Ejercicio 1

library(rio)
datita = import("dataPeru.xlsx")

str(datita)

## 'data.frame':    25 obs. of  8 variables:
##  $ DEPARTAMENTO       : chr  "AMAZONAS" "ÁNCASH" "APURÍMAC" "AREQUIPA" ...
##  $ UBIGEO             : chr  "010000" "020000" "030000" "040000" ...
##  $ buenEstado         : num  18.6 13.9 8.7 27.4 17 18 33.8 11.9 10.1 15.6 ...
##  $ contribuyentesSunat: num  75035 302906 103981 585628 151191 ...
##  $ peaOcupada         : num  130019 387976 140341 645001 235857 ...
##  $ pobUrbana          : num  205976 806065 243354 1383694 444473 ...
##  $ PobRural           : num  211389 333050 180905 76739 206467 ...
##  $ pobTotal           : num  417365 1139115 424259 1460433 650940 ...

Regresión Gaussiana

Pasar a porcentaje

h1 = formula(buenEstado ~ contribuyentesSunat/pobTotal + peaOcupada/pobTotal)

h1 = formula(buenEstado ~ (((contribuyentesSunat/pobTotal)100) + (peaOcupada/pobTotal)100))

reg1=lm(h1,data=datita)
summary(reg1)

## 
## Call:
## lm(formula = h1, data = datita)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -12.6468  -4.0593  -0.1762   3.4804  20.0829 
## 
## Coefficients:
##                                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                   1.728e+01  3.941e+00   4.384 0.000287 ***
## contribuyentesSunat           1.205e-04  5.981e-05   2.015 0.057556 .  
## peaOcupada                   -1.023e-04  6.608e-05  -1.548 0.137226    
## contribuyentesSunat:pobTotal -3.766e-11  3.644e-11  -1.033 0.313751    
## pobTotal:peaOcupada           3.817e-11  3.983e-11   0.958 0.349349    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.34 on 20 degrees of freedom
## Multiple R-squared:  0.3419, Adjusted R-squared:  0.2103 
## F-statistic: 2.598 on 4 and 20 DF,  p-value: 0.06734

h2 = formula(peaOcupada ~ contribuyentesSunat + buenEstado)

rp2=glm(h2, data = datita, 
        offset=log(pobTotal), 
        family = poisson(link = "log"))

summary(rp2)

## 
## Call:
## glm(formula = h2, family = poisson(link = "log"), data = datita, 
##     offset = log(pobTotal))
## 
## Coefficients:
##                       Estimate Std. Error z value Pr(>|z|)    
## (Intercept)         -1.159e+00  9.827e-04 -1179.0   <2e-16 ***
## contribuyentesSunat  2.092e-08  1.904e-10   109.9   <2e-16 ***
## buenEstado           8.075e-03  5.023e-05   160.7   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for poisson family taken to be 1)
## 
##     Null deviance: 192616  on 24  degrees of freedom
## Residual deviance:  55608  on 22  degrees of freedom
## AIC: 55975
## 
## Number of Fisher Scoring iterations: 3

library(magrittr)
library(kableExtra)
overdispersion=AER::dispersiontest(rp2,alternative='greater')$ p.value<0.05
underdispersion=AER::dispersiontest(rp2,alternative='less')$ p.value<0.05
# tabla
testResult=as.data.frame(rbind(overdispersion,underdispersion))
names(testResult)='Es probable?'
testResult%>%kable(caption = "Test de Equidispersión")%>%kableExtra::kable_styling()

Test de Equidispersión
	Es probable?
overdispersion	TRUE
underdispersion	FALSE

rq2 = glm(h2, data = datita,
          offset=log(pobTotal),
          family = quasipoisson(link = "log"))

library(MASS)
negativa=formula(peaOcupada ~ contribuyentesSunat + buenEstado + offset(log(pobTotal)))
rbn2=glm.nb(negativa,data=datita)

performance::check_overdispersion(rp2)

## # Overdispersion test
## 
##        dispersion ratio =  2526.621
##   Pearson's Chi-Squared = 55585.662
##                 p-value =   < 0.001

## Overdispersion detected.

performance::check_overdispersion(rq2)

## # Overdispersion test
## 
##        dispersion ratio =  2526.621
##   Pearson's Chi-Squared = 55585.662
##                 p-value =   < 0.001

## Overdispersion detected.

performance::check_overdispersion(rbn2)

## # Overdispersion test
## 
##  dispersion ratio = 0.140
##           p-value = 0.168

## No overdispersion detected.

library(modelsummary)

## `modelsummary` 2.0.0 now uses `tinytable` as its default table-drawing
##   backend. Learn more at: https://vincentarelbundock.github.io/tinytable/
## 
## Revert to `kableExtra` for one session:
## 
##   options(modelsummary_factory_default = 'kableExtra')
## 
## Change the default backend persistently:
## 
##   config_modelsummary(factory_default = 'gt')
## 
## Silence this message forever:
## 
##   config_modelsummary(startup_message = FALSE)

modelsQP_BN=list('Poisson asegurados (II)'=rp2,
                 'QuasiPoisson asegurados (II)'=rq2,
                 'Binomial Negativa asegurados (II)'=rbn2)


modelsummary(modelsQP_BN,
             exponentiate = T, 
             statistic = 'conf.int',
             title = "EXP() de la Regresiones Poisson, Quasi Poisson  y Binomial Negativa",
             stars = TRUE,
             output = "kableExtra")

EXP() de la Regresiones Poisson, Quasi Poisson y Binomial Negativa
	Poisson asegurados (II)	QuasiPoisson asegurados (II)	Binomial Negativa asegurados (II)
(Intercept)	0.314***	0.314***	0.312***
	[0.313, 0.315]	[0.285, 0.346]	[0.286, 0.341]
contribuyentesSunat	1.000***	1.000*	1.000
	[1.000, 1.000]	[1.000, 1.000]	[1.000, 1.000]
buenEstado	1.008***	1.008**	1.009***
	[1.008, 1.008]	[1.003, 1.013]	[1.004, 1.014]
Num.Obs.	25	25	25
AIC	55974.5		587.1
BIC	55978.2		592.0
Log.Lik.	-27984.274		-289.566
F	68713.131	27.195	9.985
RMSE	30706.19	30706.19	31601.43
+ p < 0.1, * p < 0.05, p < 0.01, * p < 0.001

Ejercicio 1

Interpretación: