Proyecto final
Helian A. Cruz Lopez
2023-06-21
MODELO LINEALES MIXTOS
EJEMPLO CO2
Variable 1= Type Variable 2= Treatment Variable 3= Plant (Aleatoria) Variable 4= Conc *Variable5= Uptake (Co2)
library(tidyverse)## Warning: package 'tidyverse' was built under R version 4.3.1## Warning: package 'lubridate' was built under R version 4.3.1## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.2 ✔ readr 2.1.4
## ✔ forcats 1.0.0 ✔ stringr 1.5.0
## ✔ ggplot2 3.4.2 ✔ tibble 3.2.1
## ✔ lubridate 1.9.2 ✔ tidyr 1.3.0
## ✔ purrr 1.0.1
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## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(broom.mixed)## Warning: package 'broom.mixed' was built under R version 4.3.1library(lme4)## Warning: package 'lme4' was built under R version 4.3.1## Loading required package: Matrix
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## Attaching package: 'Matrix'
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## The following objects are masked from 'package:tidyr':
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## expand, pack, unpacklibrary(ggplot2)1. BASE DE DATOS
- base de datos donde se tienen datos de la captación de CO2 de las plantas sometidas adiferentes tipos de concentraciones de CO2 y a distintas temperaturas, que sería el tratamiento experimental (chilled y nonchilled). No obstante, se le introduce ruido a los datos
data2023= "co2"
print(CO2)## Grouped Data: uptake ~ conc | Plant
## Plant Type Treatment conc uptake
## 1 Qn1 Quebec nonchilled 95 16.0
## 2 Qn1 Quebec nonchilled 175 30.4
## 3 Qn1 Quebec nonchilled 250 34.8
## 4 Qn1 Quebec nonchilled 350 37.2
## 5 Qn1 Quebec nonchilled 500 35.3
## 6 Qn1 Quebec nonchilled 675 39.2
## 7 Qn1 Quebec nonchilled 1000 39.7
## 8 Qn2 Quebec nonchilled 95 13.6
## 9 Qn2 Quebec nonchilled 175 27.3
## 10 Qn2 Quebec nonchilled 250 37.1
## 11 Qn2 Quebec nonchilled 350 41.8
## 12 Qn2 Quebec nonchilled 500 40.6
## 13 Qn2 Quebec nonchilled 675 41.4
## 14 Qn2 Quebec nonchilled 1000 44.3
## 15 Qn3 Quebec nonchilled 95 16.2
## 16 Qn3 Quebec nonchilled 175 32.4
## 17 Qn3 Quebec nonchilled 250 40.3
## 18 Qn3 Quebec nonchilled 350 42.1
## 19 Qn3 Quebec nonchilled 500 42.9
## 20 Qn3 Quebec nonchilled 675 43.9
## 21 Qn3 Quebec nonchilled 1000 45.5
## 22 Qc1 Quebec chilled 95 14.2
## 23 Qc1 Quebec chilled 175 24.1
## 24 Qc1 Quebec chilled 250 30.3
## 25 Qc1 Quebec chilled 350 34.6
## 26 Qc1 Quebec chilled 500 32.5
## 27 Qc1 Quebec chilled 675 35.4
## 28 Qc1 Quebec chilled 1000 38.7
## 29 Qc2 Quebec chilled 95 9.3
## 30 Qc2 Quebec chilled 175 27.3
## 31 Qc2 Quebec chilled 250 35.0
## 32 Qc2 Quebec chilled 350 38.8
## 33 Qc2 Quebec chilled 500 38.6
## 34 Qc2 Quebec chilled 675 37.5
## 35 Qc2 Quebec chilled 1000 42.4
## 36 Qc3 Quebec chilled 95 15.1
## 37 Qc3 Quebec chilled 175 21.0
## 38 Qc3 