Ajuste de modelos aditivos generalizados para posición, escala y forma (GAMLSS) con datos Dengue-Clima en Cali
Modelo Poisson
library(gamlss)
modelo_PO <- gamlss(
formula = casos ~ cs(prec1, df = 8)+cs(tmax1, df = 8)+cs(hum3, df = 8)+cs(ao, df = 8)+cs(mes, df = 8)+cs(lncasos1, df = 8),
family = PO,
data = data,
trace = FALSE
)
summary(modelo_PO)
## ******************************************************************
## Family: c("PO", "Poisson")
##
## Call: gamlss(formula = casos ~ cs(prec1, df = 8) + cs(tmax1,
## df = 8) + cs(hum3, df = 8) + cs(ao, df = 8) + cs(mes,
## df = 8) + cs(lncasos1, df = 8), family = PO, data = data,
## trace = FALSE)
##
## Fitting method: RS()
##
## ------------------------------------------------------------------
## Mu link function: log
## Mu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -6.680e+01 2.539e+00 -26.306 < 2e-16 ***
## cs(prec1, df = 8) 1.801e-02 4.109e-03 4.382 3.82e-05 ***
## cs(tmax1, df = 8) 1.820e-01 7.765e-03 23.445 < 2e-16 ***
## cs(hum3, df = 8) -8.295e-03 1.376e-03 -6.030 5.94e-08 ***
## cs(ao, df = 8) 3.174e-02 6.658e-04 47.675 < 2e-16 ***
## cs(mes, df = 8) -4.372e-02 1.742e-03 -25.093 < 2e-16 ***
## cs(lncasos1, df = 8) 7.199e-01 7.177e-03 100.311 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## NOTE: Additive smoothing terms exist in the formulas:
## i) Std. Error for smoothers are for the linear effect only.
## ii) Std. Error for the linear terms maybe are not accurate.
## ------------------------------------------------------------------
## No. of observations in the fit: 129
## Degrees of Freedom for the fit: 55.00002
## Residual Deg. of Freedom: 73.99998
## at cycle: 20
##
## Global Deviance: 2337.892
## AIC: 2447.892
## SBC: 2605.182
## ******************************************************************
Modelo Yule
modelo_YU <- gamlss(
formula = casos ~ cs(prec1, df = 8)+cs(tmax1, df = 8)+cs(hum3, df = 8)+cs(ao, df = 8)+cs(mes, df = 8)+cs(lncasos1, df = 8),
family = YULE,
mu.fix = TRUE,
method = mixed(1,2),
data = data,
trace = FALSE
)
summary(modelo_YU)
## ******************************************************************
## Family: c("YULE", "Yule")
##
## Call: gamlss(formula = casos ~ cs(prec1, df = 8) + cs(tmax1,
## df = 8) + cs(hum3, df = 8) + cs(ao, df = 8) + cs(mes,
## df = 8) + cs(lncasos1, df = 8), family = YULE,
## data = data, method = mixed(1, 2), mu.fix = TRUE, trace = FALSE)
##
## Fitting method: mixed(1, 2)
##
## ------------------------------------------------------------------
## Mu parameter is fixed
## Mu = 251.2713
## ------------------------------------------------------------------
## No. of observations in the fit: 129
## Degrees of Freedom for the fit: 0
## Residual Deg. of Freedom: 129
## at cycle: 1
##
## Global Deviance: 2628.616
## AIC: 2628.616
## SBC: 2628.616
## ******************************************************************
Modelo Binomial negativo II
modelo_NB <- gamlss(
formula = casos ~ cs(prec1, df = 8)+cs(tmax1, df = 8)+cs(hum3, df = 8)+cs(ao, df = 8)+cs(mes, df = 8)+cs(lncasos1, df = 8),
sigma.formula = ~ cs(prec1, df = 8)+cs(tmax1, df = 8)+cs(hum3, df = 8)+cs(ao, df = 8)+cs(mes, df = 8)+cs(lncasos1, df = 8),
family = NBII,
mu.fix = TRUE,
sigma.fix = TRUE,
method = mixed(1,2),
data = data,
trace = FALSE
)
summary(modelo_NB)
