Trabajo final - Estadística III
24-07-2022
Alumno: Diego Gabriel Gornati
Recreación del análisis del informe
En la ponencia “Análisis exploratorio multivaiado. Combinación de procedimientos para clasificar departamentos de cuatro provincias argentinas según el impacto del desarrollo en las condiciones de vida” los y las autoras construyen dimensiones relativas al impacto del desarrollo económico en las condiciones de vida (IDECV) y a partir de éstos dividen en sustratos de los departamentos de las provincias incluídas en el análisis, los cuales se busca que sean coherentes a su interior y lo más diferenciados posibles entre sí. A tal efecto, en la ponencia se efectúa un desarrollo analítico que se puede resulir en los siguientes puntos:
1- Análisis factorial de 25 indicadores. Resultan 6 dimensiones (factores) 2- Análisis de clusters. Se construyen 4 estratos (clusters/conglomerados) 3- Análisis de correlación entre los estratos obtenidos y los datos de NBI, análisis de varianza
En tal sentido, el presente trabajo buscará reproducir dicho trayecto analítico, partiendo de los mismos datos empleados en la ponencia y empleando las mismas herramientas analíticas, para lo cual se abordará este desarrollo en tres etapas que buscarán replicar cada uno de los puntos previamente detallados.
Primer etapa: Análisis factorial de 25 indicadores
# Cargo las librerias necesarias
library(haven)
library(psych)
library(tidyverse)## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.1 ──## ✔ ggplot2 3.3.6 ✔ purrr 0.3.4
## ✔ tibble 3.1.7 ✔ dplyr 1.0.9
## ✔ tidyr 1.2.0 ✔ stringr 1.4.0
## ✔ readr 2.1.2 ✔ forcats 0.5.1## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ ggplot2::%+%() masks psych::%+%()
## ✖ ggplot2::alpha() masks psych::alpha()
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()library(ca)
library(cluster)
library(factoextra)## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBalibrary(PerformanceAnalytics)## Loading required package: xts## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric##
## Attaching package: 'xts'## The following objects are masked from 'package:dplyr':
##
## first, last##
## Attaching package: 'PerformanceAnalytics'## The following object is masked from 'package:graphics':
##
## legend# Cargo la base con los datos del paper
basejor3 <- read_sav("basejor3.sav")
#View(basejor3)
# Le quito a la base los resultados obtenidos por el grupo de investigadorxs
base <- basejor3[,-(30:45),drop=FALSE]
base <- base[,-(1:2),drop=FALSE]
base <- base %>% remove_rownames %>% column_to_rownames(var="DEPTO")
base <- base[,-4,drop=FALSE]Análisis de la correlación de las variables
Para comenzar este recorrido analítico se realizará un breve análisis de correlación entre las variables seleccionadas.
chart.Correlation(base, histogram = F, pch = 19)
Análisis de factibilidad
A los efectos de determinar la factibilidad de realizar una factorización de las variables propuestas se empleará un test de Kaiser-Meyer-Olkin y un test de esfericidad de Bartlett:
KMO(base)## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = base)
## Overall MSA = 0.73
## MSA for each item =
## PURBANA MIGINTPR MIGLIMIT VSINAGUA VSINELEC HSINGAS CONDESAG MORTINF
## 0.78 0.63 0.74 0.83 0.79 0.84 0.81 0.56
## MORTNEON NACVIV20 SINCOBSA ESCMEDIO ANALFAB ASISHTPI PRPERHOG JEFMUJER
## 0.57 0.73 0.74 0.79 0.75 0.83 0.64 0.68
## VIVPREC IRRTENVI TASACTTO TASACTMU TASDESTO TASDESMU ASALPUBL CTAPROP
## 0.75 0.77 0.65 0.71 0.73 0.78 0.68 0.57
## PRECASAL
## 0.67cortest.bartlett(base)## R was not square, finding R from data## $chisq
## [1] 2049.968
##
## $p.value
## [1] 8.694932e-258
##
## $df
## [1] 300De allí obtenemos que el valor de KMO para este conjunto de variables es de 0.73, lo que indica que es apropiado realizar una factorización con estas variables (ya que el valor obtenido supera ampliamente 0,6). Por otro lado se obtiene mediante el test de Bartlett un p-value de 8.694932e-258, descartando la hipótesis de que las variables no están correlacionadas.
Análisis de componentes principales
A continuación se realiza un análisis de componentes principales para determinar cuál es la cantidad óptima de factores a tomar con este modelo.
