 3.178e-02
## A.cinza 0.2514 0.1455 568 1.7280 8.453e-02
## A.famF48:agr0-2 mm -11.7084 5.8452 568 -2.0031 4.564e-02
## A.famF48:cinza -0.1692 0.1976 568 -0.8564 3.922e-01
## A.agr0-2 mm:cinza -0.7410 0.2045 568 -3.6241 3.160e-04
## A.famF48:agr0-2 mm:cinza 0.6993 0.2791 568 2.5057 1.250e-02
## d50.(Intercept) 30.0030 0.5851 568 51.2756 2.803e-215
## d50.blc2 0.4303 0.8261 568 0.5209 6.026e-01
## d50.blc3 2.1504 0.8315 568 2.5862 9.953e-03
## S.(Intercept) 5.6847 0.1648 568 34.4923 1.897e-141
## S.blc2 -0.1759 0.2262 568 -0.7777 4.371e-01
## S.blc3 0.1189 0.2316 568 0.5131 6.081e-01
VarCorr(nn3)
## parcela = pdLogChol(list(A ~ 1,d50 ~ 1,S ~ 1))
## Variance StdDev Corr
## A.(Intercept) 80.9886 8.9994 A.(In) d50.(I
## d50.(Intercept) 8.8802 2.9800 -0.273
## S.(Intercept) 0.4895 0.6996 -0.413 0.343
## Residual 9.1305 3.0217
plot(nn3)
par(mfrow=c(1,3)); apply(ranef(nn3), 2, qqnorm); layout(1)
## $`A.(Intercept)`
## $`A.(Intercept)`$x
## [1] -0.54852 -1.04155 -1.61117 0.73181 -0.89826 -1.27480 -0.99153 -1.09433 0.54852
## [10] 0.61931 0.41441 0.25643 -0.16487 -0.13469 1.51036 1.21023 -0.65587 0.16487
## [19] -0.61931 -0.35020 -0.38211 0.69334 -1.42291 -1.15035 -1.51036 0.38211 1.15035
## [28] 0.51416 0.89826 0.28740 -0.41441 -0.01492 -0.04478 1.42291 -0.10463 -1.34517
## [37] -0.22571 0.10463 1.04155 -2.10017 1.27480 1.34517 -0.94387 -0.58355 0.81222
## [46] -0.73181 1.73166 -0.25643 0.07467 0.22571 2.51495 0.04478 0.35020 -1.88430
## [55] 0.85445 1.09433 0.99153 -0.19520 0.58355 -2.51495 -0.81222 -0.28740 0.65587
## [64] -0.85445 1.61117 -0.51416 0.94387 0.19520 1.88430 0.13469 -0.07467 -0.31864
## [73] -0.69334 -0.44716 0.48039 0.01492 -0.48039 0.77139 2.10017 -1.73166 -1.21023
## [82] 0.44716 -0.77139 0.31864
##
## $`A.(Intercept)`$y
## 1_F29_4-10 mm_0 2_F29_4-10 mm_0 3_F29_4-10 mm_0 1_F48_4-10 mm_0 2_F48_4-10 mm_0
## -3.60533 -8.64383 -15.45888 4.98278 -5.32475
## 3_F48_4-10 mm_0 1_F29_0-2 mm_0 2_F29_0-2 mm_0 3_F29_0-2 mm_0 1_F48_0-2 mm_0
## -12.29445 -5.76029 -9.48200 3.68673 4.28961
## 2_F48_0-2 mm_0 3_F48_0-2 mm_0 1_F29_4-10 mm_1.5 2_F29_4-10 mm_1.5 3_F29_4-10 mm_1.5
## 3.48915 2.81946 0.60153 0.80958 11.64878
## 1_F48_4-10 mm_1.5 2_F48_4-10 mm_1.5 3_F48_4-10 mm_1.5 1_F29_0-2 mm_1.5 2_F29_0-2 mm_1.5
## 9.04998 -3.77457 2.25550 -3.69238 -0.73035
## 3_F29_0-2 mm_1.5 1_F48_0-2 mm_1.5 2_F48_0-2 mm_1.5 3_F48_0-2 mm_1.5 1_F29_4-10 mm_3
## -1.37915 4.96120 -13.61538 -9.54387 -14.40260
## 2_F29_4-10 mm_3 3_F29_4-10 mm_3 1_F48_4-10 mm_3 2_F48_4-10 mm_3 3_F48_4-10 mm_3
## 3.11431 8.77012 3.59956 6.50053 2.85207
## 1_F29_0-2 mm_3 2_F29_0-2 mm_3 3_F29_0-2 mm_3 1_F48_0-2 mm_3 2_F48_0-2 mm_3
## -2.27078 1.63017 1.26078 11.10946 0.96481
## 3_F48_0-2 mm_3 1_F29_4-10 mm_6 2_F29_4-10 mm_6 3_F29_4-10 mm_6 1_F48_4-10 mm_6
## -12.49766 -0.19112 2.05688 6.87439 -24.00354
## 2_F48_4-10 mm_6 3_F48_4-10 mm_6 1_F29_0-2 mm_6 2_F29_0-2 mm_6 3_F29_0-2 mm_6
## 10.73206 11.10091 -5.68924 -3.63348 5.97820
## 1_F48_0-2 mm_6 2_F48_0-2 mm_6 3_F48_0-2 mm_6 1_F29_4-10 mm_12 2_F29_4-10 mm_12
## -4.20845 11.95479 -0.38657 1.90625 2.69700
## 3_F29_4-10 mm_12 1_F48_4-10 mm_12 2_F48_4-10 mm_12 3_F48_4-10 mm_12 1_F29_0-2 mm_12
## 17.06289 1.68515 3.05126 -20.00644 6.32719
## 2_F29_0-2 mm_12 3_F29_0-2 mm_12 1_F48_0-2 mm_12 2_F48_0-2 mm_12 3_F48_0-2 mm_12
## 6.93204 6.83916 -0.08675 4.26523 -25.07204
## 1_F29_4-10 mm_24 2_F29_4-10 mm_24 3_F29_4-10 mm_24 1_F48_4-10 mm_24 2_F48_4-10 mm_24
## -4.41452 -0.46060 4.85043 -4.70588 11.94227
## 3_F48_4-10 mm_24 1_F29_0-2 mm_24 2_F29_0-2 mm_24 3_F29_0-2 mm_24 1_F48_0-2 mm_24
## -3.17672 6.83729 2.45173 13.42414 2.16750
## 2_F48_0-2 mm_24 3_F48_0-2 mm_24 1_F29_4-10 mm_48 2_F29_4-10 mm_48 3_F29_4-10 mm_48
## 1.10764 -0.68383 -4.08659 -2.29114 3.59248
## 1_F48_4-10 mm_48 2_F48_4-10 mm_48 3_F48_4-10 mm_48 1_F29_0-2 mm_48 2_F29_0-2 mm_48
## 1.63670 -3.12702 5.43996 14.42825 -18.26929
## 3_F29_0-2 mm_48 1_F48_0-2 mm_48 2_F48_0-2 mm_48 3_F48_0-2 mm_48
## -10.96966 3.53505 -4.34705 3.01327
##
##
## $`d50.(Intercept)`
## $`d50.(Intercept)`$x
## [1] -0.44716 0.35020 2.10017 -1.61117 -2.10017 -0.13469 -1.21023 0.69334 -0.16487
## [10] -1.42291 0.16487 -0.31864 -0.73181 -1.88430 -2.51495 0.04478 1.34517 1.51036
## [19] 0.41441 -0.35020 -0.85445 0.77139 0.99153 0.73181 1.73166 -0.01492 0.22571
## [28] -1.15035 -0.10463 -0.61931 0.58355 -0.04478 1.27480 -0.54852 -0.99153 -0.19520
## [37] -0.69334 -0.51416 0.28740 2.51495 1.21023 0.10463 -1.27480 -0.38211 -0.77139
## [46] 1.09433 0.51416 0.44716 1.42291 0.48039 -0.25643 0.85445 -0.41441 0.13469
## [55] -0.07467 1.15035 0.61931 -0.28740 -0.22571 0.89826 -1.73166 -1.51036 -1.34517
## [64] 1.88430 0.07467 -1.04155 -0.48039 -1.09433 -0.94387 0.38211 0.54852 1.04155
## [73] 0.94387 0.81222 0.31864 -0.65587 -0.81222 0.01492 0.25643 1.61117 0.65587
## [82] -0.89826 0.19520 -0.58355
##
## $`d50.