Last updated: 2022-07-04

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Knit directory: ms_mariposas_biodiversity/

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File	Version	Author	Date	Message
Rmd	a9c1df0	ajpelu	2022-07-04	eliminar TP_ES_OE y rehacer modelos
html	2a10774	ajpelu	2022-01-30	Build site.
Rmd	b29b528	ajpelu	2022-01-30	add equations
Rmd	04d5a3b	ajpelu	2022-01-28	modelling
html	04d5a3b	ajpelu	2022-01-28	modelling

library(tidyverse)
library(readxl)
library(janitor)
library(here)
library(correlation)

Warning: package 'correlation' was built under R version 4.0.5

library(patchwork)
library(vegan)
library(glmulti)
library(DHARMa)
library(MuMIn)
library(performance)
library(tweedie)
library(kableExtra)
library(visreg)
library(tab)
library(MASS)
library(equatiomatic)
library(report)

Warning: package 'report' was built under R version 4.0.5

Introduction

Prepara datos

De las variables climáticas según nuestra selección previa tenemos:

variables_sel <- c("Pp_anu", "TP_PEND", "FR_MATDE", 
             "TP_SU_NO", "FR_QUERC", "FR_CONIF", 
             "TP_RSH_V", "HIDRO_ITH", "temp_anu",
             "TP_RSD_P", "Pp_ver", "TP_ES_OE", "TP_EXPO",
             "DS_ARBOL", "elev")

Por tanto de las variables climáticas anuales solo cogeré: Pp_anu, t_anual, Pp_ver

diversidad_year <- read_csv(here::here("data/diversidad_by_year.csv"))
riqueza_year <- read_csv(here::here("data/riqueza_by_year.csv"))
densidad_year <- read_csv(here::here("data/densidad_by_year.csv"))

env <- read_csv(here::here("data/matrix_env_variables_selected.csv")) %>% 
  dplyr::select(-elev, -temp_anu, -Pp_ver, -Pp_anu)
climate_year <- read_csv(here::here("data/climate_year.csv")) %>% 
  dplyr::select(Id_transect, year, p_anu_year, p_ver_year, t_anu_year = t_anual) 

m <- riqueza_year %>% 
  inner_join(diversidad_year) %>% 
  inner_join(densidad_year) %>% 
  dplyr::select(-longitud, -min_altitu, -max_altitu, -long_total, -abundancia) %>% 
  unite("id", c("id_transecto", "year")) %>% 
  inner_join(
    (climate_year %>% unite("id", c("Id_transect", "year"), remove = FALSE)),
    by="id") %>% 
  inner_join(env) %>% 
  rowwise() %>% 
  mutate(FR_ARBOL = sum(FR_CONIF, FR_QUERC)) %>% 
  rename(div = diversidad) %>% 
  relocate(transecto, id, Id_transect, site, elev,year) %>% 
  dplyr::select(-Transecto, -Abreviatura)

Exploración y selección de variables

Correlaciones

co <- correlation((m %>% dplyr::select(p_anu_year:FR_ARBOL)))

co %>% summary() %>% 
  corrplot(size_point = .5, 
       show_values = TRUE,
       show_p = TRUE,
       show_legend = FALSE,
       size_text = 3.5) + 
  theme(axis.text = element_text(size = 8))

Evaluar variables de arbolado

Creamos una variable llamada FR_ARBOL = FR_CONIF + FR_QUERC
Analizar correlación entre variables

FR_CONIF y FR_QUERC (r = -0.1884633)
FR_CONIF y DS_ARBOL (r = -0.5334323)
FR_QUERC y DS_ARBOL (r = -0.366733)
FR_ARBOL y DS_ARBOL (r = -0.7147883)

Evaluar relación entre variables:

theme_set(theme_bw())
(m %>% ggplot(aes(x=DS_ARBOL, y=FR_ARBOL)) + geom_point()) + 
(m %>% ggplot(aes(x=DS_ARBOL, y=FR_QUERC)) + geom_point()) +
(m %>% ggplot(aes(x=DS_ARBOL, y=FR_CONIF)) + geom_point())

Version	Author	Date
04d5a3b	ajpelu	2022-01-28

En caso de querer dejar alguna variable de arbolado, dejaríamos la FR_ARBOL, pero esta variable está muy correlacionada con DS_ARBOL (\(r > |.7|\)), por lo tanto, nos quedamos con DS_ARBOL y descartamos FR_QUERC y FR_CONIF.

Evaluar variables de gradientes topográficos

Las variables TP_RSD_P y TP_SU_NO están muy correlacionadas (r = -0.9459845)

(m %>% ggplot(aes(x=TP_RSD_P, y=TP_SU_NO)) + geom_point())

Version	Author	Date
04d5a3b	ajpelu	2022-01-28

Elegimos a TP_RSD_P, por ser una varible de mayor sentido biológico (cantidad de radiación que recibe)
Analizamos ahora TP_PEND. Esta variable aparece muy correlacionada con HIDRO_ITH (r = -0.6925104) y con TP_RSH_V (r = -0.6747214), aunque valores muy cercanos a <|.7|. Puede ser buena idea descartar TP_PEND.

