MULTI-LEVEL ANALYSIS OF STRESS RESPONSES IN AMPHIBIAN OF EXTREME HABITATS

Resultados Salida de Campo 2019 - Afloramientos Rocosos Reserva Natural Bojonawi

Resultados morfológicos

Se utilizaron 7 posturas diferentes. Cada postura se dividió en 3 tratamientos (HW-High water treatment, LW-low water treatment y DD-Dry down treatment. para un total de 21 cajas. En cada caja se introdujeron 10 renacuajos. Al final del experimento, de cada caja se tomaron entre 8 y 10 renacuajos y a cada renacuajo se le tomaron tres veces las siguientes medidas morfológicas:

Altura de la cabeza
Altura de la cola
Longitud de la cola
Perímetro del músculo
Longitud de la cabeza

*Eliminé la longitud total por estar relacionada directamente con la longitud de la cola y la longitud de la cabeza (evitar redundancia)

Analisis para evaluar la repetibilidad de las medidas tomadas en cada renacuajo:

La Base de datos

##   Id_Random_Foto Tratamiento Replica Caja Individuo Medicion Altura_Cabeza
## 1              1          AE      R2   16         4        1         2.787
## 2              1          AE      R2   16         4        2         2.308
## 3              1          AE      R2   16         4        3         2.364
## 4              2          AE      R3   17         1        1         2.183
## 5              2          AE      R3   17         1        2         2.164
## 6              2          AE      R3   17         1        3         2.146
##   Longitud_Total Altura_Cola Longitud_Cola Perim_Musculo1 Longitud_Cabeza
## 1         25.214       1.614        17.883         38.806           7.633
## 2         24.261       1.416        16.859         37.148           7.723
## 3         25.454       1.666        17.839         38.997           7.543
## 4         23.777       1.474        16.800         34.641           7.115
## 5         23.795       1.455        16.853         34.516           7.124
## 6         23.749       1.474        16.882         34.992           7.104

Para evaluar la repetibilidad entre las tres medidas tomadas para cada animal se realizaron modelos mixtos NULOS sin varible independiente. A partir de ese modelo se calculó el valor ICC (intraclass correlation coefficient) que permite determinar la “estabilidad en la medida” (Tomado de Finch et al., 2014: Multilevel modeling using R-p44).

ICC>0.90: Excelente

ICC entre 0,75 y 0,89: Bueno

ICC entre 0,50 y 0,74: Moderado

ICC<0.50: Malo

Se usó el paquete performance para ese cálculo de ICC.

Librerias

####Long_cabeza:

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Longitud_Cabeza ~ 1 + (1 | Id_Random_Foto)
##    Data: datos_morfo
## 
## REML criterion at convergence: 329.6
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.0533 -0.1848 -0.0115  0.1830  6.0879 
## 
## Random effects:
##  Groups         Name        Variance Std.Dev.
##  Id_Random_Foto (Intercept) 0.9498   0.9746  
##  Residual                   0.0213   0.1459  
## Number of obs: 525, groups:  Id_Random_Foto, 175
## 
## Fixed effects:
##              Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)   6.13404    0.07394 173.99998   82.95   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## # ICC by Group
## 
## Group          |   ICC
## ----------------------
## Id_Random_Foto | 0.978

	Longitud_Cabeza
Predictors	Estimates	CI	p
(Intercept)	6.13	5.99 – 6.28	<0.001
Random Effects
σ²	0.02
τ₀₀ _{Id_Random_Foto}	0.95
ICC	0.98
N _{Id_Random_Foto}	175
Observations	525
Marginal R² / Conditional R²	0.000 / 0.978

####Altura_Cabeza:

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Altura_Cabeza ~ 1 + (1 | Id_Random_Foto)
##    Data: datos_morfo
## 
## REML criterion at convergence: -469.7
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.6323 -0.3158 -0.0283  0.2970  4.3991 
## 
## Random effects:
##  Groups         Name        Variance Std.Dev.
##  Id_Random_Foto (Intercept) 0.087848 0.29639 
##  Residual                   0.007021 0.08379 
## Number of obs: 525, groups:  Id_Random_Foto, 175
## 
## Fixed effects:
##             Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)   2.0141     0.0227 174.0000   88.72   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## # ICC by Group
## 
## Group          |   ICC
## ----------------------
## Id_Random_Foto | 0.926

	Altura_Cabeza
Predictors	Estimates	CI	p
(Intercept)	2.01	1.97 – 2.06	<0.001
Random Effects
σ²	0.01
τ₀₀ _{Id_Random_Foto}	0.09
ICC	0.93
N _{Id_Random_Foto}	175
Observations	525
Marginal R² / Conditional R²	0.000 / 0.926

####Longitud_Total

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Longitud_Total ~ 1 + (1 | Id_Random_Foto)
##    Data: datos_morfo
## 
## REML criterion at convergence: 1518.8
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.2728 -0.1337 -0.0034  0.1411  6.1981 
## 
## Random effects:
##  Groups         Name        Variance Std.Dev.
##  Id_Random_Foto (Intercept) 9.1547   3.0257  
##  Residual                   0.2064   0.4543  
## Number of obs: 525, groups:  Id_Random_Foto, 175
## 
## Fixed effects:
##             Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)  20.5020     0.2296 174.0000    89.3   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## # ICC by Group
## 
## Group          |   ICC
## ----------------------
## Id_Random_Foto | 0.978

	Longitud_Total
Predictors	Estimates	CI	p
(Intercept)	20.50	20.05 – 20.95	<0.001
Random Effects
σ²	0.21
τ₀₀ _{Id_Random_Foto}	9.15
ICC	0.98
N _{Id_Random_Foto}	175
Observations	525
Marginal R² / Conditional R²	0.000 / 0.978

####Altura_Cola

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Altura_Cola ~ 1 + (1 | Id_Random_Foto)
##    Data: datos_morfo
## 
## REML criterion at convergence: -1035.3
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.5269 -0.4111 -0.0115  0.3671  4.7982 
## 
## Random effects:
##  Groups         Name        Variance Std.Dev.
##  Id_Random_Foto (Intercept) 0.057823 0.24046 
##  Residual                   0.001732 0.04161 
## Number of obs: 525, groups:  Id_Random_Foto, 175
## 
## Fixed effects:
##              Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)   1.30511    0.01827 173.99999   71.44   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## # ICC by Group
## 
## Group          |   ICC
## ----------------------
## Id_Random_Foto | 0.971

	Altura_Cola
Predictors	Estimates	CI	p
(Intercept)	1.31	1.27 – 1.34	<0.001
Random Effects
σ²	0.00
τ₀₀ _{Id_Random_Foto}	0.06
ICC	0.97
N _{Id_Random_Foto}	175
Observations	525
Marginal R² / Conditional R²	0.000 / 0.971

####Longitud_Cola

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Longitud_Cola ~ 1 + (1 | Id_Random_Foto)
##    Data: datos_morfo
## 
## REML criterion at convergence: 1237
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.3111 -0.1864  0.0006  0.1569  5.7480 
## 
## Random effects:
##  Groups         Name        Variance Std.Dev.
##  Id_Random_Foto (Intercept) 4.734    2.1757  
##  Residual                   0.128    0.3577  
## Number of obs: 525, groups:  Id_Random_Foto, 175
## 
## Fixed effects:
##             Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)  14.3668     0.1652 174.0000   86.96   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## # Intraclass Correlation Coefficient
## 
##     Adjusted ICC: 0.974
##   Unadjusted ICC: 0.974

	Longitud_Cola
Predictors	Estimates	CI	p
(Intercept)	14.37	14.04 – 14.69	<0.001
Random Effects
σ²	0.13
τ₀₀ _{Id_Random_Foto}	4.73
ICC	0.97
N _{Id_Random_Foto}	175
Observations	525
Marginal R² / Conditional R²	0.000 / 0.974

####Perímetro_Musculo

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Perim_Musculo1 ~ 1 + (1 | Id_Random_Foto)
##    Data: datos_morfo
## 
## REML criterion at convergence: 2094.4
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.9709 -0.2947 -0.0076  0.3260  4.6020 
## 
## Random effects:
##  Groups         Name        Variance Std.Dev.
##  Id_Random_Foto (Intercept) 22.5095  4.7444  
##  Residual                    0.6826  0.8262  
## Number of obs: 525, groups:  Id_Random_Foto, 175
## 
## Fixed effects:
##             Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)  30.6241     0.3605 174.0000   84.96   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## # ICC by Group
## 
## Group          |   ICC
## ----------------------
## Id_Random_Foto | 0.971

	Perim_Musculo1
Predictors	Estimates	CI	p
(Intercept)	30.62	29.92 – 31.33	<0.001
Random Effects
σ²	0.68
τ₀₀ _{Id_Random_Foto}	22.51
ICC	0.97
N _{Id_Random_Foto}	175
Observations	525
Marginal R² / Conditional R²	0.000 / 0.971

Dada la repetibilidad encontrada en las medidas para todas las variables, usé la mediana de cada individuo y con ese valor realicé el resto de los análisis.

Use la mediana porque esta no es afectada por los valores extremos y se recomienda mas cuando los valores no tienen distribución normal.

###Figuras exploratorias

##   Id_Random_Foto TREATMENT Postura Tra_Pos Caja Individuo Longitud_Total  Peso
## 1             23        LW      C1    LWC1    1         1       24.24000 0.036
## 2            112        LW      C1    LWC1    1         2       20.99000 0.027
## 3             27        LW      C1    LWC1    1         3       24.96900 0.043
## 4             53        LW      C1    LWC1    1         4       23.77800 0.025
## 5             28        LW      C1    LWC1    1         5       22.34067 0.036
## 6            162        LW      C1    LWC1    1         8       21.71933 0.027
##   Altura_Cabeza Altura_Cola Longitud_Cola Perim_Musculo1 Longitud_Cabeza
## 1      2.147000    1.695000      17.33133       37.49933        6.612667
## 2      2.520000    1.315000      14.07900       30.67567        7.106333
## 3      2.454667    1.475333      16.94933       35.16267        8.026667
## 4      2.148000    1.758333      17.08367       37.15100        6.708000
## 5      2.054000    1.493667      15.58667       34.36867        6.583667
## 6      2.071000    1.134667      15.72333       32.51500        6.031667
##   L_Longitud_Total    L_Peso L_Altura_Cabeza L_Altura_Cola L_Longitud_Cola
## 1         1.384533 -1.443697       0.3318320     0.2291697        1.238832
## 2         1.322012 -1.568636       0.4014005     0.1189258        1.148572
## 3         1.397401 -1.366532       0.3899925     0.1688902        1.229153
## 4         1.376175 -1.602060       0.3320343     0.2451012        1.232581
## 5         1.349096 -1.443697       0.3126004     0.1742537        1.192753
## 6         1.336846 -1.568636       0.3161801     0.0548683        1.196545
##   L_Perimetro_Musculo L_Longitud_Cabeza  Dim.1   Dim.2     Pcrot
## 1            1.574024         0.8203766 2.7424 -0.6554 1.2360673
## 2            1.486794         0.8516456 1.3287  1.2499 0.5988692
## 3            1.546082         0.9045352 3.2396  0.2805 1.4601928
## 4            1.569971         0.8265931 2.4339 -0.2507 1.0970335
## 5            1.536163         0.8184678 1.7652 -0.4652 0.7956281
## 6            1.512084         0.7804373 0.5242 -0.6478 0.2362660

Comparisons plot:

The blue bars on the plot are the confidence intervals. The red arrowed lines represent a scheme to determine homogeneous groups. If the red lines overlap for two groups, then they are not signficantly different using the method chosen.