(Intercept)`$y
## 1_F29_4-10 mm_0 2_F29_4-10 mm_0 3_F29_4-10 mm_0 1_F48_4-10 mm_0 2_F48_4-10 mm_0
## -1.52552 0.51232 6.17073 -4.19495 -5.31971
## 3_F48_4-10 mm_0 1_F29_0-2 mm_0 2_F29_0-2 mm_0 3_F29_0-2 mm_0 1_F48_0-2 mm_0
## -0.62508 -3.42359 2.11279 -0.66924 -3.50245
## 2_F48_0-2 mm_0 3_F48_0-2 mm_0 1_F29_4-10 mm_1.5 2_F29_4-10 mm_1.5 3_F29_4-10 mm_1.5
## 0.23688 -1.16280 -2.75635 -4.80182 -5.61667
## 1_F48_4-10 mm_1.5 2_F48_4-10 mm_1.5 3_F48_4-10 mm_1.5 1_F29_0-2 mm_1.5 2_F29_0-2 mm_1.5
## 0.06251 4.10067 4.19718 0.68128 -1.18845
## 3_F29_0-2 mm_1.5 1_F48_0-2 mm_1.5 2_F48_0-2 mm_1.5 3_F48_0-2 mm_1.5 1_F29_4-10 mm_3
## -2.85608 2.42401 3.06132 2.39791 4.57373
## 2_F29_4-10 mm_3 3_F29_4-10 mm_3 1_F48_4-10 mm_3 2_F48_4-10 mm_3 3_F48_4-10 mm_3
## -0.01103 0.35346 -3.35480 -0.38653 -2.21870
## 1_F29_0-2 mm_3 2_F29_0-2 mm_3 3_F29_0-2 mm_3 1_F48_0-2 mm_3 2_F48_0-2 mm_3
## 1.98255 -0.06989 3.85940 -1.86243 -3.07159
## 3_F48_0-2 mm_3 1_F29_4-10 mm_6 2_F29_4-10 mm_6 3_F29_4-10 mm_6 1_F48_4-10 mm_6
## -0.87141 -2.66106 -1.85438 0.38096 9.71077
## 2_F48_4-10 mm_6 3_F48_4-10 mm_6 1_F29_0-2 mm_6 2_F29_0-2 mm_6 3_F29_0-2 mm_6
## 3.82594 0.20756 -3.47394 -1.39574 -2.79065
## 1_F48_0-2 mm_6 2_F48_0-2 mm_6 3_F48_0-2 mm_6 1_F29_4-10 mm_12 2_F29_4-10 mm_12
## 3.38154 1.76269 0.81279 4.17698 1.55557
## 3_F29_4-10 mm_12 1_F48_4-10 mm_12 2_F48_4-10 mm_12 3_F48_4-10 mm_12 1_F29_0-2 mm_12
## -0.96606 2.75079 -1.42312 0.23429 -0.34525
## 2_F29_0-2 mm_12 3_F29_0-2 mm_12 1_F48_0-2 mm_12 2_F48_0-2 mm_12 3_F48_0-2 mm_12
## 3.50334 2.03240 -0.96919 -0.87583 2.89336
## 1_F29_4-10 mm_24 2_F29_4-10 mm_24 3_F29_4-10 mm_24 1_F48_4-10 mm_24 2_F48_4-10 mm_24
## -4.39546 -3.67574 -3.48237 5.79737 0.13622
## 3_F48_4-10 mm_24 1_F29_0-2 mm_24 2_F29_0-2 mm_24 3_F29_0-2 mm_24 1_F48_0-2 mm_24
## -3.13417 -1.74213 -3.14860 -3.01051 0.53212
## 2_F48_0-2 mm_24 3_F48_0-2 mm_24 1_F29_4-10 mm_48 2_F29_4-10 mm_48 3_F29_4-10 mm_48
## 1.86332 3.22495 3.01037 2.66980 0.43902
## 1_F48_4-10 mm_48 2_F48_4-10 mm_48 3_F48_4-10 mm_48 1_F29_0-2 mm_48 2_F29_0-2 mm_48
## -2.36690 -2.79244 0.05815 0.37491 4.43256
## 3_F29_0-2 mm_48 1_F48_0-2 mm_48 2_F48_0-2 mm_48 3_F48_0-2 mm_48
## 2.06286 -2.88489 0.24144 -1.92131
##
##
## $`S.