Evaluar elevación

La elevación presenta alta correlación con la t_anual_year (r = -0.8056942).
Asímismo, la elevación presenta una correlación cercana al umbral (|.7|) con DS_ARBOL (r = 0.5965598) y con HIDRO_ITH (r = -0.6394274).
Sin embargo, la elevación a priori es una covariable que nos interesa mantener, por lo que descartamos t_anu_year.

theme_set(theme_bw())
(m %>% ggplot(aes(x=elev, y=t_anu_year)) + geom_point()) + 
(m %>% ggplot(aes(x=elev, y=DS_ARBOL)) + geom_point()) +
(m %>% ggplot(aes(x=elev, y=HIDRO_ITH)) + geom_point())

Version	Author	Date
04d5a3b	ajpelu	2022-01-28

Evaluar VIF

myvars <- m %>% 
  dplyr::select(-transecto, -id, -Id_transect, -site, -year, 
                -riq, -div, -den, 
                -t_anu_year, -FR_QUERC, -FR_CONIF, 
                -TP_SU_NO) %>% names()
corvif(m[,myvars])



Variance inflation factors

                GVIF
elev        5.353464
p_anu_year  1.210317
p_ver_year  1.187311
TP_PEND    18.681484
FR_MATDE    2.360937
TP_RSH_V    5.410423
HIDRO_ITH   9.707477
TP_RSD_P    5.095531
TP_ES_OE    1.726852
TP_EXPO     4.495690
DS_ARBOL    8.592039
FR_ARBOL    4.955440

Efectivamente vemos altos valores de VIF para TP_PEND (la descartamos)

myvars <- m %>% 
  dplyr::select(-transecto, -id, -Id_transect, -site, -year, 
                -riq, -div, -den, 
                -t_anu_year, -FR_QUERC, -FR_CONIF, 
                -TP_SU_NO, -TP_PEND) %>% names()

corvif(m[,myvars])



Variance inflation factors

               GVIF
elev       5.291071
p_anu_year 1.181742
p_ver_year 1.179339
FR_MATDE   2.289574
TP_RSH_V   2.717009
HIDRO_ITH  3.024327
TP_RSD_P   2.345438
TP_ES_OE   1.639223
TP_EXPO    4.495657
DS_ARBOL   7.108273
FR_ARBOL   3.415775

La siguente candidata a eliminar es DS_ARBOL, aunque dependerá del umbral que seleccionemos. Algunos autores hablan de VIF < 3, otros VIF < 5 y otros de VIF < 10. No obstante, antes vemos la posible relación con FR_ARBOL (r = -0.7147883), que es una variable derivada (combinada de FR_CONIF y FR_QUERC). Proponemos descartar FR_ARBOL.

myvars <- m %>% 
  dplyr::select(-transecto, -id, -Id_transect, -site, -year, 
                -riq, -div, -den, 
                -elev, -FR_QUERC, -FR_CONIF, 
                -TP_SU_NO, -TP_PEND, -FR_ARBOL, -TP_ES_OE) %>% names()

corvif(m[,myvars])



Variance inflation factors

               GVIF
p_anu_year 1.172004
p_ver_year 1.190846
t_anu_year 2.180990
FR_MATDE   1.606927
TP_RSH_V   2.572037
HIDRO_ITH  2.284596
TP_RSD_P   2.062400
TP_EXPO    3.793956
DS_ARBOL   2.437238

Por tanto tenemos seleccionadas las siguientes variables:

m %>% 
  dplyr::select(-transecto, -id, -Id_transect, -site, -year, 
                -riq, -div, -den, 
                -t_anu_year, -FR_QUERC, -FR_CONIF, 
                -TP_SU_NO, -TP_PEND, -FR_ARBOL, -TP_ES_OE) %>% names()

[1] "elev"       "p_anu_year" "p_ver_year" "FR_MATDE"   "TP_RSH_V"  
[6] "HIDRO_ITH"  "TP_RSD_P"   "TP_EXPO"    "DS_ARBOL"

nobs_var <- nrow(m)/
  ncol(m %>% 
 dplyr::select(-transecto, -id, -Id_transect, -site, -year, 
                -riq, -div, -den, 
                -t_anu_year, -FR_QUERC, -FR_CONIF, 
                -TP_SU_NO, -TP_PEND, -FR_ARBOL, -TP_ES_OE))

Algunos hablan de tener entre 15 - 25 veces el numero de observaciones por cada covariable. Actualmente tenemos 17.3333333