Factores <- prcomp(base)
summary(Factores)## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6
## Standard deviation 46.3845 23.4894 19.7017 16.05986 12.9826 10.14293
## Proportion of Variance 0.5553 0.1424 0.1002 0.06656 0.0435 0.02655
## Cumulative Proportion 0.5553 0.6977 0.7978 0.86441 0.9079 0.93446
## PC7 PC8 PC9 PC10 PC11 PC12 PC13
## Standard deviation 7.83166 6.37494 5.74480 5.10384 4.69287 4.04959 3.64176
## Proportion of Variance 0.01583 0.01049 0.00852 0.00672 0.00568 0.00423 0.00342
## Cumulative Proportion 0.95029 0.96078 0.96930 0.97602 0.98171 0.98594 0.98936
## PC14 PC15 PC16 PC17 PC18 PC19 PC20
## Standard deviation 3.21335 2.75650 2.46133 2.31921 1.90586 1.7614 1.59269
## Proportion of Variance 0.00266 0.00196 0.00156 0.00139 0.00094 0.0008 0.00065
## Cumulative Proportion 0.99203 0.99399 0.99555 0.99694 0.99788 0.9987 0.99933
## PC21 PC22 PC23 PC24 PC25
## Standard deviation 1.09021 0.76870 0.70858 0.53292 0.16710
## Proportion of Variance 0.00031 0.00015 0.00013 0.00007 0.00001
## Cumulative Proportion 0.99964 0.99979 0.99992 0.99999 1.00000plot(Factores)
print(Factores$rotation,sort=T)## PC1 PC2 PC3 PC4 PC5
## PURBANA -0.6989933258 0.065198502 -0.563945224 0.364274629 -0.067387674
## MIGINTPR -0.0095109945 0.064331278 -0.051322097 -0.037564791 -0.083890118
## MIGLIMIT -0.0098795014 -0.021327804 0.003867086 -0.031344725 -0.017494660
## VSINAGUA 0.2701279703 -0.394536125 -0.251520366 -0.092511153 -0.219117282
## VSINELEC 0.3120323253 0.142222547 -0.425427205 0.053350435 -0.217658062
## HSINGAS 0.4141296669 0.282873051 -0.299325233 0.175771685 -0.079600675
## CONDESAG -0.2293657605 0.073998167 -0.046119040 -0.609668426 -0.671672938
## MORTINF -0.0219854656 0.153954382 -0.254086513 -0.407145644 0.445570932
## MORTNEON -0.0363653743 0.111461372 -0.156719879 -0.331489992 0.338976742
## NACVIV20 0.0244459711 0.018933192 0.007112322 0.140919037 0.036163432
## SINCOBSA 0.0656542451 -0.230891078 -0.323364965 -0.022723998 0.149597310
## ESCMEDIO -0.2249451768 0.162786870 0.146163634 0.003418360 0.055588555
## ANALFAB 0.0346121307 -0.051566744 -0.028539030 0.011074198 0.035358048
## ASISHTPI 0.1087817635 -0.197812179 -0.127453904 0.047899072 0.060322727
## PRPERHOG 0.0009011224 -0.002651774 0.003665993 0.008897510 0.002809708
## JEFMUJER 0.0196784628 0.196577213 -0.111551217 -0.008195263 -0.001070991
## VIVPREC 0.1501731895 -0.071751612 -0.202095011 0.066526653 -0.119033699
## IRRTENVI 0.0180294013 -0.189299890 0.053628820 0.104177162 -0.010512447
## TASACTTO 0.0387155733 0.057133037 -0.046553398 -0.149579479 0.126693368
## TASACTMU 0.0433580202 0.257971677 -0.130536286 -0.208573165 0.173342429
## TASDESTO -0.0311903822 -0.031529014 -0.010162251 0.023556715 0.009192653
## TASDESMU -0.0437269617 -0.081257640 0.002273952 0.049016894 0.005091989
## ASALPUBL 0.1104329803 0.480037846 0.120893073 0.245340729 -0.099540344
## CTAPROP 0.0043009401 0.015734682 -0.138442947 -0.087835282 0.050372270
## PRECASAL -0.0684580797 -0.428913780 -0.043722321 -0.017078273 0.131143665
## PC6 PC7 PC8 PC9 PC10
## PURBANA 0.067699079 -0.019808495 0.071507909 -0.0907530287 -0.044200861
## MIGINTPR -0.175638303 -0.242855285 -0.281700344 -0.3901387546 -0.330121900
## MIGLIMIT -0.027709183 -0.002480982 0.036382098 -0.0255248250 -0.033564781
## VSINAGUA 0.372969668 -0.372520293 0.141746347 0.1879021678 -0.196739880
## VSINELEC 0.158768164 -0.276538447 -0.045176916 0.0183544378 -0.030499221
## HSINGAS -0.279026605 0.252209800 -0.370905803 0.0341199257 -0.054954946
## CONDESAG -0.134338230 0.135287573 -0.072473485 -0.0208434605 0.190543765
## MORTINF 0.307531654 0.022539805 -0.276687135 -0.1857398229 0.073401804
## MORTNEON 0.252573061 0.044544565 -0.085386968 0.0837872282 0.126667446
## NACVIV20 -0.060001480 0.109030166 -0.090718427 -0.1085049142 0.239740895
## SINCOBSA -0.396783640 -0.050406151 0.051151885 0.3035502120 0.261315272
## ESCMEDIO -0.014735074 -0.179553603 -0.150086859 0.6396550898 -0.073963958
## ANALFAB -0.047677539 -0.004433362 0.095841645 -0.0357461048 0.159233849
## ASISHTPI -0.176581746 -0.147328116 0.166526700 -0.2285757344 0.583133776
## PRPERHOG 0.003389791 0.006383955 -0.003610032 -0.0072288331 0.003006073
## JEFMUJER -0.107144588 0.110174763 -0.001432467 0.1261884938 -0.056724928
## VIVPREC 0.237586992 0.632933963 0.181940775 0.0526262952 -0.095604582
## IRRTENVI 0.144427897 0.330805487 -0.001470735 0.0469829170 -0.112584415
## TASACTTO -0.182779495 0.022256165 0.402148019 -0.1164853953 -0.180493466
## TASACTMU -0.259541306 -0.013683035 0.527506184 -0.0097803203 -0.314456458
## TASDESTO 0.085139278 0.049100228 -0.003956820 0.0367235395 0.062974560
## TASDESMU 0.158226374 0.100375198 -0.020154519 0.0694886477 0.130923941
## ASALPUBL 0.137105647 -0.189178222 0.050082859 0.0009658379 0.162829277
## CTAPROP -0.196627125 0.034978933 -0.077474920 0.3839018179 0.015628564
## PRECASAL -0.266820680 0.013514399 -0.336269955 -0.0732559635 -0.294182000
## PC11 PC12 PC13 PC14 PC15
## PURBANA 0.0569490581 -0.1127503797 0.052682795 -0.008909583 0.0472854340
## MIGINTPR -0.0245690302 0.3905290680 -0.037944647 -0.085660803 0.4882871855
## MIGLIMIT 0.0490679818 0.0431907278 -0.049846654 0.039117920 0.0446308589
## VSINAGUA 0.3056527298 -0.2275803058 0.168758710 0.212477074 0.2295640940
## VSINELEC -0.3477006713 0.1821688624 -0.173826690 -0.262190235 -0.4741333016
## HSINGAS 0.1435564530 -0.3001260060 0.324062395 -0.120271435 0.1030199208
## CONDESAG 0.1579701844 -0.0469216409 -0.035046245 -0.050927622 -0.0679203432
## MORTINF 0.1263090630 -0.0482969290 -0.108120048 0.116302852 0.0419330182
## MORTNEON 0.0557012879 0.0757559560 0.123407129 -0.203785577 0.0009745577
## NACVIV20 0.1614302323 -0.1261605915 0.051239677 0.410785609 -0.1438064802
## SINCOBSA 0.1643952952 0.2131976160 -0.416628740 0.103154240 0.0681030135
## ESCMEDIO 0.1825901450 0.3052614949 0.378323824 -0.195724679 -0.0273817303
## ANALFAB 0.0684888771 -0.0018876818 0.017256087 -0.162419468 0.0250828597
## ASISHTPI 0.0642129401 0.1382222302 0.376444123 -0.261056841 0.1191547438
## PRPERHOG 0.0080098779 -0.0047861685 -0.001351834 -0.009700674 -0.0119738384
## JEFMUJER 0.0009213703 -0.0891907882 0.101222787 0.218359838 -0.0614214828
## VIVPREC 0.0523800739 0.5779452739 0.078942312 0.171886752 0.0686798772
## IRRTENVI 0.2284700016 -0.2442714999 -0.284741140 -0.596928062 0.1656715491
## TASACTTO 0.1161285245 -0.0005614221 0.008808335 -0.153528547 0.0082962355