The ‘adjust’ argument can take one of several useful methods. ‘tukey’ is default, but others including ‘sidak,’ ‘bonferroni,’ etc can be specified. Specifying ‘none’ produces unadjusted p-values. See help with ‘?emmeans::summary.emmGrid’ for details. Here is an example using the ‘holm’ method of adjustment.

emmmeans posthoc

Normalidad variables transformadas:

#####Log Longitud_Total

## # A tibble: 3 × 4
##   TREATMENT variable         statistic        p
##   <chr>     <chr>                <dbl>    <dbl>
## 1 DD        L_Longitud_Total     0.911 0.000306
## 2 HW        L_Longitud_Total     0.977 0.319   
## 3 LW        L_Longitud_Total     0.989 0.891

#####Log Peso

## # A tibble: 3 × 4
##   TREATMENT variable statistic       p
##   <chr>     <chr>        <dbl>   <dbl>
## 1 DD        L_Peso       0.939 0.00425
## 2 HW        L_Peso       0.972 0.188  
## 3 LW        L_Peso       0.977 0.383

Homogenidad de varianza variables transformadas (de cada variable por separado):

Levene’s test: A robust alternative to the Bartlett’s test that is less sensitive to departures from normality.

Fligner-Killeen’s test: a non-parametric test which is very robust against departures from normality.

log(Longitud_Total)

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value Pr(>F)
## group  20  0.6051 0.9047
##       154

log Peso

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value Pr(>F)
## group   2  1.7396 0.1787
##       172

###Figuras exploratorias datos transformados

##   Id_Random_Foto TREATMENT Postura Tra_Pos Caja Individuo Longitud_Total  Peso
## 1             23        LW      C1    LWC1    1         1       24.24000 0.036
## 2            112        LW      C1    LWC1    1         2       20.99000 0.027
## 3             27        LW      C1    LWC1    1         3       24.96900 0.043
## 4             53        LW      C1    LWC1    1         4       23.77800 0.025
## 5             28        LW      C1    LWC1    1         5       22.34067 0.036
## 6            162        LW      C1    LWC1    1         8       21.71933 0.027
##   Altura_Cabeza Altura_Cola Longitud_Cola Perim_Musculo1 Longitud_Cabeza
## 1      2.147000    1.695000      17.33133       37.49933        6.612667
## 2      2.520000    1.315000      14.07900       30.67567        7.106333
## 3      2.454667    1.475333      16.94933       35.16267        8.026667
## 4      2.148000    1.758333      17.08367       37.15100        6.708000
## 5      2.054000    1.493667      15.58667       34.36867        6.583667
## 6      2.071000    1.134667      15.72333       32.51500        6.031667
##   L_Longitud_Total    L_Peso L_Altura_Cabeza L_Altura_Cola L_Longitud_Cola
## 1         1.384533 -1.443697       0.3318320     0.2291697        1.238832
## 2         1.322012 -1.568636       0.4014005     0.1189258        1.148572
## 3         1.397401 -1.366532       0.3899925     0.1688902        1.229153
## 4         1.376175 -1.602060       0.3320343     0.2451012        1.232581
## 5         1.349096 -1.443697       0.3126004     0.1742537        1.192753
## 6         1.336846 -1.568636       0.3161801     0.0548683        1.196545
##   L_Perimetro_Musculo L_Longitud_Cabeza  Dim.1   Dim.2     Pcrot
## 1            1.574024         0.8203766 2.7424 -0.6554 1.2360673
## 2            1.486794         0.8516456 1.3287  1.2499 0.5988692
## 3            1.546082         0.9045352 3.2396  0.2805 1.4601928
## 4            1.569971         0.8265931 2.4339 -0.2507 1.0970335
## 5            1.536163         0.8184678 1.7652 -0.4652 0.7956281
## 6            1.512084         0.7804373 0.5242 -0.6478 0.2362660

Altura_cabeza

#### Altura_cola

Longitud total

Longitud cola

Perímetro músculo

Longitud Cabeza

Peso

Análisis de componentes pricipales variables transformadas

####Correlación entre variables transformadas

##      L_Peso L_Altura_Cabeza L_Altura_Cola L_Longitud_Cola L_Perimetro_Musculo
## 1 -1.443697       0.3318320     0.2291697        1.238832            1.574024
## 2 -1.568636       0.4014005     0.1189258        1.148572            1.486794
## 3 -1.366532       0.3899925     0.1688902        1.229153            1.546082
## 4 -1.602060       0.3320343     0.2451012        1.232581            1.569971
## 5 -1.443697       0.3126004     0.1742537        1.192753            1.536163
## 6 -1.568636       0.3161801     0.0548683        1.196545            1.512084
##   L_Longitud_Cabeza
## 1         0.8203766
## 2         0.8516456
## 3         0.9045352
## 4         0.8265931
## 5         0.8184678
## 6         0.7804373

#####La Correlación

Las figuras de las correlaciones con coeficientes

####El PCA con las variables transformadas

#####Los paquetes:

para hacer el test de barlett y el analisis de componentes: library(psych)

para graficar que variables pesan mas en que PC library(corrplot)

for ggplot2-based visualization: library(factoextra)

#####El test de bartlett: Ho:the sample correlation matrix came from a multivariate normal population in which the variables of interest are independent.

Rejection of the hypothesis is taken as an indication that the data are appropriate for analysis.

(CHARLES D. DZIUBAN, 1974) Bartlett’s test of sphericity tests the hypothesis that your correlation matrix is an identity matrix,which would indicate that your variables are unrelated and therefore unsuitable for structure detection. Small values (less than 0.05) of the significance level indicate that a factor analysis may be useful with your data.

## $chisq
## [1] 1364.241
## 
## $p.value
## [1] 8.14692e-282
## 
## $df
## [1] 15

KMO: Test alternativo al test de barlett. Measure of Sampling Adequacy

This is just a function of the squared elements of the ‘image’ matrix compared to the squares of the original correlations. The overall MSA as well as estimates for each item are found.The index is known as the Kaiser-Meyer-Olkin (KMO) index.Kaiser-Meyer-Olkin (KMO). KMO Test is a measure of how suited your data is for Factor Analysis.

## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = morfo)
## Overall MSA =  0.88
## MSA for each item = 
##              L_Peso     L_Altura_Cabeza       L_Altura_Cola     L_Longitud_Cola 
##                0.96                0.92                0.95                0.79 
## L_Perimetro_Musculo   L_Longitud_Cabeza 
##                0.79                0.93

#####Análisis de Componentes principales:

componentes factorMineR

## 
## Call:
## PCA(X = morfo, scale.unit = TRUE, ncp = 6, graph = FALSE) 
## 
## 
## Eigenvalues
##                        Dim.1   Dim.2   Dim.3   Dim.4   Dim.5   Dim.6
## Variance               4.894   0.373   0.294   0.240   0.184   0.015
## % of var.             81.569   6.217   4.901   3.997   3.063   0.252
## Cumulative % of var.  81.569  87.786  92.687  96.685  99.748 100.000
## 
## Individuals (the 10 first)
##                         Dist    Dim.1    ctr   cos2    Dim.2    ctr   cos2  
## 1                   |  2.914 |  2.742  0.878  0.886 | -0.655  0.658  0.051 |
## 2                   |  2.001 |  1.329  0.206  0.441 |  1.250  2.393  0.390 |
## 3                   |  3.369 |  3.240  1.225  0.925 |  0.281  0.121  0.007 |
## 4                   |  2.735 |  2.434  0.692  0.792 | -0.251  0.096  0.008 |
## 5                   |  1.919 |  1.765  0.364  0.846 | -0.465  0.331  0.059 |
## 6                   |  1.240 |  0.524  0.032  0.179 | -0.648  0.643  0.273 |
## 7                   |  1.159 |  0.642  0.048  0.307 |  0.187  0.054  0.026 |
## 8                   |  1.992 |  1.964  0.450  0.973 |  0.205  0.064  0.011 |
## 9                   |  2.701 |  2.448  0.700  0.821 |  0.393  0.236  0.021 |
## 10                  |  0.844 | -0.685  0.055  0.658 |  0.331  0.168  0.154 |
##                      Dim.3    ctr   cos2  
## 1                    0.648  0.816  0.049 |
## 2                   -0.538  0.562  0.072 |
## 3                   -0.416  0.337  0.015 |
## 4                    0.542  0.571  0.039 |
## 5                    0.455  0.403  0.056 |
## 6                   -0.700  0.952  0.319 |
## 7                   -0.433  0.365  0.140 |
## 8                    0.061  0.007  0.001 |
## 9                   -0.033  0.002  0.000 |
## 10                   0.182  0.065  0.047 |
## 
## Variables
##                        Dim.1    ctr   cos2    Dim.2    ctr   cos2    Dim.3
## L_Peso              |  0.890 16.172  0.791 | -0.174  8.141  0.030 |  0.162
## L_Altura_Cabeza     |  0.871 15.509  0.759 |  0.391 40.917  0.153 | -0.132
## L_Altura_Cola       |  0.872 15.553  0.761 |  0.141  5.361  0.020 |  0.427
## L_Longitud_Cola     |  0.940 18.053  0.884 | -0.269 19.461  0.073 | -0.114
## L_Perimetro_Musculo |  0.947 18.319  0.897 | -0.243 15.883  0.059 | -0.118
## L_Longitud_Cabeza   |  0.896 16.394  0.802 |  0.195 10.237  0.038 | -0.204
##                        ctr   cos2  
## L_Peso               8.876  0.026 |
## L_Altura_Cabeza      5.947  0.017 |
## L_Altura_Cola       61.946  0.182 |
## L_Longitud_Cola      4.408  0.013 |
## L_Perimetro_Musculo  4.700  0.014 |
## L_Longitud_Cabeza   14.124  0.042 |

##           Dim.1         Dim.2         Dim.3        Dim.4        Dim.5
## 1    2.74236350 -0.6554173613  0.6480155952 -0.329143448 -0.078599094
## 2    1.32866320  1.2498788200 -0.5375808491  0.459301061  0.416956899
## 3    3.23961296  0.2805463680 -0.4161732621  0.758537271  0.017174702
## 4    2.43390052 -0.2506912864  0.5420189102 -0.950385692 -0.537703528
## 5    1.76519634 -0.4651881116  0.4554623958  0.340299584 -0.025592661
## 6    0.52418441 -0.6478130762 -0.7000372933  0.152446666  0.557450618
## 7    0.64228706  0.1870495739 -0.4334845788  0.764352301 -0.306586799
## 8    1.96406254  0.2047403915  0.0608398683 -0.109563001 -0.185070328
## 9    2.44828107  0.3926745510 -0.0334100949  1.065121941 -0.100174494
## 10  -0.68455411  0.3313160092  0.1822646967  0.097068877 -0.284832083
## 11  -1.79771241  0.8630487372 -0.0759901156 -0.954599389  0.519807556
## 12  -1.73113028 -0.1559480094  0.7576616044 -0.815249641 -0.704788696
## 13   0.22695506  0.6367779312 -0.6253380680 -0.667374957 -0.905298396
## 14  -4.83371905  1.5488360930  0.2713597367  0.366059536  0.292284162
## 15  -1.62018582  0.1366680436  0.4951317579 -0.054150769  0.252956499
## 16   1.31881684  0.8378695228 -0.6600172811 -0.286361726 -0.626040565
## 17  -1.64794651  0.2312191650  0.0928712000 -0.042313860 -0.117659375
## 18  -2.67496873  0.0895723063  0.7208582309 -0.305916428  0.012046576
## 19   1.55982400  0.3414877222 -0.7468740874 -0.336412413 -0.446610043
## 20  -3.88270835  1.0168925745 -0.3734532783 -0.187213059  0.441850872
## 21  -2.88304939  0.1333168671  0.3835939052 -0.498190017 -0.099566510
## 22   1.35366703  0.4926308547 -0.8200329949 -0.578453606 -0.966176930
## 23  -2.33021431 -0.1019342410 -0.9629324352 -0.217400237 -0.901238307
## 24  -2.83050067  0.4748869985  0.2525912724 -0.602389482 -0.162882009
## 25  -1.63991518 -0.2371396508 -1.0480573526 -0.243295529  0.378810207
## 26  -0.43327776  0.4110483230 -0.6106493642  0.007690087 -0.420683063
## 27  -2.24373600 -0.6798671878  1.5750364323 -0.721384807 -0.454144598
## 28  -1.79035695  0.7524407009  0.7677303285  0.119054034 -0.017527568
## 29  -4.00379965 -0.0129118854  0.5352778061  0.180583617 -0.431337995
## 30  -0.90506368  0.6371444910 -0.2876781702  0.225792426  0.297837122
## 31  -1.53057224 -0.2622948928  0.0926983268  0.066400163  0.289455046
## 32  -0.30200141  0.0873254389  0.7503350071 -0.142322706  0.642232880
## 33  -3.60152118 -0.3940982660  0.0670718496 -0.521572376 -0.010686727
## 34  -0.45847044 -0.0290749505  0.4747039358  0.138948004  0.126835745
## 35  -0.92800498  0.1040522202  1.2005184720 -0.130690250 -0.233043216
## 36  -0.72105547  0.6566377207 -0.1027221396  0.035936551  0.669238702
## 37  -2.11713235 -0.0139208859 -0.0533228102  0.240646793  0.533248754
## 38  -4.33564030  0.3901250551  0.2320327691  0.187747956  0.441904636
## 39   1.00203704 -0.5359453571  0.1102655284  0.111678229  0.037554733
## 40  -0.25715891 -0.1132322226  0.3299238503 -0.362091359  0.331303902
## 41   0.85166847 -0.4420184135  0.1936991497 -0.294496490  0.746243859
## 42  -0.26026300 -0.1202505715 -0.4039922906  0.123393971  0.568848944
## 43   0.83715520 -0.2164505970  0.3074413018 -0.386940273  0.285766198
## 44  -1.56352318  0.5393511916 -0.2157140757  0.556668939 -0.106581637
## 45  -2.24995704 -0.6475364454  0.4691218729 -0.062133611 -0.391710813
## 46  -0.62995719 -0.4575022433 -0.2811759968 -0.074786632  0.088216769
## 47   0.01844112  0.0213951725  0.1920855710 -0.570212765 -0.349167714
## 48   0.06428149 -0.7797749136 -0.7308613387  0.243824935  0.789776832
## 49  -2.94113751 -1.0902693622 -0.5988439965  0.115830801 -0.359053551
## 50  -0.21935540 -0.4870750081 -0.4926308388 -0.003097605 -0.025728205
## 51  -0.97481372 -0.7866013235 -0.6899091266 -0.533916933  0.343820619
## 52  -1.35565003 -0.9457291633 -0.5036848250  0.769887664 -0.322753705
## 53  -1.60371556 -0.6555117424 -0.4214481959  0.399965256 -0.151732356
## 54  -3.54087886 -0.7462846386  0.2131653031  0.785163082 -0.507780988
## 55   7.02725419 -0.4973493240  0.2847739294  0.339050686  0.069577791
## 56   6.51775575 -0.3322648927 -0.0548539021  0.375194224  0.120427291
## 57   6.04633322  0.5509026557 -0.2029868865 -0.554611579  0.283229509
## 58   5.92958589 -1.4849034363  0.4049040602  0.548923161 -0.233370930
## 59   5.87492976 -0.5259243123  0.5934506464  0.430612284 -0.399057261
## 60   5.81156300 -1.1262717809 -0.6027587904  0.425920381  0.164815919
## 61   1.91414409 -0.8276371499  0.2205054510 -0.013943982  0.038361339
## 62   5.16089712 -0.2051753369  0.2531205562  0.492090187  0.366304979
## 63   1.33671666  0.6409999128  0.5547494526  0.069730984  0.070858022
## 64   0.88272900  0.3535639471 -0.4551862895  0.812740425 -0.518119681
## 65   1.66520239  0.1496060602 -0.0628009658  0.069684991 -0.157465678
## 66   4.10001058  0.2468816616 -0.0920036122 -0.981184167 -0.868564029
## 67   1.42046341 -0.0875966768 -0.1769806778 -0.034412997 -0.028460226
## 68   4.21590231  0.0217200507  0.3817159240 -0.291533538 -0.308516470
## 69   0.19596442  0.1350209470  0.5120999193  0.662451171  0.255039303
## 70   0.96248651 -0.3353938284  1.2246146825  0.245200835 -0.458500305
## 71  -1.59836012  0.1207419905  0.5922396617  0.347548679 -0.269743138
## 72   0.70473782  0.5499556000 -0.1168560858 -0.144630134  0.333811320
## 73   0.74796979  0.0754943263 -0.3426685698  0.014859733 -0.192194998
## 74   1.36080966  0.5110409776 -0.5348099486 -0.574167080 -0.816871028
## 75  -1.32983479  0.3205504523 -0.0143589579  0.271304782  0.208965882
## 76  -1.90863595  0.2378658986 -0.4424559593 -0.599027121 -0.215952242
## 77  -0.28360886  0.7775195741 -0.1537350892  0.362598721  0.029007223
## 78  -0.39941777  0.8434665670 -0.5516728787 -0.274338367 -0.441582926
## 79   0.05269538  0.1856479430  0.2765780358  0.276364401 -0.076379937
## 80  -0.68225004  0.5413195622  0.2786041835  1.039432305 -0.481219515
## 81  -1.77378948  0.1327766946 -1.3471314121 -0.607326010 -0.271479090
## 82   1.05676240  1.2207026676 -0.4924615385 -0.882791651 -0.177924425
## 83  -0.27525291  0.0995153608 -1.7220896756 -0.486254695  0.180897467
## 84  -1.22032824 -0.3291631103  0.1154420957 -0.062292923 -0.207713059
## 85  -2.34174274 -0.5731779026  0.1401932460  0.235422909  0.208827915
## 86   1.31350300  0.3021591147 -0.0158878125 -0.883887448 -0.743818751
## 87  -1.98365587 -0.4109234699 -0.6294907803  0.413376010  0.219678397
## 88  -3.02530497 -0.2370094652  0.1160098247  0.251677610 -0.001890055
## 89  -2.53217744  0.0169389602 -0.3268087312  0.521463688 -0.495258475
## 90   1.09366998  0.7182226482  1.3818615048  0.394498926 -0.015354072
## 91   1.35021369  0.5697812242  0.4667729758  0.580224380  0.546076476
## 92   0.04505815 -0.3141835614  0.0579144506  0.102680884  0.315486797
## 93  -0.22550603 -0.2601319229  0.3909579667  0.315193382  0.231301096
## 94   4.15038941  0.5298250017 -0.4111213802 -0.534537248  0.362853800
## 95  -1.23731660 -0.2740744016  0.1277258363  0.111016258  0.191598502
## 96   1.59923209  0.6285490377  0.1381031651  0.752349818  0.074512957
## 97  -1.28895539  0.9490028300  0.1125500214  1.250249476 -0.081469513
## 98   0.26769125  1.1582607543 -0.3317988388  0.919261685 -0.055083764
## 99   3.04564775  0.7793979195  0.5075706578 -0.568477820  0.872275076
## 100  0.42260148 -0.1817777928  0.3647068256 -0.856322471  0.472433263
## 101  0.67843488  0.3562208159  0.2431131659 -0.383433126  0.921653247
## 102  2.89968971 -0.1933147967 -0.0051745360 -0.235757267  0.437700555
## 103 -0.02121621 -0.1518774325 -0.0923869769  0.143565239  0.280582875
## 104  0.20952036 -1.0201756175  0.2800104662 -0.302226149 -0.324949750
## 105  0.01028680 -0.6629385541 -0.0427910682  0.306345757  0.041203692
## 106 -1.84291074 -0.6429867669 -0.6239474394 -0.175313739  0.249829960
## 107  0.90630068 -0.2816024777  0.8376566123 -0.590418815  0.138585715
## 108  0.70397768 -0.6024263406 -0.2817654442 -0.209250325 -0.001344548
## 109  2.08298533 -0.2416942660  0.5420374411  0.106615724 -0.001148914
## 110  1.23698627 -0.3480166944  0.2199694243  0.360195446 -0.197087211
## 111  1.59959761 -1.9003667027 -0.6303880993 -0.829535940  1.773014515
## 112 -2.07658367 -0.6247838489 -0.3161417719 -0.182601084  0.279224304
## 113  1.07403374 -0.6606277412  0.4594269401 -0.158005743 -0.113439401
## 114 -0.25441690 -1.1535926917  0.3358863017  0.053165270 -0.650212262
## 115 -2.61787392 -0.6677463277  0.3839579640 -0.618861166 -0.748822764
## 116  0.16644592 -0.2704737029  0.3130186708  0.308266233 -0.367655952
## 117 -0.17882789 -0.4277775877 -0.1851728697 -0.435202816 -0.088771097
## 118  1.42839858  0.1426621510  0.4928804849  0.097361084  0.043726111
## 119  3.37179575  0.9166981827 -1.0730218832 -0.738827799 -1.220447826
## 120  0.10645466 -0.8328074211 -0.4969140603  0.457301304 -0.376525435
## 121 -0.61554080 -0.3166518640 -0.1290885005  0.388425741  0.077459531
## 122  0.01581282  0.4335553187  0.7476480324  0.005732329 -0.268582550
## 123  1.20636402  0.6185887406  0.4937120631 -0.336998593  0.535893376
## 124 -3.30889866  0.3854305042  0.7151904462  0.023710852 -0.195323035
## 125  1.47634075 -0.2742630006 -0.3911487357 -0.239593228 -0.164086875
## 126  1.79696776 -0.2617583234 -0.0003603035 -0.173639715  0.250923067
## 127  0.59863724  0.0671864752 -0.1346416473  0.816197394 -0.010438765
## 128  3.26317644  0.2258902683 -0.4886353711 -0.381703410 -0.154855342
## 129  1.37899789 -0.8199253892  0.0502805148  0.049989179  0.021791434
## 130 -1.49705175  0.3299138318  0.0147933576  0.085755233  0.006687474
## 131  1.13849382  0.1576861543  0.6751348050  0.551815215 -0.222793721
## 132  1.89201654  0.7679483540  0.4757330475 -0.151177390  0.719032633
## 133 -0.31568792  0.1506749843  1.0731293570 -0.167172893 -0.058576317
## 134  2.48539825 -0.4660107388  0.0823674596  0.597172975  0.018690471
## 135 -0.63565019 -0.4671184611 -0.3185478591  0.244576359  0.405649127
## 136 -0.62685721  0.8119930245 -0.0010919830  0.436827655  0.452810857
## 137 -1.52528509 -0.3388334473  0.1105707656  0.225970008  0.242492460
## 138 -2.74515560 -0.2587877422  0.1049615026 -0.332008026 -0.126125106
## 139  2.21549312  1.4922232508 -1.0520946325 -0.193781201 -0.622862681
## 140 -1.64005340 -0.1245504602 -0.1451445950  0.456558316  0.288713324
## 141 -1.14628746  0.1651978083  0.4823181671 -0.125366945 -0.078193638
## 142  1.04944565  0.5193304723  0.3343118215  0.236547115  0.369009630
## 143 -3.34367592  0.3018754601 -0.5278815336  0.773229990  0.249609169
## 144 -1.45122127  0.5632998622  0.5547870880 -0.682262027 -0.082774557
## 145  0.99806353 -0.0721809677 -0.1972799018 -0.331647452  0.520023000
## 146 -0.96468916 -0.1199569687  0.0945364147 -0.987872003 -0.169255968
## 147 -1.48605633 -0.7943983772 -0.5945279365 -0.660233467 -0.203931677
## 148 -3.07283675  0.8842737062  1.0572091462 -0.162768819 -0.498844364
## 149 -0.46127422  1.6037972203 -0.9465286421 -0.724060646  0.429457989
## 150 -2.93948821  0.0083507071  0.5812699078 -0.088296300 -0.072649795
## 151  2.24890774  0.0906313842 -0.2863385679 -0.521211822  0.239445232
## 152  4.54290561  0.4057355602 -0.5234267263 -0.069725999 -0.411841308
## 153  0.20465024 -0.1576837846 -0.2845711201  0.457893099  0.111398642
## 154 -0.77743673 -0.7298231097 -0.1024249002  0.026487715  0.316839809
## 155  2.02516058  0.4685589146  0.1202141394  1.256470097 -0.396731879
## 156 -3.36484589 -0.4159558999  0.0667821197  0.672251809 -0.124146942
## 157 -0.41152061  0.5657279126  0.1600053608  0.532205302  0.307754554
## 158  0.08767643 -0.0010629522  0.4300202820  0.555012375 -0.142469940
## 159  1.88849957  0.5929659614 -0.3617385341  1.083547516  0.220211339
## 160 -0.60117896 -0.9987519203  0.3837405933  0.032054322 -0.453675001
## 161 -1.28286525  0.4618197618 -0.7593069819 -0.374226881  0.547531217
## 162 -1.55182835  0.2099055661 -0.2002879036 -0.230590854  0.739043761
## 163 -0.64333371  1.3838835803 -0.5745688503  1.063393503 -0.453411228
## 164 -0.17796956  0.4091591500  0.5115079820 -0.547622773  0.843362890
## 165 -1.21178942 -0.3527341311  0.3893850684  0.282174875 -0.105642762
## 166 -2.25245452 -0.8743855021  0.3242485657 -0.409690145 -0.646033045
## 167 -1.94306834  0.0007871925  0.2813213524  0.115262937 -0.030359984
## 168 -2.24352243 -0.0469419787 -0.5173338383  0.022535107  0.240385818
## 169 -3.80975027 -0.1499940585 -0.9139855945 -0.131669796  0.981185875
## 170  0.91763019 -0.0306949201  0.1834965648 -0.364964118  0.889360054
## 171  1.69438597  0.7940780944  1.3942833145 -1.328676335 -0.048898411
## 172 -2.04722471 -0.5980788563 -0.9808553289 -0.089850998 -0.243818410
## 173 -1.29885142 -0.8238108798 -0.1061243617 -0.175052492 -0.104675729
## 174 -0.54575631 -1.3630059411 -0.7964102122 -0.119115832 -0.190206300
## 175 -1.63352957 -1.2284047372 -0.8828761081  0.524076624 -0.769894854
##            Dim.6
## 1   -0.069804195
## 2   -0.065629977
## 3    0.168417502
## 4   -0.083687885
## 5   -0.164653675
## 6    0.136048674
## 7    0.171540579
## 8    0.130169510
## 9   -0.059282068
## 10  -0.102276691
## 11  -0.099429054
## 12   0.113446316
## 13  -0.209080176
## 14   0.089758727
## 15   0.104715849
## 16   0.236738593
## 17  -0.139721852
## 18   0.052193884
## 19   0.162273770
## 20   0.047634703
## 21   0.087143212
## 22  -0.151390867
## 23  -0.138052875
## 24  -0.061615759
## 25  -0.126836541
## 26  -0.269304076
## 27   0.008054668
## 28  -0.007127540
## 29   0.043307163
## 30  -0.119542713
## 31  -0.110871180
## 32  -0.015810604
## 33  -0.161692447
## 34  -0.170933896
## 35  -0.147100059
## 36   0.189205830
## 37   0.087724929
## 38   0.083922027
## 39  -0.121225581
## 40   0.011460515
## 41   0.047719168
## 42   0.045506067
## 43  -0.067078175
## 44   0.086008973
## 45   0.060919586
## 46   0.089128669
## 47  -0.077476844
## 48  -0.066201432
## 49  -0.050031996
## 50  -0.037952538
## 51  -0.087479014
## 52   0.108509275
## 53   0.118431109
## 54   0.115996188
## 55  -0.104857055
## 56  -0.143051132
## 57  -0.057843951
## 58  -0.089944520
## 59  -0.060708371
## 60   0.148925338
## 61   0.112578972
## 62   0.127312866
## 63  -0.147610086
## 64  -0.229436712
## 65  -0.025553910
## 66   0.093157309
## 67  -0.190140463
## 68   0.002774389
## 69   0.113880521
## 70   0.110023059
## 71   0.077297749
## 72  -0.091966087
## 73  -0.148503263
## 74   0.152454310
## 75  -0.140559259
## 76  -0.089176088
## 77  -0.113745730
## 78   0.154186490
## 79   0.118054110
## 80   0.112108553
## 81   0.048374584
## 82  -0.039090944
## 83  -0.034563689
## 84  -0.075380733
## 85  -0.028933849
## 86   0.075534182
## 87   0.107655049
## 88   0.071048700
## 89   0.087929417
## 90  -0.097532385
## 91   0.117892598
## 92  -0.060405739
## 93  -0.059606962
## 94   0.195104316
## 95  -0.037137086
## 96   0.196638582
## 97   0.096362686
## 98   0.119106290
## 99   0.155842918
## 100  0.041829621
## 101 -0.152623392
## 102  0.143751714
## 103 -0.225045596
## 104  0.073466254
## 105  0.120352542
## 106  0.101555252
## 107  0.068497475
## 108 -0.088346430
## 109 -0.222538459
## 110 -0.173163374
## 111  0.150242633
## 112 -0.083337963
## 113  0.147646517
## 114  0.132758219
## 115  0.070101783
## 116 -0.109457183
## 117  0.020866008
## 118 -0.046719363
## 119  0.233162094
## 120 -0.197066784
## 121 -0.129032037
## 122  0.046109002
## 123  0.074148449
## 124  0.018282311
## 125 -0.088871947
## 126 -0.028899579
## 127 -0.116390336
## 128 -0.084626882
## 129 -0.069977675
## 130 -0.081260784
## 131  0.117199695
## 132  0.093238575
## 133  0.018794661
## 134  0.171919374
## 135 -0.129437752
## 136 -0.229511147
## 137 -0.029516199
## 138 -0.201717809
## 139  0.140972833
## 140  0.065537638
## 141  0.171710980
## 142  0.085642920
## 143 -0.015647935
## 144 -0.026728865
## 145  0.269025679
## 146 -0.068584171
## 147  0.043071758
## 148  0.048898174
## 149  0.172188404
## 150  0.055049633
## 151 -0.123925702
## 152 -0.130879214
## 153 -0.093371834
## 154 -0.133110662
## 155 -0.237360399
## 156 -0.123612849
## 157  0.347638960
## 158  0.101553278
## 159  0.125973792
## 160  0.092938398
## 161 -0.112052868
## 162 -0.120154848
## 163 -0.302393324
## 164 -0.151632553
## 165  0.066639954
## 166  0.074670664
## 167  0.055183072
## 168 -0.102824417
## 169  0.043289969
## 170 -0.046121115
## 171 -0.062519846
## 172  0.040901144
## 173  0.111437693
## 174  0.118517574
## 175  0.120515849

#####Rotando los componentes

Abdi & Williams, 2010, Principal component analysis: After the number of components has been determined, and in order to facilitate the interpretation,the analysis often involves a rotation of the components that were retained. principal: Standardized loadings (pattern matrix) based upon correlation matrix

Para extraer los componentes ya rotados

####Figuras con el PCrotado para ver el efecto del tratamiento

###El modelo mixto para evaluar el efecto del tratamiento de desecación:

Aqui otra forma de presentar los resultados, calculando el R2 del modelo y haciendo un ajuste en la significancia:

Como crear una tabla con los resultados de los análisis de modelos mixtos

*Daniel Lüdecke

The marginal R-squared considers only the variance of the fixed effects, while the conditional R-squared takes both the fixed and random effects into account.

The p-value is a simple approximation, based on the t-statistics and using the normal distribution function. A more precise p-value can be computed using p.val = “kr”. In this case, which only applies to linear mixed models, the computation of p-values is based on conditional F-tests with Kenward-Roger approximation for the degrees of freedom (using the using the pbkrtest-package). Note that here the computation is more time consuming and thus not used as default. You can also display the approximated degrees of freedom with show.df.

Para calcular el R*2 del modelo

R*2 en modelos mixtos

R* en modelos mixtos 2

Nakagawa S, Johnson P, Schielzeth H (2017) The coefficient of determination R2 and intra-class correlation coefficient from generalized linear mixed-effects models revisted and expanded. J. R. Soc. Interface 14. doi: 10.1098/rsif.2017.0213.

El modelo mixto con peso transformado

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: L_Peso ~ TREATMENT + (1 | Caja) + (1 | Postura)
##    Data: datos_morfo_trans
## 
## REML criterion at convergence: -211.1
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.7125 -0.4795  0.0077  0.5846  3.4941 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Caja     (Intercept) 0.008624 0.09287 
##  Postura  (Intercept) 0.009873 0.09936 
##  Residual             0.012490 0.11176 
## Number of obs: 175, groups:  Caja, 21; Postura, 7
## 
## Fixed effects:
##             Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept) -1.68116    0.05340 12.01296 -31.484 6.49e-13 ***
## TREATMENTDD  0.10379    0.05365 11.94032   1.935   0.0771 .  
## TREATMENTLW -0.04935    0.05395 12.20180  -0.915   0.3780    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) TREATMENTD
## TREATMENTDD -0.503           
## TREATMENTLW -0.500  0.498

## Type III Analysis of Variance Table with Satterthwaite's method
##            Sum Sq  Mean Sq NumDF  DenDF F value Pr(>F)  
## TREATMENT 0.10531 0.052654     2 12.103  4.2158 0.0408 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

	L_Peso
Predictors	Estimates	CI	p
(Intercept)	-1.68	-1.79 – -1.58	<0.001
TREATMENT [DD]	0.10	-0.00 – 0.21	0.055
TREATMENT [LW]	-0.05	-0.16 – 0.06	0.362
Random Effects
σ²	0.01
τ₀₀ _Caja	0.01
τ₀₀ _Postura	0.01
ICC	0.60
N _Caja	21
N _Postura	7
Observations	175
Marginal R² / Conditional R²	0.117 / 0.644

##  contrast estimate     SE   df t.ratio p.value
##  HW - DD   -0.1038 0.0536 11.8  -1.935  0.1159
##  HW - LW    0.0494 0.0540 12.1   0.915  0.3782
##  DD - LW    0.1531 0.0539 12.1   2.840  0.0445
## 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: fdr method for 3 tests

El modelo mixto con PC rotado

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Pcrot ~ TREATMENT + (1 | Caja) + (1 | Postura)
##    Data: datos_morfo_trans
## 
## REML criterion at convergence: 421.9
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.57051 -0.62221 -0.03631  0.61635  2.54916 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Caja     (Intercept) 0.1713   0.4139  
##  Postura  (Intercept) 0.2663   0.5161  
##  Residual             0.5249   0.7245  
## Number of obs: 175, groups:  Caja, 21; Postura, 7
## 
## Fixed effects:
##             Estimate Std. Error      df t value Pr(>|t|)  
## (Intercept)  -0.1370     0.2670 11.3731  -0.513   0.6176  
## TREATMENTDD   0.5940     0.2576 11.9251   2.306   0.0399 *
## TREATMENTLW  -0.2403     0.2601 12.3826  -0.924   0.3732  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) TREATMENTD
## TREATMENTDD -0.483           
## TREATMENTLW -0.479  0.496

## Type III Analysis of Variance Table with Satterthwaite's method
##           Sum Sq Mean Sq NumDF  DenDF F value  Pr(>F)  
## TREATMENT 5.7703  2.8851     2 12.207  5.4971 0.01985 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

	Pcrot
Predictors	Estimates	CI	p
(Intercept)	-0.14	-0.66 – 0.39	0.608
TREATMENT [DD]	0.59	0.09 – 1.10	0.022
TREATMENT [LW]	-0.24	-0.75 – 0.27	0.357
Random Effects
σ²	0.52
τ₀₀ _Caja	0.17
τ₀₀ _Postura	0.27
ICC	0.45
N _Caja	21
N _Postura	7
Observations	175
Marginal R² / Conditional R²	0.114 / 0.517

	Pcrot
Predictors	Estimates	CI	p
(Intercept)	-0.14	-0.66 – 0.39	0.608
TREATMENT [DD]	0.59	0.09 – 1.10	0.022
TREATMENT [LW]	-0.24	-0.75 – 0.27	0.357
Random Effects
σ²	0.52
τ₀₀ _Caja	0.17
τ₀₀ _Postura	0.27
ICC	0.45
N _Caja	21
N _Postura	7
Observations	175
Marginal R² / Conditional R²	0.114 / 0.517

El modelo mixto con PC rotado usando solo caja random

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Pcrot ~ TREATMENT + (1 | Caja)
##    Data: datos_morfo_trans
## 
## REML criterion at convergence: 426.7
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.4876 -0.5807 -0.0398  0.6089  2.4549 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Caja     (Intercept) 0.4371   0.6611  
##  Residual             0.5251   0.7247  
## Number of obs: 175, groups:  Caja, 21
## 
## Fixed effects:
##             Estimate Std. Error      df t value Pr(>|t|)
## (Intercept)  -0.1365     0.2669 17.7648  -0.511    0.615
## TREATMENTDD   0.5946     0.3772 17.7279   1.576    0.133
## TREATMENTLW  -0.2397     0.3790 18.0529  -0.632    0.535
## 
## Correlation of Fixed Effects:
##             (Intr) TREATMENTD
## TREATMENTDD -0.707           
## TREATMENTLW -0.704  0.498

## Type III Analysis of Variance Table with Satterthwaite's method
##           Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## TREATMENT 2.7082  1.3541     2 17.93  2.5785 0.1037

	Pcrot
Predictors	Estimates	CI	p
(Intercept)	-0.14	-0.66 – 0.39	0.610
TREATMENT [DD]	0.59	-0.15 – 1.34	0.117
TREATMENT [LW]	-0.24	-0.99 – 0.51	0.528
Random Effects
σ²	0.53
τ₀₀ _Caja	0.44
ICC	0.45
N _Caja	21
Observations	175
Marginal R² / Conditional R²	0.114 / 0.517

	Pcrot
Predictors	Estimates	CI	p
(Intercept)	-0.14	-0.66 – 0.39	0.608
TREATMENT [DD]	0.59	0.09 – 1.10	0.022
TREATMENT [LW]	-0.24	-0.75 – 0.27	0.357
Random Effects
σ²	0.52
τ₀₀ _Caja	0.17
τ₀₀ _Postura	0.27
ICC	0.45
N _Caja	21
N _Postura	7
Observations	175
Marginal R² / Conditional R²	0.114 / 0.517

Haciendo el ajuste en la significancia:

“The p-value is a simple approximation, based on the t-statistics and using the normal distribution function. A more precise p-value can be computed using p.val =”kr”. In this case, which only applies to linear mixed models, the computation of p-values is based on conditional F-tests with Kenward-Roger approximation for the degrees of freedom (using the using the pbkrtest-package). Note that here the computation is more time consuming and thus not used as default. You can also display the approximated degrees of freedom with show.df.”

	Pcrot
Predictors	Estimates	CI	p	df
(Intercept)	-0.14	-0.72 – 0.45	0.618	11.40
TREATMENT [DD]	0.59	0.03 – 1.16	0.040	11.71
TREATMENT [LW]	-0.24	-0.81 – 0.33	0.374	12.16
Random Effects
σ²	0.52
τ₀₀ _Caja	0.17
τ₀₀ _Postura	0.27
ICC	0.45
N _Caja	21
N _Postura	7
Observations	175
Marginal R² / Conditional R²	0.114 / 0.517

##  [1] "serif"                "sans"                 "mono"                
##  [4] "AvantGarde"           "Bookman"              "Courier"             
##  [7] "Helvetica"            "Helvetica-Narrow"     "NewCenturySchoolbook"
## [10] "Palatino"             "Times"                "URWGothic"           
## [13] "URWBookman"           "NimbusMon"            "NimbusSan"           
## [16] "URWHelvetica"         "NimbusSanCond"        "CenturySch"          
## [19] "URWPalladio"          "NimbusRom"            "URWTimes"            
## [22] "ArialMT"              "Japan1"               "Japan1HeiMin"        
## [25] "Japan1GothicBBB"      "Japan1Ryumin"         "Korea1"              
## [28] "Korea1deb"            "CNS1"                 "GB1"

pirate plot

## quartz_off_screen 
##                 2

##  contrast estimate    SE   df t.ratio p.value
##  HW - DD    -0.594 0.258 11.7  -2.306  0.0604
##  HW - LW     0.240 0.260 12.2   0.924  0.3736
##  DD - LW     0.834 0.260 12.1   3.210  0.0222
## 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: fdr method for 3 tests