Modelo de Densidad

Explorar densidad frente a todas las variables

theme_set(theme_bw())
m %>% 
  pivot_longer(p_anu_year:FR_ARBOL) %>% 
  ggplot(aes(x=value, y=den)) +
  geom_point() + geom_smooth() + 
  facet_wrap(~name, scales = "free_x")

Version	Author	Date
04d5a3b	ajpelu	2022-01-28

# Define formula 
fden <- as.formula(
  paste("den", 
      paste(
        names(
          m %>% dplyr::select(-transecto, -id, -Id_transect, -site, -year, 
                -riq, -div, -den, 
                -t_anu_year, -FR_QUERC, -FR_CONIF, 
                -TP_SU_NO, -TP_PEND, -FR_ARBOL, -TP_ES_OE)), collapse = "+"),
      sep = "~")
  )

fden

den ~ elev + p_anu_year + p_ver_year + FR_MATDE + TP_RSH_V + 
    HIDRO_ITH + TP_RSD_P + TP_EXPO + DS_ARBOL

Aproximación modelo GLM

Probamos con varias familias, y optamos por Gamma

# Probamos varias familias, entre ellas Tweedie 
library(statmod)
library(tweedie)
profile1 <- tweedie.profile(den ~ 1 + FR_MATDE + HIDRO_ITH + DS_ARBOL, data = m, p.vec = seq(1.1, 3.0, 0.1), fit.glm = TRUE)
print(profile1$p.max)

# automatic model selection 
set.seed(1234)
# fam <- "poisson"
# fam <- "gaussian"
fam <- "gamma" 
select_fden <- glmulti(fden, data = m,
              level= 1, 
              chunk = 1, chunks = 4, 
              method = "ga", crit = "bic", 
              family = Gamma(link ="log"), 
              marginality = TRUE,
              confsetsize = 5, 
              plotty = FALSE, report = FALSE)

TASK: Genetic algorithm in the candidate set.
Initialization...
Algorithm started...
Improvements in best and average IC have bebingo en below the specified goals.
Algorithm is declared to have converged.
Completed.

fden1 <- glm(select_fden@formulas[[1]], 
             family = Gamma(link ="log"), data = m)
fden2 <- glm(select_fden@formulas[[2]], 
             family = Gamma(link ="log"), data = m)
fden3 <- glm(select_fden@formulas[[3]], 
             family = Gamma(link ="log"), data = m)
fden4 <- glm(select_fden@formulas[[4]], 
             family = Gamma(link ="log"), data = m)
fden5 <- glm(select_fden@formulas[[5]], 
             family = Gamma(link ="log"), data = m)

Generar tabla de top five modelos

top5_table_fden <- as.data.frame(model.sel(fden1, fden2, fden3, fden4, fden5, rank = BIC)) %>% 
    dplyr::select(-family) %>% 
    mutate(model = 
             c(fden1$formula, fden2$formula, fden3$formula, fden4$formula, fden5$formula)) %>% 
    relocate(model)

write.csv(as.matrix(top5_table_fden), file=here::here("data/mod_den_selectionBIC.csv"))

### Model validation

performance::check_model(fden1)

Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
"none")` instead.

Version	Author	Date
04d5a3b	ajpelu	2022-01-28

performance(fden1) %>% 
  kbl() %>% 
  kable_styling()

AIC	BIC	R2_Nagelkerke	RMSE	Sigma
511.9234	527.1727	0.727684	1.642396	0.4541641

Modelo seleccionado

select_fden@formulas[[1]]

den ~ 1 + FR_MATDE + HIDRO_ITH + DS_ARBOL
<environment: 0x7fb04c1d6198>

modelo_densidad <- glm(den ~ 1 + FR_MATDE + HIDRO_ITH + DS_ARBOL, 
                       family = Gamma(link ="log"), data = m)

Visualización

ytitle <- "Density" 

visreg(modelo_densidad, scale="response", partial=TRUE,
       ylab = ytitle, "FR_MATDE", xlab = "FR_MATDE")

Version	Author	Date
04d5a3b	ajpelu	2022-01-28

visreg(modelo_densidad, scale="response", partial=TRUE,
       ylab = ytitle, "DS_ARBOL", xlab = "DS_ARBOL")

Version	Author	Date
04d5a3b	ajpelu	2022-01-28

visreg(modelo_densidad, scale="response", partial=TRUE,
       "HIDRO_ITH", xlab = "HIDRO_ITH")

Version	Author	Date
04d5a3b	ajpelu	2022-01-28

Parámetros

ms <- modelo_densidad
tc <- tab::tabglm(ms, columns = c("beta.se",  "test", "p"), decimals = 4) 
names(tc) <- c("Variable", "Estimate", "Zvalue", "pvalue") 
  
tablita_auxiliar <- data.frame(
    Variable = c("DegreeFreedom", "AIC", "BIC", "DevianceExplained"), 
    Estimate = as.character(c(df.residual(ms), round(AIC(ms),0), round(BIC(ms), 0), 
                              round( ((ms$null.deviance - ms$deviance) / ms$null.deviance),3))),
    Zvalue = "", pvalue = "")
  
tc <- bind_rows(tc, tablita_auxiliar)
write.csv(tc, here::here("data/mod_den_coefficients.csv"))

tc %>% kbl() %>% kable_styling()