Quebec chilled 250 38.1
## 39 Qc3 Quebec chilled 350 34.0
## 40 Qc3 Quebec chilled 500 38.9
## 41 Qc3 Quebec chilled 675 39.6
## 42 Qc3 Quebec chilled 1000 41.4
## 43 Mn1 Mississippi nonchilled 95 10.6
## 44 Mn1 Mississippi nonchilled 175 19.2
## 45 Mn1 Mississippi nonchilled 250 26.2
## 46 Mn1 Mississippi nonchilled 350 30.0
## 47 Mn1 Mississippi nonchilled 500 30.9
## 48 Mn1 Mississippi nonchilled 675 32.4
## 49 Mn1 Mississippi nonchilled 1000 35.5
## 50 Mn2 Mississippi nonchilled 95 12.0
## 51 Mn2 Mississippi nonchilled 175 22.0
## 52 Mn2 Mississippi nonchilled 250 30.6
## 53 Mn2 Mississippi nonchilled 350 31.8
## 54 Mn2 Mississippi nonchilled 500 32.4
## 55 Mn2 Mississippi nonchilled 675 31.1
## 56 Mn2 Mississippi nonchilled 1000 31.5
## 57 Mn3 Mississippi nonchilled 95 11.3
## 58 Mn3 Mississippi nonchilled 175 19.4
## 59 Mn3 Mississippi nonchilled 250 25.8
## 60 Mn3 Mississippi nonchilled 350 27.9
## 61 Mn3 Mississippi nonchilled 500 28.5
## 62 Mn3 Mississippi nonchilled 675 28.1
## 63 Mn3 Mississippi nonchilled 1000 27.8
## 64 Mc1 Mississippi chilled 95 10.5
## 65 Mc1 Mississippi chilled 175 14.9
## 66 Mc1 Mississippi chilled 250 18.1
## 67 Mc1 Mississippi chilled 350 18.9
## 68 Mc1 Mississippi chilled 500 19.5
## 69 Mc1 Mississippi chilled 675 22.2
## 70 Mc1 Mississippi chilled 1000 21.9
## 71 Mc2 Mississippi chilled 95 7.7
## 72 Mc2 Mississippi chilled 175 11.4
## 73 Mc2 Mississippi chilled 250 12.3
## 74 Mc2 Mississippi chilled 350 13.0
## 75 Mc2 Mississippi chilled 500 12.5
## 76 Mc2 Mississippi chilled 675 13.7
## 77 Mc2 Mississippi chilled 1000 14.4
## 78 Mc3 Mississippi chilled 95 10.6
## 79 Mc3 Mississippi chilled 175 18.0
## 80 Mc3 Mississippi chilled 250 17.9
## 81 Mc3 Mississippi chilled 350 17.9
## 82 Mc3 Mississippi chilled 500 17.9
## 83 Mc3 Mississippi chilled 675 18.9
## 84 Mc3 Mississippi chilled 1000 19.9Ruido=runif(84,0.02,0.04)
Uptake2= Ruido+CO2$uptake
print(Uptake2)## [1] 16.024269 30.430803 34.830751 37.236099 35.338709 39.233665 39.739403
## [8] 13.625062 27.332062 37.133075 41.836500 40.629038 41.426623 44.336706
## [15] 16.226614 32.435378 40.331728 42.123874 42.931842 43.923327 45.522295
## [22] 14.234168 24.120403 30.338876 34.625652 32.520859 35.427634 38.735680
## [29] 9.323210 27.335237 35.026381 38.826496 38.626286 37.520760 42.439008
## [36] 15.134291 21.028970 38.120407 34.020015 38.923176 39.620840 41.429767
## [43] 10.629146 19.232918 26.235948 30.022028 30.924584 32.427455 35.525549
## [50] 12.025922 22.025837 30.634936 31.821229 32.427029 31.130845 31.533873
## [57] 11.327390 19.427482 25.824640 27.939488 28.521386 28.137217 27.830469
## [64] 10.539310 14.929518 18.121689 18.933059 19.532601 22.222825 21.926568
## [71] 7.738803 11.426874 12.331619 13.031225 12.534495 13.738229 14.421754
## [78] 10.633734 18.029090 17.921885 17.931126 17.931070 18.938221 19.934600hist(Uptake2)
2.ANÁLISIS DESCRIPTIVO