(Intercept)`
## $`S.(Intercept)`$x
## [1] 0.54852 -0.16487 1.09433 -0.13469 1.27480 0.77139 -0.85445 0.81222 -0.81222
## [10] -1.42291 0.35020 0.51416 -0.04478 0.48039 -0.19520 -0.77139 0.04478 -0.94387
## [19] 1.42291 -0.38211 -0.65587 -0.58355 1.88430 0.44716 1.73166 -0.01492 -0.51416
## [28] 0.31864 0.07467 -0.73181 0.16487 0.65587 0.89826 0.69334 -1.51036 2.10017
## [37] -0.35020 -1.04155 0.22571 1.51036 -0.69334 -1.73166 1.15035 -1.34517 -0.48039
## [46] 0.28740 -1.21023 0.13469 -0.28740 -0.44716 -1.09433 -0.61931 -0.10463 1.61117
## [55] -0.54852 0.19520 0.10463 0.85445 -0.22571 2.51495 -0.89826 1.21023 -2.10017
## [64] 0.94387 0.58355 0.25643 -1.27480 -2.51495 -0.31864 1.34517 -0.07467 0.41441
## [73] -0.25643 0.99153 -1.61117 -1.15035 0.01492 -0.41441 -0.99153 1.04155 0.73181
## [82] -1.88430 0.61931 0.38211
##
## $`S.(Intercept)`$y
## 1_F29_4-10 mm_0 2_F29_4-10 mm_0 3_F29_4-10 mm_0 1_F48_4-10 mm_0 2_F48_4-10 mm_0
## 0.206165 -0.209442 0.855659 -0.208421 0.951276
## 3_F48_4-10 mm_0 1_F29_0-2 mm_0 2_F29_0-2 mm_0 3_F29_0-2 mm_0 1_F48_0-2 mm_0
## 0.457502 -0.493412 0.508088 -0.471061 -0.741090
## 2_F48_0-2 mm_0 3_F48_0-2 mm_0 1_F29_4-10 mm_1.5 2_F29_4-10 mm_1.5 3_F29_4-10 mm_1.5
## 0.012563 0.205299 -0.121825 0.149054 -0.214224
## 1_F48_4-10 mm_1.5 2_F48_4-10 mm_1.5 3_F48_4-10 mm_1.5 1_F29_0-2 mm_1.5 2_F29_0-2 mm_1.5
## -0.470109 -0.064441 -0.523294 1.027413 -0.266233
## 3_F29_0-2 mm_1.5 1_F48_0-2 mm_1.5 2_F48_0-2 mm_1.5 3_F48_0-2 mm_1.5 1_F29_4-10 mm_3
## -0.418618 -0.392260 1.313630 0.146900 1.239079
## 2_F29_4-10 mm_3 3_F29_4-10 mm_3 1_F48_4-10 mm_3 2_F48_4-10 mm_3 3_F48_4-10 mm_3
## -0.118510 -0.381368 0.010809 -0.061887 -0.444072
## 1_F29_0-2 mm_3 2_F29_0-2 mm_3 3_F29_0-2 mm_3 1_F48_0-2 mm_3 2_F48_0-2 mm_3
## -0.037287 0.402563 0.682788 0.418046 -0.762900
## 3_F48_0-2 mm_3 1_F29_4-10 mm_6 2_F29_4-10 mm_6 3_F29_4-10 mm_6 1_F48_4-10 mm_6
## 1.318852 -0.262566 -0.559398 -0.007061 1.029842
## 2_F48_4-10 mm_6 3_F48_4-10 mm_6 1_F29_0-2 mm_6 2_F29_0-2 mm_6 3_F29_0-2 mm_6
## -0.443158 -0.897042 0.863804 -0.690747 -0.332583
## 1_F48_0-2 mm_6 2_F48_0-2 mm_6 3_F48_0-2 mm_6 