## $lsmeans
##  TREATMENT lsmean    SE   df lower.CL upper.CL
##  HW        -0.137 0.267 11.4   -0.722    0.448
##  DD         0.457 0.267 11.3   -0.128    1.042
##  LW        -0.377 0.269 11.8   -0.965    0.211
## 
## Degrees-of-freedom method: kenward-roger 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast estimate    SE   df t.ratio p.value
##  HW - DD    -0.594 0.258 11.7  -2.306  0.0604
##  HW - LW     0.240 0.260 12.2   0.924  0.3736
##  DD - LW     0.834 0.260 12.1   3.210  0.0222
## 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: fdr method for 3 tests

## $`emmeans of TREATMENT`
##  TREATMENT emmean    SE   df lower.CL upper.CL
##  HW        -0.137 0.267 11.4   -0.722    0.448
##  DD         0.457 0.267 11.3   -0.128    1.042
##  LW        -0.377 0.269 11.8   -0.965    0.211
## 
## Degrees-of-freedom method: kenward-roger 
## Confidence level used: 0.95 
## 
## $`pairwise differences of TREATMENT`
##  1       estimate    SE   df t.ratio p.value
##  HW - DD   -0.594 0.258 11.7  -2.306  0.0943
##  HW - LW    0.240 0.260 12.2   0.924  0.6362
##  DD - LW    0.834 0.260 12.1   3.210  0.0188
## 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: tukey method for comparing a family of 3 estimates

##  contrast estimate    SE   df t.ratio p.value
##  HW - DD    -0.594 0.258 11.7  -2.306  0.0402
##  HW - LW     0.240 0.260 12.2   0.924  0.3736
##  DD - LW     0.834 0.260 12.1   3.210  0.0074
## 
## Degrees-of-freedom method: kenward-roger

##  contrast estimate    SE   df t.ratio p.value
##  HW - DD    -0.594 0.258 11.7  -2.306  0.0402
##  HW - LW     0.240 0.260 12.2   0.924  0.3736
##  DD - LW     0.834 0.260 12.1   3.210  0.0074
## 
## Degrees-of-freedom method: kenward-roger

## 
## To cite package 'emmeans' in publications use:
## 
##   Lenth R (2022). _emmeans: Estimated Marginal Means, aka Least-Squares
##   Means_. R package version 1.8.3,
##   <https://CRAN.R-project.org/package=emmeans>.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {emmeans: Estimated Marginal Means, aka Least-Squares Means},
##     author = {Russell V. Lenth},
##     year = {2022},
##     note = {R package version 1.8.3},
##     url = {https://CRAN.R-project.org/package=emmeans},
##   }

##  contrast estimate    SE   df t.ratio p.value
##  HW - DD    -0.594 0.258 11.7  -2.306  0.0943
##  HW - LW     0.240 0.260 12.2   0.924  0.6362
##  DD - LW     0.834 0.260 12.1   3.210  0.0188
## 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: tukey method for comparing a family of 3 estimates

## 
## To cite package 'emmeans' in publications use:
## 
##   Lenth R (2022). _emmeans: Estimated Marginal Means, aka Least-Squares
##   Means_. R package version 1.8.3,
##   <https://CRAN.R-project.org/package=emmeans>.
## 
## A BibTeX entry for LaTeX users is
## 
##   @Manual{,
##     title = {emmeans: Estimated Marginal Means, aka Least-Squares Means},
##     author = {Russell V. Lenth},
##     year = {2022},
##     note = {R package version 1.8.3},
##     url = {https://CRAN.R-project.org/package=emmeans},
##   }

## 
## 2011 for generalized additive model method; 2016 for beyond exponential
## family; 2004 for strictly additive GCV based model method and basics of
## gamm; 2017 for overview; 2003 for thin plate regression splines.
## 
##   Wood, S.N. (2011) Fast stable restricted maximum likelihood and
##   marginal likelihood estimation of semiparametric generalized linear
##   models. Journal of the Royal Statistical Society (B) 73(1):3-36
## 
##   Wood S.N., N. Pya and B. Saefken (2016) Smoothing parameter and model
##   selection for general smooth models (with discussion). Journal of the
##   American Statistical Association 111:1548-1575.
## 
##   Wood, S.N. (2004) Stable and efficient multiple smoothing parameter
##   estimation for generalized additive models. Journal of the American
##   Statistical Association. 99:673-686.
## 
##   Wood, S.N. (2017) Generalized Additive Models: An Introduction with R
##   (2nd edition). Chapman and Hall/CRC.
## 
##   Wood, S.N. (2003) Thin-plate regression splines. Journal of the Royal
##   Statistical Society (B) 65(1):95-114.
## 
## To see these entries in BibTeX format, use 'print(<citation>,
## bibtex=TRUE)', 'toBibtex(.)', or set
## 'options(citation.bibtex.max=999)'.

Control vs groups comparison

1.Prueba de homogeneidad del modelo mixto rotado pc1

mixto1pc1<-lmer(Pcrot~TREATMENT+(1|Caja)+(1|Postura),data=datos_morfo_trans)

Prueba de homogeneidad sin considerar los factores aleatorios (lineal model)

Prueba de homogeneidad Breusch Pagan:

## 
##  Breusch Pagan Test for Heteroskedasticity
##  -----------------------------------------
##  Ho: the variance is constant            
##  Ha: the variance is not constant        
## 
##               Data                
##  ---------------------------------
##  Response : Pcrot 
##  Variables: fitted values of Pcrot 
## 
##         Test Summary          
##  -----------------------------
##  DF            =    1 
##  Chi2          =    0.01377641 
##  Prob > Chi2   =    0.9065645

Otra forma de evaluar la homogeneidad propuesta por Michael Palmeri

## Analysis of Variance Table
## 
## Response: mixto1pc1.Res2
##            Df Sum Sq Mean Sq F value Pr(>F)
## Caja        1  0.049 0.04949  0.1074 0.7435
## Postura     6  2.171 0.36190  0.7855 0.5824
## Residuals 167 76.944 0.46074

2.Evaluando los supuestos de los modelos mixtos:

evaluando los supuestos en modelos mixtos

Francisco Juretig. “R Statistics Cookbook.”: Mixed models can be impacted greatly by outliers. Even a minor contamination causes major estimation problems. Solución: evaluar que tan robusto es el modelo.

Re-estimando el modelo con “robust errors”

Based on central model approach: That is, we assume the model to be true, but a part of the data to possibly be contaminated. Irrespective of this contamination, we would like to estimate the parameters that define the central model and these estimates should be only minimally influenced by the contamination.

A robust estimation method should give reasonable results in the presence of such contaminated error distributions, while still maintain- ing efficiency in case there is no contamination.

## Robust linear mixed model fit by DAStau 
## Formula: Pcrot ~ TREATMENT + (1 | Caja) + (1 | Postura) 
##    Data: datos_morfo_trans 
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.75764 -0.63946 -0.01392  0.56091  2.71445 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Caja     (Intercept) 0.1009   0.3176  
##  Postura  (Intercept) 0.2182   0.4671  
##  Residual             0.4980   0.7057  
## Number of obs: 175, groups: Caja, 21; Postura, 7
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)   0.3333     0.2378   1.401
## TREATMENTHW  -0.5191     0.2184  -2.377
## TREATMENTLW  -0.7522     0.2210  -3.404
## 
## Correlation of Fixed Effects:
##             (Intr) TREATMENTH
## TREATMENTHW -0.458           
## TREATMENTLW -0.452  0.493    
## 
## Robustness weights for the residuals: 
##  139 weights are ~= 1. The remaining 36 ones are summarized as
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.488   0.687   0.794   0.788   0.923   0.999 
## 
## Robustness weights for the random effects: 
##  26 weights are ~= 1. The remaining 2 ones are
##     8    22 
## 0.407 0.691 
## 
## Rho functions used for fitting:
##   Residuals:
##     eff: smoothed Huber (k = 1.345, s = 10) 
##     sig: smoothed Huber, Proposal 2 (k = 1.345, s = 10) 
##   Random Effects, variance component 1 (Caja):
##     eff: smoothed Huber (k = 1.345, s = 10) 
##     vcp: smoothed Huber, Proposal 2 (k = 1.345, s = 10) 
##   Random Effects, variance component 2 (Postura):
##     eff: smoothed Huber (k = 1.345, s = 10) 
##     vcp: smoothed Huber, Proposal 2 (k = 1.345, s = 10)

	Pcrot
Predictors	Estimates	CI	p
(Intercept)	0.33	-0.13 – 0.80	0.161
TREATMENT [HW]	-0.52	-0.95 – -0.09	0.017
TREATMENT [LW]	-0.75	-1.19 – -0.32	0.001
Random Effects
σ²	0.50
τ₀₀ _Caja	0.10
τ₀₀ _Postura	0.22
ICC	0.39
N _Caja	21
N _Postura	7
Observations	175
Marginal R² / Conditional R²	0.108 / 0.457

Evaluando los residuos del modelo

Excerpt From: Francisco Juretig. “R Statistics Cookbook.” Apple Books.

“In the fitted-residual relationship; ideally, there should be no structure there. We then plotted boxplots for the residuals in each group.

Excerpt From: Francisco Juretig. “R Statistics Cookbook.” Apple Books.

Efecto aleatorio:La postura

“Now, let’s plot the fitted versus the actuals. There should be a positive linear relationship here. If this weren’t the case, it would imply that we were missing some structure in the model:”

Efecto aleatorio: La caja

3. Calculando la magnitud del efecto del modelo

La magnitud del efecto:

Effect sizes, are metrics that represent the amount of differences between two sample means.

Cohen’s d and Hedges’ g are interpreted in a similar way. Cohen suggested using the following rule of thumb for interpreting results:

Small effect (cannot be discerned by the naked eye) = 0.2 Medium Effect = 0.5 Large Effect (can be seen by the naked eye) = 0.8

Cohen, J. (1977). Statistical power analysis for the behavioral sciences. Routledge.

calculo de eta-squared

## # Effect Size for ANOVA (Type III)
## 
## Parameter | Eta2 (partial) |       95% CI
## -----------------------------------------
## TREATMENT |           0.47 | [0.07, 1.00]
## 
## - One-sided CIs: upper bound fixed at [1.00].

## # Effect Size for ANOVA (Type III)
## 
## Parameter | Cohen's f (partial) |      95% CI
## ---------------------------------------------
## TREATMENT |                0.95 | [0.27, Inf]
## 
## - One-sided CIs: upper bound fixed at [Inf].

Para contrastar entre tratamientos:

##  contrast estimate    SE   df t.ratio p.value
##  DD - HW     0.594 0.258 11.7   2.306  0.0943
##  DD - LW     0.834 0.260 12.1   3.210  0.0188
##  HW - LW     0.240 0.260 12.2   0.924  0.6362
## 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: tukey method for comparing a family of 3 estimates

A partir de esos contrastes, la magnitud del efecto:

##  contrast effect.size    SE   df lower.CL upper.CL
##  DD - HW        0.820 0.367 11.3   0.0157     1.62
##  DD - LW        1.152 0.359 11.3   0.3636     1.94
##  HW - LW        0.332 0.365 11.4  -0.4692     1.13
## 
## sigma used for effect sizes: 0.7245 
## Degrees-of-freedom method: inherited from kenward-roger when re-gridding 
## Confidence level used: 0.95

Effect size in mixed models

Effect size in mixed models1

Plotting Random Effects of Mixed Models

Visualizing (generalized) linear mixed effects models

Forest plot

Forest plot in mixed models 5

Comparación con DD

Comparación con HW

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Pcrot ~ TREATMENT + (1 | Caja) + (1 | Postura)
##    Data: datos_morfo_trans
## 
## REML criterion at convergence: 421.9
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.57051 -0.62221 -0.03631  0.61635  2.54916 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Caja     (Intercept) 0.1713   0.4139  
##  Postura  (Intercept) 0.2663   0.5161  
##  Residual             0.5249   0.7245  
## Number of obs: 175, groups:  Caja, 21; Postura, 7
## 
## Fixed effects:
##             Estimate Std. Error      df t value Pr(>|t|)  
## (Intercept)  -0.1370     0.2670 11.3731  -0.513   0.6176  
## TREATMENTDD   0.5940     0.2576 11.9251   2.306   0.0399 *
## TREATMENTLW  -0.2403     0.2601 12.3826  -0.924   0.3732  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) TREATMENTD
## TREATMENTDD -0.483           
## TREATMENTLW -0.479  0.496

Comparación con LW

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Pcrot ~ TREATMENT + (1 | Caja) + (1 | Postura)
##    Data: datos_morfo_trans
## 
## REML criterion at convergence: 421.9
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.57051 -0.62221 -0.03631  0.61635  2.54916 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Caja     (Intercept) 0.1713   0.4139  
##  Postura  (Intercept) 0.2663   0.5161  
##  Residual             0.5249   0.7245  
## Number of obs: 175, groups:  Caja, 21; Postura, 7
## 
## Fixed effects:
##             Estimate Std. Error      df t value Pr(>|t|)   
## (Intercept)  -0.3774     0.2692 11.7403  -1.402  0.18684   
## TREATMENTHW   0.2403     0.2601 12.3826   0.924  0.37318   
## TREATMENTDD   0.8344     0.2598 12.3280   3.211  0.00725 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) TREATMENTH
## TREATMENTHW -0.492           
## TREATMENTDD -0.492  0.509

Probando otras opciones para ver magnitud del efecto:

## # Standardization method: refit
## 
## Parameter   | Std. Coef. |         95% CI
## -----------------------------------------
## (Intercept) |       0.46 | [-0.07,  0.98]
## TREATMENTHW |      -0.59 | [-1.10, -0.09]
## TREATMENTLW |      -0.83 | [-1.35, -0.32]

## # Standardization method: refit
## 
## Parameter   | Std. Coef. |        95% CI
## ----------------------------------------
## (Intercept) |      -0.14 | [-0.66, 0.39]
## TREATMENTDD |       0.59 | [ 0.09, 1.10]
## TREATMENTLW |      -0.24 | [-0.75, 0.27]

## # Standardization method: refit
## 
## Parameter   | Std. Coef. |        95% CI
## ----------------------------------------
## (Intercept) |      -0.38 | [-0.91, 0.15]
## TREATMENTHW |       0.24 | [-0.27, 0.75]
## TREATMENTDD |       0.83 | [ 0.32, 1.35]

El modelo mixto con PC2

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Dim.2 ~ TREATMENT + (1 | Caja) + (1 | Postura)
##    Data: datos_morfo_trans
## 
## REML criterion at convergence: 301.9
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.33675 -0.67522 -0.03272  0.60761  2.69881 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Caja     (Intercept) 0.01687  0.1299  
##  Postura  (Intercept) 0.09440  0.3072  
##  Residual             0.28331  0.5323  
## Number of obs: 175, groups:  Caja, 21; Postura, 7
## 
## Fixed effects:
##             Estimate Std. Error       df t value Pr(>|t|)
## (Intercept) -0.06993    0.14334  9.48768  -0.488    0.637
## TREATMENTLW  0.10352    0.12161 12.58436   0.851    0.411
## TREATMENTHW  0.10150    0.11917 11.70540   0.852    0.411
## 
## Correlation of Fixed Effects:
##             (Intr) TREATMENTL
## TREATMENTLW -0.405           
## TREATMENTHW -0.413  0.487

	Dim.2
Predictors	Estimates	CI	p
(Intercept)	-0.07	-0.35 – 0.21	0.626
TREATMENT [LW]	0.10	-0.14 – 0.34	0.396
TREATMENT [HW]	0.10	-0.13 – 0.34	0.396
Random Effects
σ²	0.28
τ₀₀ _Caja	0.02
τ₀₀ _Postura	0.09
ICC	0.28
N _Caja	21
N _Postura	7
Observations	175
Marginal R² / Conditional R²	0.006 / 0.286

## Type III Analysis of Variance Table with Satterthwaite's method
##            Sum Sq Mean Sq NumDF  DenDF F value Pr(>F)
## TREATMENT 0.27623 0.13812     2 12.301  0.4875 0.6255

Haciendo el ajuste en la significancia:

	Dim.2
Predictors	Estimates	CI	p	df
(Intercept)	-0.07	-0.39 – 0.25	0.637	9.55
TREATMENT [LW]	0.10	-0.16 – 0.37	0.411	12.21
TREATMENT [HW]	0.10	-0.16 – 0.36	0.412	11.35
Random Effects
σ²	0.28
τ₀₀ _Caja	0.02
τ₀₀ _Postura	0.09
ICC	0.28
N _Caja	21
N _Postura	7
Observations	175
Marginal R² / Conditional R²	0.006 / 0.286

##RESULTADOS DESEMPEÑO LOCOMOTOR

Para este experimento se utilizaron 7 posturas diferentes. Cada postura se dividió en 3 tratamientos (Agua Baja AB,Agua Estable AE ,Agua Desecación AD), para un total de 21 cajas.5 individuos provenientes de cada caja fueron utilizados para las pruebas de desempeño locomotor. Estas pruebas se realizaron entre las 9 y las 16 horas del día. Se evaluó el desempeño locomotor a 25, 30, 33, 37 y 40 grados centígrados. El desempeño de cada renacuajo fue evaluado a una única temperatura y para esto el animal fue introducido en recipiente con agua durante 3 minutos y se filmó su respuesta al ser estimulado con un estilete. A partir de los videos y utlizando el programa Tracker se determinó para cada renacuajo los valores máximos de velocidad, aceleración y distancia.

programa para análisis de videos

Los datos:

##   TREATMENT postura caja temp Id_Random_Foto individuo       vel     acel
## 1        HW      C2   16 37.0              1         4 0.2733747 3.651805
## 2        HW      C3   17 25.5              2         1 0.2534460 2.922191
## 3        DD      C5   12 33.0              3         5 0.3889761 4.750895
## 4        HW      C2   16 40.0              4         6 0.1649230 1.672477
## 5        DD      C1    8 40.0              5         6 0.3145094 2.745355
## 6        DD      C6   13 30.0              6         3 0.5120589 6.788423
##         long     vel_a      mag_p  peso Longitud_Total  Peso Altura_Cabeza
## 1 0.09981042 121.49333 0.10714760 0.030       24.97633 0.030      2.486333
## 2 0.08462006 167.03079 0.09233168 0.042       23.77367 0.042      2.164333
## 3 0.80143725 288.22802 0.17048985 0.035       26.36967 0.035      2.817333
## 4 0.16512646  53.92223 0.12073766 0.017       18.02033 0.017      1.881667
## 5 0.06470735 554.99910 0.08438124 0.070       29.31800 0.070      2.485333
## 6 0.39807844 186.40142 0.16396688 0.021       20.78933 0.021      2.109000
##   Altura_Cola Longitud_Cola Perim_Musculo1 Longitud_Cabeza L_Longitud_Total
## 1    1.565333      17.52700       38.31700        7.633000         1.397529
## 2    1.467667      16.84500       34.71633        7.114333         1.376096
## 3    1.675667      18.74700       38.77133        7.669667         1.421105
## 4    1.168667      12.53900       27.13233        5.639667         1.255763
## 5    2.054333      20.18367       43.89933        8.744000         1.467134
## 6    1.413333      15.22967       32.12367        5.471000         1.317841
##      L_Peso L_Altura_Cabeza L_Altura_Cola L_Longitud_Cola L_Perimetro_Musculo
## 1 -1.522879       0.3955594    0.19460683        1.243708            1.583391
## 2 -1.376751       0.3353241    0.16662743        1.226471            1.540534
## 3 -1.455932       0.4498382    0.22418763        1.272932            1.588511
## 4 -1.769551       0.2745427    0.06769066        1.098263            1.433487
## 5 -1.154902       0.3953846    0.31267091        1.305000            1.642458
## 6 -1.677781       0.3240766    0.15024460        1.182690            1.506825
##   L_Longitud_Cabeza   Dim.1   Dim.2      Pcrot
## 1         0.8826953  3.2632  0.2259  1.4708136
## 2         0.8521342  2.4854 -0.4660  1.1202452
## 3         0.8847765  4.1504  0.5298  1.8707077
## 4         0.7512534 -1.4971  0.3299 -0.6747671
## 5         0.9417101  5.8749 -0.5259  2.6480109
## 6         0.7380667  0.4226 -0.1818  0.1904794

Librerias para las figuras:

Figuras exploratorias

#####Aceleración

###Modelo MixtoGAM

effect size

Paquetes para hacer el análisis

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## acel ~ s(temp, k = 5) + TREATMENT
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   4.1384     0.1668  24.814  < 2e-16 ***
## TREATMENTHW  -0.8273     0.2358  -3.508 0.000682 ***
## TREATMENTLW  -0.7143     0.2376  -3.006 0.003357 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##          edf Ref.df    F  p-value    
## s(temp) 2.35   2.83 7.54 0.000196 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.251   Deviance explained = 28.2%
## GCV = 1.0262  Scale est. = 0.9734    n = 104

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## acel ~ s(temp, k = 5) + TREATMENT
## 
## Parametric Terms:
##           df     F p-value
## TREATMENT  2 7.214 0.00119
## 
## Approximate significance of smooth terms:
##          edf Ref.df    F  p-value
## s(temp) 2.35   2.83 7.54 0.000196

	acel
Predictors	Estimates	CI	p	df
(Intercept)	4.14	3.81 – 4.47	<0.001	98.65
TREATMENT [HW]	-0.83	-1.30 – -0.36	0.001	98.65
TREATMENT [LW]	-0.71	-1.19 – -0.24	0.003	98.65
Smooth term (temp)			<0.001
Observations	104
R²	0.251

Para contrastar entre tratamientos:

##  contrast estimate    SE   df t.ratio p.value
##  DD - HW     0.827 0.236 98.7   3.508  0.0020
##  DD - LW     0.714 0.238 98.7   3.006  0.0093
##  HW - LW    -0.113 0.238 98.7  -0.475  0.8830
## 
## P value adjustment: tukey method for comparing a family of 3 estimates

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## acel ~ s(temp, k = 5) + TREATMENT
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   3.3112     0.1668  19.854  < 2e-16 ***
## TREATMENTDD   0.8273     0.2358   3.508 0.000682 ***
## TREATMENTLW   0.1130     0.2376   0.475 0.635511    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##          edf Ref.df    F  p-value    
## s(temp) 2.35   2.83 7.54 0.000196 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.251   Deviance explained = 28.2%
## GCV = 1.0262  Scale est. = 0.9734    n = 104

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## acel ~ s(temp, k = 5) + TREATMENT
## 
## Parametric Terms:
##           df     F p-value
## TREATMENT  2 7.214 0.00119
## 
## Approximate significance of smooth terms:
##          edf Ref.df    F  p-value
## s(temp) 2.35   2.83 7.54 0.000196

	acel
Predictors	Estimates	CI	p	df
(Intercept)	3.31	2.98 – 3.64	<0.001	98.65
TREATMENT [DD]	0.83	0.36 – 1.30	0.001	98.65
TREATMENT [LW]	0.11	-0.36 – 0.58	0.636	98.65
Smooth term (temp)			<0.001
Observations	104
R²	0.251

## # Standardization method: refit
## 
## Component    |   Parameter | Std. Coef. |         95% CI
## --------------------------------------------------------
## conditional  | (Intercept) |       0.45 | [ 0.16,  0.74]
## conditional  | TREATMENTHW |      -0.73 | [-1.14, -0.32]
## conditional  | TREATMENTLW |      -0.63 | [-1.04, -0.21]
## smooth_terms |     s(temp) |            |

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## acel ~ s(temp, k = 5) + TREATMENT + postura
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  4.23104    0.28073  15.072  < 2e-16 ***
## TREATMENTHW -0.82729    0.22906  -3.612 0.000494 ***
## TREATMENTLW -0.71910    0.23091  -3.114 0.002454 ** 
## posturaC2    0.16988    0.34990   0.486 0.628462    
## posturaC3   -0.24780    0.35644  -0.695 0.488661    
## posturaC4   -0.81810    0.34990  -2.338 0.021534 *  
## posturaC5    0.15368    0.34990   0.439 0.661531    
## posturaC6    0.07425    0.34990   0.212 0.832403    
## posturaC7    0.02050    0.34990   0.059 0.953403    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##           edf Ref.df     F  p-value    
## s(temp) 2.373  2.855 8.054 0.000113 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.293   Deviance explained = 36.4%
## GCV =  1.031  Scale est. = 0.91822   n = 104

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## acel ~ s(temp, k = 5) + TREATMENT + postura
## 
## Parametric Terms:
##           df     F  p-value
## TREATMENT  2 7.682 0.000819
## postura    6 1.981 0.076269
## 
## Approximate significance of smooth terms:
##           edf Ref.df     F  p-value
## s(temp) 2.373  2.855 8.054 0.000113

	acel
Predictors	Estimates	CI	p	df
(Intercept)	4.23	3.67 – 4.79	<0.001	92.63
TREATMENT [HW]	-0.83	-1.28 – -0.37	<0.001	92.63
TREATMENT [LW]	-0.72	-1.18 – -0.26	0.002	92.63
postura [C2]	0.17	-0.52 – 0.86	0.628	92.63
postura [C3]	-0.25	-0.96 – 0.46	0.489	92.63
postura [C4]	-0.82	-1.51 – -0.12	0.022	92.63
postura [C5]	0.15	-0.54 – 0.85	0.662	92.63
postura [C6]	0.07	-0.62 – 0.77	0.832	92.63
postura [C7]	0.02	-0.67 – 0.72	0.953	92.63
Smooth term (temp)			<0.001
Observations	104
R²	0.293

Desempeño locomotor con el tamaño corporal como covariable

El componente principal rotado correspondiente a Body size (Pcrot) se usó como covariable del modelo

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## acel ~ s(temp, k = 5) + TREATMENT + Pcrot
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.93881    0.17346  22.707  < 2e-16 ***
## TREATMENTHW -0.61372    0.23749  -2.584  0.01124 *  
## TREATMENTLW -0.50831    0.23841  -2.132  0.03551 *  
## Pcrot        0.29687    0.09863   3.010  0.00332 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##           edf Ref.df     F  p-value    
## s(temp) 2.411  2.897 7.633 0.000149 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.308   Deviance explained = 34.4%
## GCV = 0.95797  Scale est. = 0.89892   n = 104

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## acel ~ s(temp, k = 5) + TREATMENT + Pcrot
## 
## Parametric Terms:
##           df     F p-value
## TREATMENT  2 3.723 0.02765
## Pcrot      1 9.060 0.00332
## 
## Approximate significance of smooth terms:
##           edf Ref.df     F  p-value
## s(temp) 2.411  2.897 7.633 0.000149

	acel
Predictors	Estimates	CI	p	df
(Intercept)	3.94	3.59 – 4.28	<0.001	97.59
TREATMENT [HW]	-0.61	-1.09 – -0.14	0.011	97.59
TREATMENT [LW]	-0.51	-0.98 – -0.04	0.036	97.59
Pcrot	0.30	0.10 – 0.49	0.003	97.59
Smooth term (temp)			<0.001
Observations	104
R²	0.308

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## acel ~ s(temp, k = 5) + TREATMENT * Pcrot
## 
## Parametric coefficients:
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         4.0541     0.1848  21.935  < 2e-16 ***
## TREATMENTHW        -0.7185     0.2441  -2.943  0.00408 ** 
## TREATMENTLW        -0.6216     0.2456  -2.530  0.01302 *  
## Pcrot               0.1251     0.1396   0.896  0.37233    
## TREATMENTHW:Pcrot   0.3925     0.2355   1.667  0.09885 .  
## TREATMENTLW:Pcrot   0.2768     0.2421   1.143  0.25570    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##          edf Ref.df     F  p-value    
## s(temp) 2.43  2.917 7.708 0.000128 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.317   Deviance explained = 36.6%
## GCV = 0.96593  Scale est. = 0.88763   n = 104

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## acel ~ s(temp, k = 5) + TREATMENT * Pcrot
## 
## Parametric Terms:
##                 df     F p-value
## TREATMENT        2 4.870 0.00968
## Pcrot            1 0.803 0.37233
## TREATMENT:Pcrot  2 1.581 0.21114
## 
## Approximate significance of smooth terms:
##           edf Ref.df     F  p-value
## s(temp) 2.430  2.917 7.708 0.000128

	acel
Predictors	Estimates	CI	p	df
(Intercept)	4.05	3.69 – 4.42	<0.001	95.57
TREATMENT [HW]	-0.72	-1.20 – -0.23	0.004	95.57
TREATMENT [LW]	-0.62	-1.11 – -0.13	0.013	95.57
Pcrot	0.13	-0.15 – 0.40	0.372	95.57
TREATMENT [HW] × Pcrot	0.39	-0.07 – 0.86	0.099	95.57
TREATMENT [LW] × Pcrot	0.28	-0.20 – 0.76	0.256	95.57
Smooth term (temp)			<0.001
Observations	104
R²	0.317

## # Standardization method: refit
## 
## Component    |   Parameter | Std. Coef. |         95% CI
## --------------------------------------------------------
## conditional  | (Intercept) |       0.33 | [ 0.04,  0.62]
## conditional  | TREATMENTHW |      -0.54 | [-0.95, -0.12]
## conditional  | TREATMENTLW |      -0.45 | [-0.86, -0.03]
## conditional  |       Pcrot |       0.26 | [ 0.09,  0.44]
## smooth_terms |     s(temp) |            |

Errores modelo mixto-GAM

library(mgcv) library(lme4) desloc1\(tratamiento <- as.factor(desloc1\)tratamiento) desloc1\(postura <- as.factor(desloc1\)postura) mixtogam<-gamm(acel~tratamiento+s(temp,k=3)+(1|postura),data=desloc1)

Error in gamm(acel ~ tratamiento + s(temp, k = 3) + (1 | postura), data = desloc1) : Not enough (non-NA) data to do anything meaningful

mixtogamo<-gamm(acel_{(TREATMENT)+s(temp),random=list(postura=}1), data=desloc) Error in smooth.construct.tp.smooth.spec(object, dk\(data, dk\)knots) : A term has fewer unique covariate combinations than specified maximum degrees of freedom

MULTI-LEVEL ANALYSIS OF STRESS RESPONSES IN AMPHIBIAN OF EXTREME HABITATS

Alexandra Delgadillo M.

27/1/2022

Pregunta de investigación:

Resultados:

Resultados morfológicos

Analisis para evaluar la repetibilidad de las medidas tomadas en cada renacuajo:

La Base de datos

Normalidad variables transformadas:

Homogenidad de varianza variables transformadas (de cada variable por separado):

log(Longitud_Total)

log Peso

Altura_cabeza

Longitud total

Longitud cola

Perímetro músculo

Longitud Cabeza

Peso

Análisis de componentes pricipales variables transformadas

Las figuras de las correlaciones con coeficientes

El modelo mixto con peso transformado

El modelo mixto con PC rotado

El modelo mixto con PC rotado usando solo caja random

1.Prueba de homogeneidad del modelo mixto rotado pc1

2.Evaluando los supuestos de los modelos mixtos:

Evaluando los residuos del modelo

Efecto aleatorio:La postura

Efecto aleatorio: La caja

3. Calculando la magnitud del efecto del modelo

Comparación con DD

Comparación con HW

Comparación con LW

El modelo mixto con PC2

Figuras exploratorias

Desempeño locomotor con el tamaño corporal como covariable