ggplot(CO2, aes(x= conc, y= Uptake2, color=Type))+ geom_point()
*Podemos ver en el primer grafico que a mayor conc las mejores plantas
que captan CO2 son las del type= Quebec
ggplot(CO2, aes(x= conc, y= Uptake2, color=Type))+ geom_point(aes(shape=Treatment))+theme_bw()
*En la grafica anterior podemos ver la interaccion del primer grafico
con el Treatment o enfriamiento -Nonchilled= No Resfriado; Chilled=
Resfriado
ggplot(CO2, aes(x= conc, y= Uptake2, color=Type))+ geom_point(aes(shape=Treatment))+
geom_path(aes(group=Plant, lty=Treatment)) +theme_bw()
Podemos apreciar tres plantas del tipo Mississippi que encuentra resfriadas Podemos apreciar tres plantas del tipo Mississippi que encuentra No resfriadas * Adiferencia del type Quebec no se puede ver una tendecia clara
*Ya que la variable Plant es una variable aleatoria no podriamos interpretar adecaudamente solo con la grafica anterior
*Aunque podemos ver una interaccion entre Type y treatment
Para analizar los modelos aleatorios se usa:
MODELO LINEAL VS MODELO LINEAL MIXTO
#NOTA: Modelo exponencial se usa la función (Log).
#Modelo lineal
Fit1 <- lm(Uptake2 ~ I(log(conc)) + Type:Treatment, data = CO2)
summary(Fit1)##
## Call:
## lm(formula = Uptake2 ~ I(log(conc)) + Type:Treatment, data = CO2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.721 -2.890 0.583 2.765 8.867
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -33.5256 4.0764 -8.224 3.19e-12 ***
## I(log(conc)) 8.4840 0.6783 12.508 < 2e-16 ***
## TypeQuebec:Treatmentnonchilled 19.5190 1.4401 13.554 < 2e-16 ***
## TypeMississippi:Treatmentnonchilled 10.1361 1.4401 7.038 6.31e-10 ***
## TypeQuebec:Treatmentchilled 15.9348 1.4401 11.065 < 2e-16 ***
## TypeMississippi:Treatmentchilled NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.667 on 79 degrees of freedom
## Multiple R-squared: 0.8228, Adjusted R-squared: 0.8138
## F-statistic: 91.68 on 4 and 79 DF, p-value: < 2.2e-16##se utiliza unicamente para variables de efecto fijo.
#siendo uptake 2 la variable respuesta que depende de la concentración de CO2, y la interacción entre el tratamiento y el lugar.
#Planteamos interacción en el ejemplo al observar la gráfica. #Modelo lineal mixto
#Aleatorizar los datos, factor aleatorio (1| Plant).
#Esto hace que cada una de las plantas tenga un intercepto distinto.
Fit2 <- lmer(Uptake2 ~ I(log(conc)) + Type : Treatment + (1 | Plant), data = CO2)## fixed-effect model matrix is rank deficient so dropping 1 column / coefficientsummary(Fit2)## Linear mixed model fit by REML ['lmerMod']
## Formula: Uptake2 ~ I(log(conc)) + Type:Treatment + (1 | Plant)
## Data: CO2
##
## REML criterion at convergence: 482.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.6944 -0.5386 0.1038 0.6899 1.8917