1_F29_4-10 mm_12 2_F29_4-10 mm_12
## 0.007135 -0.663798 -0.039523 -0.242084 -0.313375
## 3_F29_4-10 mm_12 1_F48_4-10 mm_12 2_F48_4-10 mm_12 3_F48_4-10 mm_12 1_F29_0-2 mm_12
## -0.576214 -0.416104 -0.191318 1.111697 -0.384953
## 2_F29_0-2 mm_12 3_F29_0-2 mm_12 1_F48_0-2 mm_12 2_F48_0-2 mm_12 3_F48_0-2 mm_12
## -0.018769 -0.041384 0.654518 -0.216487 1.390704
## 1_F29_4-10 mm_24 2_F29_4-10 mm_24 3_F29_4-10 mm_24 1_F48_4-10 mm_24 2_F48_4-10 mm_24
## -0.511194 0.882482 -1.025912 0.753144 0.209943
## 3_F48_4-10 mm_24 1_F29_0-2 mm_24 2_F29_0-2 mm_24 3_F29_0-2 mm_24 1_F48_0-2 mm_24
## -0.003919 -0.672913 -1.540741 -0.248921 0.999032
## 2_F48_0-2 mm_24 3_F48_0-2 mm_24 1_F29_4-10 mm_48 2_F29_4-10 mm_48 3_F29_4-10 mm_48
## -0.152487 0.100283 -0.225022 0.778039 -0.817089
## 1_F48_4-10 mm_48 2_F48_4-10 mm_48 3_F48_4-10 mm_48 1_F29_0-2 mm_48 2_F29_0-2 mm_48
## -0.582579 -0.079819 -0.305671 -0.544012 0.834446
## 3_F29_0-2 mm_48 1_F48_0-2 mm_48 2_F48_0-2 mm_48 3_F48_0-2 mm_48
## 0.440525 -0.903154 0.311423 0.037748
intervals(nn3)
## Approximate 95% confidence intervals
##
## Fixed effects:
## lower est. upper
## int 4.56783 5.0501 5.5323
## A.(Intercept) 128.07321 134.6841 141.2949
## A.blc2 -6.60908 -1.3152 3.9787
## A.blc3 -11.70504 -6.2798 -0.8545
## A.famF48 -5.11254 2.9420 10.9965
## A.agr0-2 mm 0.88259 8.8981 16.9137
## A.cinza -0.03069 0.2514 0.5334
## A.famF48:agr0-2 mm -23.04218 -11.7084 -0.3746
## A.famF48:cinza -0.55234 -0.1692 0.2139
## A.agr0-2 mm:cinza -1.13750 -0.7410 -0.3446
## A.famF48:agr0-2 mm:cinza 0.15816 0.6993 1.2405
## d50.(Intercept) 28.86847 30.0030 31.1376
## d50.blc2 -1.17149 0.4303 2.0321
## d50.blc3 0.53814 2.1504 3.7628
## S.(Intercept) 5.36514 5.6847 6.0043
## S.blc2 -0.61439 -0.1759 0.2626
## S.blc3 -0.33027 0.1189 0.5680
## attr(,"label")
## [1] "Fixed effects:"
##
## Random Effects:
## Level: parcela
## lower est. upper
## sd(A.(Intercept)) 7.11540 8.9994 11.382153
## sd(d50.(Intercept)) 2.52191 2.9800 3.521223
## sd(S.(Intercept)) 0.55292 0.6996 0.885249
## cor(A.(Intercept),d50.(Intercept)) -0.50666 -0.2729 -0.001661
## cor(A.(Intercept),S.(Intercept)) -0.67041 -0.4134 -0.067897
## cor(d50.(Intercept),S.(Intercept)) 0.07584 0.3432 0.564475
##
## Within-group standard error:
## lower est. upper
## 2.823 3.022 3.235
pairs(nn3)