Variable	Estimate	Zvalue	pvalue
Intercept	0.6159 (0.2048)	3.0067	0.003
FR_MATDE	0.0243 (0.0032)	7.5854	<0.001
HIDRO_ITH	0.0802 (0.0256)	3.1338	0.002
DS_ARBOL	-0.0003 (0.0000)	-12.8372	<0.001
DegreeFreedom	152
AIC	512
BIC	527
DevianceExplained	0.664

extract_eq(modelo_densidad, wrap = TRUE, intercept = "beta", use_coefs = TRUE)

\[ \begin{aligned} \log ({ \widehat{E( \operatorname{den} )} }) &= 0.62 + 0.02(\operatorname{FR\_MATDE}) + 0.08(\operatorname{HIDRO\_ITH}) + 0(\operatorname{DS\_ARBOL}) \end{aligned} \]

report::report(modelo_densidad)

We fitted a general linear model (Gamma family with a log link) (estimated using ML) to predict den with FR_MATDE, HIDRO_ITH and DS_ARBOL (formula: den ~ 1 + FR_MATDE + HIDRO_ITH + DS_ARBOL). The model's explanatory power is substantial (Nagelkerke's R2 = 0.73). The model's intercept, corresponding to FR_MATDE = 0, HIDRO_ITH = 0 and DS_ARBOL = 0, is at 0.62 (95% CI [0.21, 1.01], t(152) = 3.01, p = 0.003). Within this model:

  - The effect of FR MATDE is statistically significant and positive (beta = 0.02, 95% CI [0.02, 0.03], t(152) = 7.59, p < .001; Std. beta = 0.31, 95% CI [0.23, 0.40])
  - The effect of HIDRO ITH is statistically significant and positive (beta = 0.08, 95% CI [0.03, 0.13], t(152) = 3.13, p = 0.002; Std. beta = 0.12, 95% CI [0.05, 0.20])
  - The effect of DS ARBOL is statistically significant and negative (beta = -3.14e-04, 95% CI [-3.62e-04, -2.64e-04], t(152) = -12.84, p < .001; Std. beta = -0.53, 95% CI [-0.61, -0.45])

Standardized parameters were obtained by fitting the model on a standardized version of the dataset. 95% Confidence Intervals (CIs) and p-values were computed using

Modelo de Diversidad

Explorar diversidad frente a todas las variables

theme_set(theme_bw())
m %>% 
  pivot_longer(p_anu_year:FR_ARBOL) %>% 
  ggplot(aes(x=value, y=div)) +
  geom_point() + geom_smooth() + 
  facet_wrap(~name, scales = "free_x")

Warning: Removed 15 rows containing non-finite values (stat_smooth).

Warning: Removed 15 rows containing missing values (geom_point).

Version	Author	Date
2a10774	ajpelu	2022-01-30

# Define formula 
fdiv <- as.formula(
  paste("div", 
      paste(
        names(
          m %>% dplyr::select(-transecto, -id, -Id_transect, -site, -year, 
                -riq, -div, -den, 
                -t_anu_year, -FR_QUERC, -FR_CONIF, 
                -TP_SU_NO, -TP_PEND, -FR_ARBOL, 
                -TP_EXPO, -TP_ES_OE, -p_anu_year, -p_ver_year)), collapse = "+"),
      sep = "~")
  )

fdiv

div ~ elev + FR_MATDE + TP_RSH_V + HIDRO_ITH + TP_RSD_P + DS_ARBOL

Aproximación modelo GLM

Probamos con varias familias, y optamos por Gaussian
Ojo, he quitado TP_EXPO, p_anu_year, p_ver_year por valores altos de vif según performance::check_model

# automatic model selection 
set.seed(1234)
# fam <- "poisson"
fam <- "gaussian"
 
select_fdiv <- glmulti(fdiv, data = m,
              level= 1, 
              chunk = 1, chunks = 4, 
              method = "ga", crit = "bic", 
              family = fam, 
              marginality = TRUE,
              confsetsize = 5, 
              plotty = FALSE, report = FALSE)

TASK: Genetic algorithm in the candidate set.
Initialization...
Algorithm started...
Improvements in best and average IC have bebingo en below the specified goals.
Algorithm is declared to have converged.
Completed.