##
## Random effects:
## Groups Name Variance Std.Dev.
## Plant (Intercept) 2.151 1.467
## Residual 20.252 4.500
## Number of obs: 84, groups: Plant, 12
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -33.5256 4.0213 -8.337
## I(log(conc)) 8.4840 0.6541 12.970
## TypeQuebec:Treatmentnonchilled 19.5190 1.8338 10.644
## TypeMississippi:Treatmentnonchilled 10.1361 1.8338 5.527
## TypeQuebec:Treatmentchilled 15.9348 1.8338 8.689
##
## Correlation of Fixed Effects:
## (Intr) I(l()) TypQbc:Trtmntn TypM:T
## I(log(cnc)) -0.947
## TypQbc:Trtmntn -0.228 0.000
## TypMssssp:T -0.228 0.000 0.500
## TypQbc:Trtmntc -0.228 0.000 0.500 0.500
## fit warnings:
## fixed-effect model matrix is rank deficient so dropping 1 column / coefficient#Se tiene en cuenta errores aleatorios por individuo. *Se observa que los interceptos y pendientes de cada modelos son muy similares
*En este caso para las variables aleatorias la varianza es de 2.166
##MODELO LINEAL.
broom::glance(Fit1)## # A tibble: 1 × 12
## r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.823 0.814 4.67 91.7 6.98e-29 4 -246. 504. 519.
## # ℹ 3 more variables: deviance <dbl>, df.residual <int>, nobs <int>- Debido a que se tiene un modelo lineal se analiza el r-squared.Para decidir si es un buen modelo ajustado, el valor debe cercano a 1.
- En este caso, nuestro valor da 0.81, lo que se considera un buen ajuste lineal.
broom::tidy(Fit1)## # A tibble: 6 × 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) -33.5 4.08 -8.22 3.19e-12
## 2 I(log(conc)) 8.48 0.678 12.5 2.02e-20
## 3 TypeQuebec:Treatmentnonchilled 19.5 1.44 13.6 2.60e-22
## 4 TypeMississippi:Treatmentnonchilled 10.1 1.44 7.04 6.31e-10
## 5 TypeQuebec:Treatmentchilled 15.9 1.44 11.1 1.00e-17
## 6 TypeMississippi:Treatmentchilled NA NA NA NA#El tidy nos indica cual sera el estimador de cada uno de los factores.Modelo lineal mixto
broom.mixed::glance(Fit2) ## # A tibble: 1 × 7
## nobs sigma logLik AIC BIC REMLcrit df.residual
## <int> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
## 1 84 4.50 -241. 496. 513. 482. 77#En este modelo no se tienen R cuadrados.*En este caso se observa la columna logLik, donde, valores negativos indican una mejor calidad del ajsute del modelo, por tanto, como el nuestor es -241.1621 es un buen ajuste.
broom.mixed::tidy(Fit2)## # A tibble: 7 × 6
## effect group term estimate std.error statistic
## <chr> <chr> <chr> <dbl> <dbl> <dbl>
## 1 fixed <NA> (Intercept) -33.5 4.02 -8.34
## 2 fixed <NA> I(log(conc)) 8.48 0.654 13.0
## 3 fixed <NA> TypeQuebec:Treatmentnonchilled 19.5 1.83 10.6
## 4 fixed <NA> TypeMississippi:Treatmentnonch… 10.1 1.83 5.53
## 5 fixed <NA> TypeQuebec:Treatmentchilled 15.9 1.83 8.69
## 6 ran_pars Plant sd__(Intercept) 1.47 NA NA
## 7 ran_pars Residual sd__Observation 4.50 NA NA*Se observa los valores de las interacciones para la columna estimate y se puede decir que se cumple con el análisis descriptivo, debido a que Quebec-nonchilled presenta mayor valor (19.519) y en la grafica concuerda con que son las plantas que más captan CO2. Por otro lado, Mississipi - nonchilled presentan menor valor (10.139) y en la grafica concuerda que captan menos CO2 en comparación con las de Quebec.