## ******************************************************************
## Family: c("NBII", "Negative Binomial type II")
##
## Call: gamlss(formula = casos ~ cs(prec1, df = 8) + cs(tmax1,
## df = 8) + cs(hum3, df = 8) + cs(ao, df = 8) + cs(mes,
## df = 8) + cs(lncasos1, df = 8), sigma.formula = ~cs(prec1,
## df = 8) + cs(tmax1, df = 8) + cs(hum3, df = 8) +
## cs(ao, df = 8) + cs(mes, df = 8) + cs(lncasos1,
## df = 8), family = NBII, data = data, method = mixed(1,
## 2), mu.fix = TRUE, sigma.fix = TRUE, trace = FALSE)
##
## Fitting method: mixed(1, 2)
##
## ------------------------------------------------------------------
## Mu parameter is fixed
## Mu is equal with the vector ( 177.6357 , 171.1357 , 189.1357 , 209.6357 , ...)
## ------------------------------------------------------------------
## Sigma parameter is fixed
## Sigma = 446.419
## ------------------------------------------------------------------
## No. of observations in the fit: 129
## Degrees of Freedom for the fit: 0
## Residual Deg. of Freedom: 129
## at cycle: 1
##
## Global Deviance: 1694.316
## AIC: 1694.316
## SBC: 1694.316
## ******************************************************************
Modelo Poisson-inv Gaussiano
modelo_PIG <- gamlss(
formula = casos ~ cs(prec1, df = 8)+cs(tmax1, df = 8)+cs(hum3, df = 8)+cs(ao, df = 8)+cs(mes, df = 8)+cs(lncasos1, df = 8),
sigma.formula = ~ cs(prec1, df = 8)+cs(tmax1, df = 8)+cs(hum3, df = 8)+cs(ao, df = 8)+cs(mes, df = 8)+cs(lncasos1, df = 8),
family = PIG,
mu.fix = TRUE,
sigma.fix = TRUE,
method = mixed(1,2),
data = data,
trace = FALSE
)
summary(modelo_PIG)
## ******************************************************************
## Family: c("PIG", "Poisson.Inverse.Gaussian")
##
## Call: gamlss(formula = casos ~ cs(prec1, df = 8) + cs(tmax1,
## df = 8) + cs(hum3, df = 8) + cs(ao, df = 8) + cs(mes,
## df = 8) + cs(lncasos1, df = 8), sigma.formula = ~cs(prec1,
## df = 8) + cs(tmax1, df = 8) + cs(hum3, df = 8) +
## cs(ao, df = 8) + cs(mes, df = 8) + cs(lncasos1,
## df = 8), family = PIG, data = data, method = mixed(1,
## 2), mu.fix = TRUE, sigma.fix = TRUE, trace = FALSE)
##
## Fitting method: mixed(1, 2)
##
## ------------------------------------------------------------------
## Mu parameter is fixed
## Mu is equal with the vector ( 177.6357 , 171.1357 , 189.1357 , 209.6357 , ...)
## ------------------------------------------------------------------
## Sigma parameter is fixed
## Sigma = 1.776641
## ------------------------------------------------------------------
## No. of observations in the fit: 129
## Degrees of Freedom for the fit: 0
## Residual Deg. of Freedom: 129
## at cycle: 1
##
## Global Deviance: 1602.082
## AIC: 1602.082
## SBC: 1602.082
## ******************************************************************
Modelo Poisson doble
modelo_DPO <- gamlss(
formula = casos ~ cs(prec1, df = 8)+cs(tmax1, df = 8)+cs(hum3, df = 8)+cs(ao, df = 8)+cs(mes, df = 8)+cs(lncasos1, df = 8),
sigma.formula = ~ cs(prec1, df = 8)+cs(tmax1, df = 8)+cs(hum3, df = 8)+cs(ao, df = 8)+cs(mes, df = 8)+cs(lncasos1, df = 8),
family = DPO,
mu.fix = TRUE,
sigma.fix = TRUE,
method = mixed(1,2),
data = data,
trace = FALSE
)
summary(modelo_DPO)
## ******************************************************************
## Family: c("DPO", "Double Poisson")
##
## Call: gamlss(formula = casos ~ cs(prec1, df = 8) + cs(tmax1,
## df = 8) + cs(hum3, df = 8) + cs(ao, df = 8) + cs(mes,
## df = 8) + cs(lncasos1, df = 8), sigma.formula = ~cs(prec1,
## df = 8) + cs(tmax1, df = 8) + cs(hum3, df = 8) +
## cs(ao, df = 8) + cs(mes, df = 8) + cs(lncasos1,
## df = 8), family = DPO, data = data, method = mixed(1,
## 2), mu.fix = TRUE, sigma.fix = TRUE, trace = FALSE)
##
## Fitting method: mixed(1, 2)
##
## ------------------------------------------------------------------
## Mu parameter is fixed
## Mu is equal with the vector ( 177.6357 , 171.1357 , 189.1357 , 209.6357 , ...)
## ------------------------------------------------------------------
## Sigma parameter is fixed
## Sigma = 1
## ------------------------------------------------------------------
## No. of observations in the fit: 129
## Degrees of Freedom for the fit: 0
## Residual Deg. of Freedom: 129
## at cycle: 1
##
## Global Deviance: 7713.224
## AIC: 7713.224
## SBC: 7713.224
## ******************************************************************
Modelo Poisson generalizado
modelo_GPO <- gamlss(
formula = casos ~ cs(prec1, df = 8)+cs(tmax1, df = 8)+cs(hum3, df = 8)+cs(ao, df = 8)+cs(mes, df = 8)+cs(lncasos1, df = 8),
sigma.formula = ~ cs(prec1, df = 8)+cs(tmax1, df = 8)+cs(hum3, df = 8)+cs(ao, df = 8)+cs(mes, df = 8)+cs(lncasos1, df = 8),
family = GPO,
mu.fix = TRUE,
sigma.fix = TRUE,
method = mixed(1,2),
data = data,
trace = FALSE
)
summary(modelo_GPO)
## ******************************************************************
## Family: c("GPO", "Generalised Poisson")
##
## Call: gamlss(formula = casos ~ cs(prec1, df = 8) + cs(tmax1,
## df = 8) + cs(hum3, df = 8) + cs(ao, df = 8) + cs(mes,
## df = 8) + cs(lncasos1, df = 8), sigma.formula = ~cs(prec1,
## df = 8) + cs(tmax1, df = 8) + cs(hum3, df = 8) +
## cs(ao, df = 8) + cs(mes, df = 8) + cs(lncasos1,
## df = 8), family = GPO, data = data, method = mixed(1,
## 2), mu.fix = TRUE, sigma.fix = TRUE, trace = FALSE)
##
## Fitting method: mixed(1, 2)
##
## ------------------------------------------------------------------
## Mu parameter is fixed
## Mu is equal with the vector ( 177.6357 , 171.1357 , 189.1357 , 209.6357 , ...)
## ------------------------------------------------------------------
## Sigma parameter is fixed
## Sigma = 0.1
## ------------------------------------------------------------------
## No. of observations in the fit: 129
## Degrees of Freedom for the fit: 0
## Residual Deg. of Freedom: 129
## at cycle: 1
##
## Global Deviance: 1648.157
## AIC: 1648.157
## SBC: 1648.157
## ******************************************************************