fdiv1 <- glm(select_fdiv@formulas[[1]], data = m)
fdiv2 <- glm(select_fdiv@formulas[[2]], data = m)
fdiv3 <- glm(select_fdiv@formulas[[3]], data = m)
fdiv4 <- glm(select_fdiv@formulas[[4]], data = m)
fdiv5 <- glm(select_fdiv@formulas[[5]], data = m)

Generar tabla de top five modelos

top5_table_fdiv <- as.data.frame(model.sel(fdiv1, fdiv2, fdiv3, fdiv4, fdiv5, rank = BIC)) %>% 
    dplyr::select(-family) %>% 
    mutate(model = 
             c(fdiv1$formula, fdiv2$formula, fdiv3$formula,
               fdiv4$formula, fdiv5$formula)) %>% 
    relocate(model)

write.csv(as.matrix(top5_table_fdiv), file=here::here("data/mod_div_selectionBIC.csv"))

### Model validation

Eligo modelo 2, no hay casi diferencias y tiene menos params.

performance::check_model(fdiv2)

Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
"none")` instead.

Version	Author	Date
2a10774	ajpelu	2022-01-30

performance(fdiv2) %>% 
  kbl() %>% 
  kable_styling()

AIC	BIC	R2	RMSE	Sigma
164.1773	179.3944	0.7052414	0.3978849	0.4031205

Modelo seleccionado

select_fdiv@formulas[[2]]

div ~ 1 + FR_MATDE + HIDRO_ITH + DS_ARBOL
<environment: 0x7fb068751ae8>

modelo_diversidad <- glm(div ~ 1 + FR_MATDE + HIDRO_ITH + DS_ARBOL, data = m)

Visualización

ytitle <- "Diversity" 

visreg(modelo_diversidad, scale="response", partial=TRUE, 
       ylab = ytitle, "FR_MATDE", xlab = "FR_MATDE")

Version	Author	Date
2a10774	ajpelu	2022-01-30

visreg(modelo_diversidad, scale="response", partial=TRUE,
       ylab = ytitle, "HIDRO_ITH", xlab = "HIDRO_ITH")

Version	Author	Date
2a10774	ajpelu	2022-01-30

#visreg(modelo_diversidad, scale="response", partial=TRUE,
#       ylab = ytitle, "TP_ES_OE", xlab = "TP_ES_OE")

visreg(modelo_diversidad, scale="response", partial=TRUE,
       ylab = ytitle, "DS_ARBOL", xlab = "DS_ARBOL")

Version	Author	Date
2a10774	ajpelu	2022-01-30

Parámetros

ms <- modelo_diversidad
tc <- tab::tabglm(ms, columns = c("beta.se",  "test", "p"), decimals = 4) 
names(tc) <- c("Variable", "Estimate", "Zvalue", "pvalue") 
  
tablita_auxiliar <- data.frame(
    Variable = c("DegreeFreedom", "AIC", "BIC", "DevianceExplained"), 
    Estimate = as.character(c(df.residual(ms), round(AIC(ms),0), round(BIC(ms), 0), 
                              round( ((ms$null.deviance - ms$deviance) / ms$null.deviance),3))),
    Zvalue = "", pvalue = "")
  
tc <- bind_rows(tc, tablita_auxiliar)
write.csv(tc, here::here("data/mod_div_coefficients.csv"))

tc %>% kbl() %>% kable_styling()

Variable	Estimate	Zvalue	pvalue
Intercept	3.3504 (0.1784)	18.7825	<0.001
FR_MATDE	0.0200 (0.0028)	7.1733	<0.001
HIDRO_ITH	-0.1323 (0.0223)	-5.9345	<0.001
DS_ARBOL	-0.0003 (0.0000)	-12.3877	<0.001
DegreeFreedom	151
AIC	164
BIC	179
DevianceExplained	0.705

extract_eq(modelo_diversidad, wrap = TRUE, intercept = "beta", use_coefs = TRUE)

\[ \begin{aligned} \widehat{E( \operatorname{div} )} &= 3.35 + 0.02(\operatorname{FR\_MATDE}) - 0.13(\operatorname{HIDRO\_ITH}) + 0(\operatorname{DS\_ARBOL}) \end{aligned} \]

report::report(modelo_diversidad)

We fitted a linear model (estimated using ML) to predict div with FR_MATDE, HIDRO_ITH and DS_ARBOL (formula: div ~ 1 + FR_MATDE + HIDRO_ITH + DS_ARBOL). The model's explanatory power is substantial (R2 = 0.71). The model's intercept, corresponding to FR_MATDE = 0, HIDRO_ITH = 0 and DS_ARBOL = 0, is at 3.35 (95% CI [3.00, 3.70], t(151) = 18.78, p < .001). Within this model:

  - The effect of FR MATDE is statistically significant and positive (beta = 0.02, 95% CI [0.01, 0.03], t(151) = 7.17, p < .001; Std. beta = 0.35, 95% CI [0.25, 0.44])
  - The effect of HIDRO ITH is statistically significant and negative (beta = -0.13, 95% CI [-0.18, -0.09], t(151) = -5.93, p < .001; Std. beta = -0.27, 95% CI [-0.36, -0.18])
  - The effect of DS ARBOL is statistically significant and negative (beta = -2.67e-04, 95% CI [-3.10e-04, -2.25e-04], t(151) = -12.39, p < .001; Std. beta = -0.61, 95% CI [-0.70, -0.51])

Standardized parameters were obtained by fitting the model on a standardized version of the dataset. 95% Confidence Intervals (CIs) and p-values were computed using

Modelo de Riqueza

Explorar riqueza frente a todas las variables

theme_set(theme_bw())
m %>% 
  pivot_longer(p_anu_year:FR_ARBOL) %>% 
  ggplot(aes(x=value, y=riq)) +
  geom_point() + geom_smooth() + 
  facet_wrap(~name, scales = "free_x")

Version	Author	Date
2a10774	ajpelu	2022-01-30

# Define formula 
friq <- as.formula(
  paste("riq", 
      paste(
        names(
          m %>% dplyr::select(-transecto, -id, -Id_transect, -site, -year, 
                -riq, -div, -den, 
                -t_anu_year, -FR_QUERC, -FR_CONIF, 
                -TP_SU_NO, -TP_ES_OE, -TP_PEND, -FR_ARBOL, 
                -p_anu_year, -p_ver_year)), collapse = "+"),
      sep = "~")
  )

friq

riq ~ elev + FR_MATDE + TP_RSH_V + HIDRO_ITH + TP_RSD_P + TP_EXPO + 
    DS_ARBOL

Aproximación modelo GLM

Probamos con varias familias, y optamos por Gamma

# automatic model selection 
set.seed(1234)
# fam <- "poisson"
fam <- "gaussian"
select_friq <- glmulti(friq, data = m,
              level= 1, 
              chunk = 1, chunks = 4, 
              method = "ga", crit = "bic", 
              family = fam, 
              marginality = TRUE,
              confsetsize = 5, 
              plotty = FALSE, report = FALSE)

TASK: Genetic algorithm in the candidate set.
Initialization...
Algorithm started...
Improvements in best and average IC have bebingo en below the specified goals.
Algorithm is declared to have converged.
Completed.

friq1 <- glm(select_friq@formulas[[1]], data = m)
friq2 <- glm(select_friq@formulas[[2]], data = m)
friq3 <- glm(select_friq@formulas[[3]], data = m)
friq4 <- glm(select_friq@formulas[[4]], data = m)
friq5 <- glm(select_friq@formulas[[5]], data = m)

Generar tabla de top five modelos

top5_table_friq <- as.data.frame(model.sel(friq1, friq2, friq3, friq4, friq5, rank = BIC)) %>% 
    dplyr::select(-family) %>% 
    mutate(model = 
             c(friq1$formula, friq3$formula, friq3$formula, friq4$formula, friq5$formula)) %>% 
    relocate(model)

write.csv(as.matrix(top5_table_friq), file=here::here("data/mod_riq_selectionBIC.csv"))

### Model validation

performance::check_model(friq1)

Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
"none")` instead.

Version	Author	Date
2a10774	ajpelu	2022-01-30
04d5a3b	ajpelu	2022-01-28

performance(friq1) %>% 
  kbl() %>% 
  kable_styling()

AIC	BIC	R2	RMSE	Sigma
1037.431	1061.83	0.8319412	6.390918	6.539318

Modelo seleccionado

select_friq@formulas[[1]]

riq ~ 1 + elev + FR_MATDE + TP_RSH_V + HIDRO_ITH + TP_RSD_P + 
    TP_EXPO
<environment: 0x7fb062a0c708>

modelo_riqueza <- glm(riq ~ 1 + elev + FR_MATDE + TP_RSH_V + HIDRO_ITH + TP_RSD_P + TP_EXPO, data = m)

Visualización

ytitle <- "Richness" 

visreg(modelo_riqueza, scale="response", partial=TRUE,
       ylab = ytitle, "elev", xlab = "elev")

Version	Author	Date
2a10774	ajpelu	2022-01-30

visreg(modelo_riqueza, scale="response", partial=TRUE,
       ylab = ytitle, "FR_MATDE", xlab = "FR_MATDE")

Version	Author	Date
2a10774	ajpelu	2022-01-30

visreg(modelo_riqueza, scale="response", partial=TRUE,
       ylab = ytitle, "TP_RSH_V", xlab = "TP_RSH_V")

Version	Author	Date
2a10774	ajpelu	2022-01-30

visreg(modelo_riqueza, scale="response", partial=TRUE,
       ylab = ytitle, "HIDRO_ITH", xlab = "HIDRO_ITH")