EJEMPLO POLLO
data("chickWeight")## Warning in data("chickWeight"): data set 'chickWeight' not foundprint(ChickWeight)## Grouped Data: weight ~ Time | Chick
## weight Time Chick Diet
## 1 42 0 1 1
## 2 51 2 1 1
## 3 59 4 1 1
## 4 64 6 1 1
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## 6 93 10 1 1
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## 578 264 21 50 4ChickWeight$Chick%>%length()## [1] 578ChickWeight$Chick%>%unique()%>%length()## [1] 50ggplot(ChickWeight, aes(x= Time, y= weight))+geom_point(aes(color=Diet))+ geom_path(aes(color=Diet, group=Chick))
Podemos ver que aun lo pollos tengan una dia establecidad su
pendiente de crecimiento va ser variable Podemos observar que con
la dieta 3 los pollos tienen una pendiente de crecimiento relevante * La
identidad (Chick) tambien es una variable importante, ya que algunos con
la dieta 3 no tuvieron buenos rendimientos
Filt1_poisson= glm(weight~Diet:Time, data = ChickWeight, family =poisson())
tidy(Filt1_poisson)## # A tibble: 5 × 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 3.86 0.00931 415. 0
## 2 Diet1:Time 0.0656 0.000722 90.8 0
## 3 Diet2:Time 0.0754 0.000768 98.1 0
## 4 Diet3:Time 0.0862 0.000729 118. 0
## 5 Diet4:Time 0.0823 0.000756 109. 0*En la tabla tenemos distintas dietas en relacion con el tiempo, donde su pendiente de crecimiento es mas alta para cada pollo en la Diet3:time con 0,086g/dia
Filt2_poisson= glmer(weight~Diet:Time+(1|Chick), data = ChickWeight, family =poisson())## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue
## - Rescale variables?tidy(Filt2_poisson)## # A tibble: 6 × 7
## effect group term estimate std.error statistic p.value
## <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl>
## 1 fixed <NA> (Intercept) 3.84 0.0315 122. 0
## 2 fixed <NA> Diet1:Time 0.0666 0.00105 63.7 0
## 3 fixed <NA> Diet2:Time 0.0749 0.00129 57.9 0
## 4 fixed <NA> Diet3:Time 0.0868 0.00123 70.5 0
## 5 fixed <NA> Diet4:Time 0.0763 0.00126 60.4 0
## 6 ran_pars Chick sd__(Intercept) 0.213 NA NA NAbroom::tidy(Filt1_poisson)## # A tibble: 5 × 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 3.86 0.00931 415. 0
## 2 Diet1:Time 0.0656 0.000722 90.8 0
## 3 Diet2:Time 0.0754 0.000768 98.1 0
## 4 Diet3:Time 0.0862 0.000729 118. 0
## 5 Diet4:Time 0.0823 0.000756 109. 0broom.mixed::tidy(Filt1_poisson)## # A tibble: 5 × 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 3.86 0.00931 415. 0
## 2 Diet1:Time 0.0656 0.000722 90.8 0
## 3 Diet2:Time 0.0754 0.000768 98.1 0
## 4 Diet3:Time 0.0862 0.000729 118. 0
## 5 Diet4:Time 0.0823 0.000756 109. 0*Se observan diferencias entre los modelos, porque, en el modelo lineal da un estimate del intercepto de 3.86 y cuando se aleatorizan la variable individuo en el modelo mixtose observaun ligero cambio de ese intercepto a 3.84.
*Por otro lado, se observa que la identidad del pollo capta alguna variabilidad y esto genera que no sean iguales los modelos.
broom.mixed::tidy(Filt2_poisson)## # A tibble: 6 × 7
## effect group term estimate std.error statistic p.value
## <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl>
## 1 fixed <NA> (Intercept) 3.84 0.0315 122. 0
## 2 fixed <NA> Diet1:Time 0.0666 0.00105 63.7 0
## 3 fixed <NA> Diet2:Time 0.0749 0.00129 57.9 0
## 4 fixed <NA> Diet3:Time 0.0868 0.00123 70.5 0
## 5 fixed <NA> Diet4:Time 0.0763 0.00126 60.4 0
## 6 ran_pars Chick sd__(Intercept) 0.213 NA NA NAConclucion: Estos modelos tienen la caracteristica de que nos ayudan a visualizar la variables como interactuan para cada uno de los modelos