summary(nn3)$tTable
## Value Std.Error DF t-value p-value
## int 5.0501 0.2487 568 20.3059 2.494e-69
## A.(Intercept) 134.6841 3.4094 568 39.5034 4.492e-165
## A.blc2 -1.3152 2.7302 568 -0.4817 6.302e-01
## A.blc3 -6.2798 2.7980 568 -2.2444 2.519e-02
## A.famF48 2.9420 4.1540 568 0.7082 4.791e-01
## A.agr0-2 mm 8.8981 4.1339 568 2.1525 3.178e-02
## A.cinza 0.2514 0.1455 568 1.7280 8.453e-02
## A.famF48:agr0-2 mm -11.7084 5.8452 568 -2.0031 4.564e-02
## A.famF48:cinza -0.1692 0.1976 568 -0.8564 3.922e-01
## A.agr0-2 mm:cinza -0.7410 0.2045 568 -3.6241 3.160e-04
## A.famF48:agr0-2 mm:cinza 0.6993 0.2791 568 2.5057 1.250e-02
## d50.(Intercept) 30.0030 0.5851 568 51.2756 2.803e-215
## d50.blc2 0.4303 0.8261 568 0.5209 6.026e-01
## d50.blc3 2.1504 0.8315 568 2.5862 9.953e-03
## S.(Intercept) 5.6847 0.1648 568 34.4923 1.897e-141
## S.blc2 -0.1759 0.2262 568 -0.7777 4.371e-01
## S.blc3 0.1189 0.2316 568 0.5131 6.081e-01
##-----------------------------------------------------------------------------
## Fazendo a predição.
pred <- expand.grid(blc="1", fam=levels(mara$fam), agr=levels(mara$agr),
cinza=seq(0,50, l=2), dias=seq(0,60,l=30))
pred$y <- predict(nn3, newdata=pred, level=0)
xyplot(y~dias|fam, groups=interaction(cinza, agr, sep=": "),
data=pred, type=c("l"), auto.key=list(columns=4, points=FALSE, lines=TRUE))
xyplot(y~dias|fam*agr, groups=cinza, data=pred, type=c("l"))
## xyplot(altura~dias|fam*agr, groups=cinza, data=marag, xlim=c(0,70))+
## as.layer(xyplot(y~dias|fam*agr, groups=cinza, data=pred, type=c("l")))
## xyplot(altura~dias|fam*agr, data=subset(marag, blc=="1"), xlim=c(0,70))+
## as.layer(xyplot(y~dias|fam*agr, groups=cinza, data=pred, type=c("l")))
##-----------------------------------------------------------------------------
pred <- expand.grid(blc="1", fam=levels(mara$fam), agr=levels(mara$agr),
cinza=seq(0,50,l=20), dias=seq(0,60,l=30))
pred$y <- predict(nn3, newdata=pred, level=0)
## colr <- brewer.pal(11, "Spectral")
## colr <- c("white","black")
## colr <- colorRampPalette(colr, space="rgb")
strip.combined <- function(which.given, which.panel, factor.levels, ...){
if(which.given==1){
panel.rect(0, 0, 1, 1, col="grey90", border=1)
panel.text(x=1, y=0.5, pos=2,
lab=paste("família:", factor.levels[which.panel[which.given]]))
}
if(which.given==2){
panel.text(x=0, y=0.5, pos=4,
lab=paste("agregado:", factor.levels[which.panel[which.given]]))
}
}
## Largura da página da coluna da revista (8 cm = 3.150 pol) e da folha
## (17 cm = 6.690 pol).
wireframe(y~dias+cinza|fam*agr, data=pred,
scales=list(arrows=FALSE), drape=TRUE, zlim=c(0, 155),
zlab=list(expression(Altura~da~planta~(cm)), rot=90, hjust=0.5, vjust=-0.2),
xlab=list(expression(Dias), vjust=1, rot=30),
ylab=list(expression(Cinza~(t~ha^{-1})), vjust=1, rot=-40),
strip=strip.combined, par.strip.text=list(lines=0.6),
par.settings=list(
layout.widths=list(xlab.axis.padding=3)))