Version	Author	Date
2a10774	ajpelu	2022-01-30

visreg(modelo_riqueza, scale="response", partial=TRUE,
       ylab = ytitle, "TP_RSD_P", xlab = "TP_RSD_P")

Version	Author	Date
2a10774	ajpelu	2022-01-30

# visreg(modelo_riqueza, scale="response", partial=TRUE,
#        ylab = ytitle, "TP_ES_OE", xlab = "TP_ES_OE")

visreg(modelo_riqueza, scale="response", partial=TRUE,
       ylab = ytitle, "TP_EXPO", xlab = "TP_EXPO")

Version	Author	Date
2a10774	ajpelu	2022-01-30

Parámetros

ms <- modelo_riqueza
tc <- tab::tabglm(ms, columns = c("beta.se",  "test", "p"), decimals = 4) 
names(tc) <- c("Variable", "Estimate", "Zvalue", "pvalue") 
  
tablita_auxiliar <- data.frame(
    Variable = c("DegreeFreedom", "AIC", "BIC", "DevianceExplained"), 
    Estimate = as.character(c(df.residual(ms), round(AIC(ms),0), round(BIC(ms), 0), 
                              round( ((ms$null.deviance - ms$deviance) / ms$null.deviance),3))),
    Zvalue = "", pvalue = "")
  
tc <- bind_rows(tc, tablita_auxiliar)
write.csv(tc, here::here("data/mod_riq_coefficients.csv"))

tc %>% kbl() %>% kable_styling()

Variable	Estimate	Zvalue	pvalue
Intercept	-48.5462 (16.8706)	-2.8776	0.005
elev	-0.0073 (0.0013)	-5.5456	<0.001
FR_MATDE	0.9570 (0.0450)	21.2517	<0.001
TP_RSH_V	8.0258 (1.2103)	6.6311	<0.001
HIDRO_ITH	-4.3652 (0.5413)	-8.0645	<0.001
TP_RSD_P	0.0021 (0.0008)	2.6954	0.008
TP_EXPO	-0.0884 (0.0174)	-5.0847	<0.001
DegreeFreedom	149
AIC	1037
BIC	1062
DevianceExplained	0.832

extract_eq(modelo_riqueza, wrap = TRUE, intercept = "beta", use_coefs = TRUE)

\[ \begin{aligned} \widehat{E( \operatorname{riq} )} &= -48.55 - 0.01(\operatorname{elev}) + 0.96(\operatorname{FR\_MATDE}) + 8.03(\operatorname{TP\_RSH\_V})\ - \\ &\quad 4.37(\operatorname{HIDRO\_ITH}) + 0(\operatorname{TP\_RSD\_P}) - 0.09(\operatorname{TP\_EXPO}) \end{aligned} \]

report::report(modelo_riqueza)

We fitted a linear model (estimated using ML) to predict riq with elev, FR_MATDE, TP_RSH_V, HIDRO_ITH, TP_RSD_P and TP_EXPO (formula: riq ~ 1 + elev + FR_MATDE + TP_RSH_V + HIDRO_ITH + TP_RSD_P + TP_EXPO). The model's explanatory power is substantial (R2 = 0.83). The model's intercept, corresponding to elev = 0, FR_MATDE = 0, TP_RSH_V = 0, HIDRO_ITH = 0, TP_RSD_P = 0 and TP_EXPO = 0, is at -48.55 (95% CI [-81.61, -15.48], t(149) = -2.88, p = 0.004). Within this model:

  - The effect of elev is statistically significant and negative (beta = -7.28e-03, 95% CI [-9.86e-03, -4.71e-03], t(149) = -5.55, p < .001; Std. beta = -0.32, 95% CI [-0.43, -0.21])
  - The effect of FR MATDE is statistically significant and positive (beta = 0.96, 95% CI [0.87, 1.05], t(149) = 21.25, p < .001; Std. beta = 0.79, 95% CI [0.71, 0.86])
  - The effect of TP RSH V is statistically significant and positive (beta = 8.03, 95% CI [5.65, 10.40], t(149) = 6.63, p < .001; Std. beta = 0.31, 95% CI [0.22, 0.40])
  - The effect of HIDRO ITH is statistically significant and negative (beta = -4.37, 95% CI [-5.43, -3.30], t(149) = -8.06, p < .001; Std. beta = -0.41, 95% CI [-0.51, -0.31])
  - The effect of TP RSD P is statistically significant and positive (beta = 2.14e-03, 95% CI [5.85e-04, 3.70e-03], t(149) = 2.70, p = 0.007; Std. beta = 0.13, 95% CI [0.04, 0.23])
  - The effect of TP EXPO is statistically significant and negative (beta = -0.09, 95% CI [-0.12, -0.05], t(149) = -5.08, p < .001; Std. beta = -0.32, 95% CI [-0.45, -0.20])

Standardized parameters were obtained by fitting the model on a standardized version of the dataset. 95% Confidence Intervals (CIs) and p-values were computed using

sessionInfo()