##-----------------------------------------------------------------------------
## Estimativas pontuais das assintotas.
summ <- summary(nn3)$tTable
rownames(summ)
## [1] "int" "A.(Intercept)" "A.blc2"
## [4] "A.blc3" "A.famF48" "A.agr0-2 mm"
## [7] "A.cinza" "A.famF48:agr0-2 mm" "A.famF48:cinza"
## [10] "A.agr0-2 mm:cinza" "A.famF48:agr0-2 mm:cinza" "d50.(Intercept)"
## [13] "d50.blc2" "d50.blc3" "S.(Intercept)"
## [16] "S.blc2" "S.blc3"
summ[grep("cinza", rownames(summ)),]
## Value Std.Error DF t-value p-value
## A.cinza 0.2514 0.1455 568 1.7280 0.084530
## A.famF48:cinza -0.1692 0.1976 568 -0.8564 0.392154
## A.agr0-2 mm:cinza -0.7410 0.2045 568 -3.6241 0.000316
## A.famF48:agr0-2 mm:cinza 0.6993 0.2791 568 2.5057 0.012500
coefs <- fixef(nn3)
names(coefs)
## [1] "int" "A.(Intercept)" "A.blc2"
## [4] "A.blc3" "A.famF48" "A.agr0-2 mm"
## [7] "A.cinza" "A.famF48:agr0-2 mm" "A.famF48:cinza"
## [10] "A.agr0-2 mm:cinza" "A.famF48:agr0-2 mm:cinza" "d50.(Intercept)"
## [13] "d50.blc2" "d50.blc3" "S.(Intercept)"
## [16] "S.blc2" "S.blc3"
vcovs <- vcov(nn3)
idA <- grep("^A\\.", names(coefs))
coefsA <- coefs[idA]
vcovsA <- vcovs[idA, idA]
length(coefsA)
## [1] 10
length(coef(m0))
## [1] 10
X0 <- LSmatrix(m0, effect=c("agr","fam"), at=list(cinza=0))
b0 <- X0%*%coefsA
v0 <- sqrt(diag(X0%*%vcovsA%*%t(X0)))
ic0 <- sapply(1:4, function(i) b0[i]+c(-1,0,1)*1.96*v0[i])
ic0 <- t(ic0)
colnames(ic0) <- c("Lower","Estimate","Upper")
rownames(ic0) <- paste(c(outer(levels(mara$fam), levels(mara$agr), paste)), "cinza 0")
X48 <- LSmatrix(m0, effect=c("agr","fam"), at=list(cinza=48))
b48 <- X48%*%coefsA
v48 <- sqrt(diag(X48%*%vcovsA%*%t(X48)))
ic48 <- sapply(1:4, function(i) b48[i]+c(-1,0,1)*1.96*v48[i])
ic48 <- t(ic48)
colnames(ic48) <- c("Lower","Estimate","Upper")
rownames(ic48) <- paste(c(outer(levels(mara$fam), levels(mara$agr), paste)), "cinza 48")
ics <- cbind(trat=c(rownames(ic0), rownames(ic48)), data.frame(rbind(ic0, ic48)))
p1 <-
segplot(reorder(trat, Estimate)~Lower+Upper, data=ics,
draw.bands=FALSE, centers=Estimate, segments.fun=panel.arrows,
ends="both", angle=90, length=.05,
par.settings=simpleTheme(pch=19, col=1),
ylab=NULL,
xlab=expression(Ganho~em~altura),
panel=function(x, y, z, ...) {
panel.abline(h=z, col="grey", lty="dashed")
panel.abline(v=0, col=1, lty="dashed")
panel.segplot(x, y, z, ...)})
## print(p1)
##-----------------------------------------------------------------------------
## Mas o contraste é uma matriz menos a outra, então.
X <- X48-X0
b <- X%*%coefsA
v <- X%*%vcovsA%*%t(X)
t <- b/sqrt(diag(v))
Z <- model.matrix(~fam*agr, expand.grid(fam=levels(mara$fam), agr=levels(mara$agr)))
d <- coefs[grep("cinza", names(coefs))]
u <- vcovs[grep("cinza", names(coefs)), grep("cinza", names(coefs))]
d <- c(Z%*%d)
u <- sqrt(diag(Z%*%u%*%t(Z)))
d/u
## 1 2 3 4
## 1.7504 0.6225 -3.4520 0.3036
ic <- sapply(1:4, function(i) d[i]+c(-1,0,1)*1.96*u[i])
ic <- t(ic)
colnames(ic) <- c("Lower","Estimate","Upper")
rownames(ic) <- c(outer(levels(mara$fam), levels(mara$agr), paste))
ic <- cbind(trat=rownames(ic), as.data.frame(ic))
p2 <-
segplot(reorder(trat, Estimate)~Lower+Upper, data=ic,
draw.bands=FALSE, centers=Estimate, segments.fun=panel.arrows,
ends="both", angle=90, length=.05,
par.settings=simpleTheme(pch=19, col=1),
ylab=NULL,
xlab=expression(Coeficiente~de~inclinação),
panel=function(x, y, z, ...) {
panel.abline(h=z, col="grey", lty="dashed")
panel.abline(v=0, col=1, lty="dashed")
panel.segplot(x, y, z, ...)})
## print(p2)
plot(p1, split=c(1,1,1,2), more=TRUE)
plot(p2, split=c(1,2,1,2), more=FALSE)