R version 4.0.2 (2020-06-22)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Catalina 10.15.3

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] report_0.5.1       equatiomatic_0.2.0 MASS_7.3-53        tab_4.1.1         
 [5] knitr_1.31         visreg_2.7.0       kableExtra_1.3.1   tweedie_2.3.3     
 [9] performance_0.8.0  MuMIn_1.43.17      DHARMa_0.3.3.0     glmulti_1.0.8     
[13] leaps_3.1          rJava_0.9-13       vegan_2.5-7        lattice_0.20-41   
[17] permute_0.9-5      patchwork_1.1.1    correlation_0.8.0  here_1.0.1        
[21] janitor_2.1.0      readxl_1.3.1       forcats_0.5.1      stringr_1.4.0     
[25] dplyr_1.0.6        purrr_0.3.4        readr_1.4.0        tidyr_1.1.3       
[29] tibble_3.1.2       ggplot2_3.3.5      tidyverse_1.3.1    workflowr_1.7.0   

loaded via a namespace (and not attached):
  [1] TH.data_1.0-10     minqa_1.2.4        colorspace_2.0-2  
  [4] ggridges_0.5.3     ellipsis_0.3.2     rprojroot_2.0.2   
  [7] estimability_1.3   snakecase_0.11.0   parameters_0.17.0 
 [10] fs_1.5.0           rstudioapi_0.13    farver_2.1.0      
 [13] ggrepel_0.9.1      mvtnorm_1.1-1      fansi_0.4.2       
 [16] lubridate_1.7.10   xml2_1.3.2         codetools_0.2-18  
 [19] splines_4.0.2      robustbase_0.93-7  jsonlite_1.7.2    
 [22] nloptr_1.2.2.2     broom_0.7.9        cluster_2.1.0     
 [25] dbplyr_2.1.1       effectsize_0.6.0.1 compiler_4.0.2    
 [28] httr_1.4.2         emmeans_1.5.4      backports_1.2.1   
 [31] assertthat_0.2.1   Matrix_1.3-2       fastmap_1.1.0     
 [34] survey_4.0         cli_2.5.0          later_1.1.0.1     
 [37] htmltools_0.5.2    tools_4.0.2        coda_0.19-4       
 [40] gtable_0.3.0       glue_1.4.2         Rcpp_1.0.7        
 [43] cellranger_1.1.0   jquerylib_0.1.3    vctrs_0.3.8       
 [46] nlme_3.1-152       iterators_1.0.13   insight_0.17.0    
 [49] xfun_0.30          ps_1.5.0           lme4_1.1-27.1     
 [52] rvest_1.0.0        lifecycle_1.0.1    DEoptimR_1.0-8    
 [55] zoo_1.8-8          getPass_0.2-2      scales_1.1.1.9000 
 [58] hms_1.0.0          promises_1.2.0.1   sandwich_3.0-0    
 [61] parallel_4.0.2     qqplotr_0.0.5      yaml_2.2.1        
 [64] gridExtra_2.3      see_0.6.4          sass_0.4.1        
 [67] stringi_1.7.4      highr_0.8          bayestestR_0.11.5 
 [70] foreach_1.5.1      boot_1.3-26        rlang_0.4.12      
 [73] pkgconfig_2.0.3    evaluate_0.14      labeling_0.4.2    
 [76] processx_3.5.1     tidyselect_1.1.1   plyr_1.8.6        
 [79] magrittr_2.0.1     R6_2.5.1           generics_0.1.0    
 [82] multcomp_1.4-16    DBI_1.1.1          pillar_1.6.1      
 [85] haven_2.3.1        whisker_0.4        withr_2.4.1       
 [88] mgcv_1.8-33        survival_3.2-7     datawizard_0.4.0  
 [91] modelr_0.1.8       crayon_1.4.1       utf8_1.1.4        
 [94] rmarkdown_2.14     grid_4.0.2         callr_3.7.0       
 [97] git2r_0.28.0       reprex_2.0.0       digest_0.6.27     
[100] webshot_0.5.2      xtable_1.8-4       httpuv_1.5.5      
[103] stats4_4.0.2       munsell_0.5.0      viridisLite_0.4.0 
[106] bslib_0.3.1        mitools_2.4

modeliza

ajpelu

2022-01-27

Introduction

Prepara datos

Exploración y selección de variables

Correlaciones

Evaluar variables de arbolado

Evaluar variables de gradientes topográficos

Evaluar elevación

Evaluar VIF

Modelo de Densidad

Aproximación modelo GLM

Modelo seleccionado

Visualización

Parámetros

Modelo de Diversidad

Aproximación modelo GLM

Modelo seleccionado

Visualización

Parámetros

Modelo de Riqueza

Aproximación modelo GLM

Modelo seleccionado

Visualización

Parámetros