## TASACTMU 0.0834509254 -0.1200855641 0.063135258 -0.031422094 -0.1280328150
## TASDESTO -0.0738269821 -0.0375766168 -0.032669715 -0.118893289 0.0364118023
## TASDESMU -0.1207691402 -0.1218309706 -0.055741102 -0.116059740 -0.1060543659
## ASALPUBL 0.5464634748 0.1089941015 -0.394518619 0.008464938 0.0153494763
## CTAPROP -0.3494810149 -0.1539091016 -0.275336357 0.077324951 0.3677344895
## PRECASAL 0.3214276806 0.0775114468 -0.053372617 -0.031083738 -0.4705170021
## PC16 PC17 PC18 PC19 PC20
## PURBANA -0.0429630055 0.0428404736 -0.075254181 0.018581096 -0.017728296
## MIGINTPR -0.0146411573 -0.2483293094 0.269606221 -0.098836031 -0.072790436
## MIGLIMIT -0.0371374064 0.0200223959 -0.122306812 -0.029780336 0.055471929
## VSINAGUA -0.0009203602 -0.0431100124 0.021861594 -0.051836387 -0.033978792
## VSINELEC 0.0433235145 -0.2078347022 -0.025897426 0.100099543 0.084223340
## HSINGAS -0.2220791467 0.1933226898 -0.045542471 -0.071836154 0.052385642
## CONDESAG -0.0166958182 -0.0201394041 -0.007591844 -0.022143607 0.014958263
## MORTINF 0.2200376861 0.0684930171 -0.042295590 -0.060520117 0.463519581
## MORTNEON -0.3046421491 -0.0930785021 0.009789738 0.136079648 -0.653389123
## NACVIV20 -0.1901465871 -0.7670949029 0.066776790 0.072939668 0.058514484
## SINCOBSA -0.2216570518 0.1795185096 0.342949691 0.139025915 0.073994487
## ESCMEDIO 0.0242411718 -0.1829346671 0.027919154 -0.030695511 0.275643355
## ANALFAB -0.0389225539 -0.1085535182 -0.048918136 0.074910033 0.239943123
## ASISHTPI 0.3602620097 -0.0398111324 -0.126911852 -0.109592149 -0.070938679
## PRPERHOG -0.0483486146 -0.0004479885 -0.010682260 -0.008358756 0.021159423
## JEFMUJER 0.6405231250 -0.0137172896 0.435592512 0.122011965 -0.192837759
## VIVPREC 0.0541828431 -0.0127787455 -0.118218108 -0.092933387 0.008127284
## IRRTENVI 0.1891760354 -0.2600611037 0.136266716 0.263283440 0.050397130
## TASACTTO -0.1900736849 -0.1358329392 -0.150770457 -0.167653746 0.202950856
## TASACTMU 0.0589879621 -0.1068320530 0.102306576 -0.099145967 -0.065475200
## TASDESTO -0.0296193451 0.0023401978 0.138156307 -0.250754655 0.133948854
## TASDESMU -0.0898764878 -0.0551314034 0.410411139 -0.760282788 -0.053981169
## ASALPUBL 0.1083300643 0.0581370279 -0.171360394 -0.204191471 -0.178184037
## CTAPROP 0.2090719047 -0.2608052876 -0.479298654 -0.218717858 -0.140690774
## PRECASAL 0.1770386794 -0.0110323111 -0.240746769 -0.209666265 -0.180906193
## PC21 PC22 PC23 PC24 PC25
## PURBANA 0.005867431 -1.134156e-02 0.01052665 -0.016360926 0.0039225525
## MIGINTPR 0.023734462 5.735597e-02 0.01397200 -0.016996552 -0.0050102223
## MIGLIMIT 0.016635215 -1.088048e-01 -0.94589928 -0.236390571 -0.0237520362
## VSINAGUA 0.035417127 4.894796e-03 0.01876785 0.012653685 -0.0066176364
## VSINELEC -0.024375712 -5.844209e-02 -0.03832411 -0.004185618 -0.0038393029
## HSINGAS -0.015633839 2.647788e-05 -0.02007926 -0.008110555 0.0163439958
## CONDESAG -0.018137238 1.377398e-02 0.02679561 0.017872484 -0.0013495251
## MORTINF -0.117406180 1.092222e-02 0.03453052 -0.040442921 0.0049437038
## MORTNEON 0.150241903 -3.514028e-02 -0.05856874 0.029629536 -0.0071627275
## NACVIV20 -0.083038226 -1.123695e-02 -0.03703353 0.067789489 0.0071991089
## SINCOBSA -0.073019752 -3.374638e-02 0.01282489 0.012054035 0.0008806107
## ESCMEDIO -0.083475362 -2.302513e-02 -0.01061314 -0.027308717 0.0012621973
## ANALFAB 0.739885113 4.615685e-01 0.04354053 -0.282455904 0.0530475163
## ASISHTPI -0.197143539 -3.558348e-02 -0.02427383 0.032973846 -0.0181902295
## PRPERHOG -0.006085499 6.464059e-02 0.03576878 -0.058940979 -0.9937305184
## JEFMUJER 0.337696280 -2.477064e-01 -0.06481174 -0.010786893 -0.0636753452
## VIVPREC -0.017055811 7.483505e-02 0.04288729 -0.003027711 0.0047012672
## IRRTENVI -0.176835792 -3.469862e-02 -0.03010542 -0.029674620 -0.0013913671
## TASACTTO 0.256126715 -6.637706e-01 0.14277676 0.042476601 -0.0260492805
## TASACTMU -0.285435938 4.772898e-01 -0.06049177 0.023762085 0.0214632885
## TASDESTO 0.223993852 1.322432e-01 -0.23778468 0.855453320 -0.0460004226
## TASDESMU -0.031126476 -2.602407e-02 0.02466595 -0.332808568 0.0282442501
## ASALPUBL 0.043883152 1.523261e-02 0.03529296 0.035527265 -0.0007608199
## CTAPROP 0.030731738 3.632677e-02 0.04858538 -0.009356010 -0.0125694114
## PRECASAL 0.090174160 5.654873e-02 0.01561857 0.058058327 0.0015789943Del análisis previo se puede aproximar la idea de que entre 5 y 7 factores pueden ser empleados eficientemente para estructurar este modelo. De allí que se presente como razonable la opción elegida por los autores de la ponencia de elegir 6 factores para continuar con el análisis.
Factorización
Se procede a factorizar con seis factores siguiendo el camino adoptado por los autores, y se extraen las cargas factoriales para este modelo:
## Factores
cor.base <- cor(base,use="complete.obs")
ff <- fa(base,nfactors=6,n.obs=20, use="complete.obs",rotate="none",fm="pa")## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.# Se imprimen las cargas factoriales ordenadas superiores a 0.50
print(ff, cut=.50, sort=TRUE)## Factor Analysis using method = pa
## Call: fa(r = base, nfactors = 6, n.obs = 20, rotate = "none", fm = "pa",
## use = "complete.obs")
## Standardized loadings (pattern matrix) based upon correlation matrix
## item PA1 PA2 PA3 PA4 PA5 PA6 h2 u2 com
## HSINGAS 6 0.94 0.96 0.039 1.2
## VSINELEC 5 0.89 0.95 0.054 1.4
## ESCMEDIO 12 -0.82 0.87 0.133 1.6
## PURBANA 1 -0.76 0.78 0.218 1.7
## TASDESTO 21 -0.70 0.86 0.140 2.4
## VIVPREC 17 0.66 0.64 0.356 2.0
## VSINAGUA 4 0.64 0.53 0.90 0.096 3.0
## ANALFAB 13 0.63 0.52 0.79 0.210 2.7
## TASDESMU 22 -0.62 0.53 0.89 0.111 2.9
## ASISHTPI 14 0.61 0.55 0.79 0.214 2.6
## CONDESAG 7 -0.57 0.66 0.340 3.2
## TASACTTO 19 0.81 0.195 4.7
## IRRTENVI 18 0.79 0.68 0.323 1.2
## JEFMUJER 16 -0.77 0.88 0.121 2.0
## TASACTMU 20 -0.77 0.90 0.104 2.1
## PRECASAL 25 0.67 0.83 0.170 2.6
## PRPERHOG 15 0.53 0.473 3.1
## MIGINTPR 2 0.35 0.654 2.8
## SINCOBSA 11 0.66 0.97 0.034 3.5
## ASALPUBL 23 -0.55 -0.65 0.89 0.112 2.7
## CTAPROP 24 0.55 0.55 0.450 2.7
## MORTNEON 9 -0.50 0.54 0.51 0.91 0.090 3.7
## MORTINF 8 0.51 0.75 0.247 3.3
## NACVIV20 10 0.54 0.457 3.9
## MIGLIMIT 3 0.59 0.410 3.3
##
## PA1 PA2 PA3 PA4 PA5 PA6
## SS loadings 7.01 5.50 3.15 1.60 1.03 0.95
## Proportion Var 0.28 0.22 0.13 0.06 0.04 0.04
## Cumulative Var 0.28 0.50 0.63 0.69 0.73 0.77
## Proportion Explained 0.36 0.29 0.16 0.08 0.05 0.05
## Cumulative Proportion 0.36 0.65 0.81 0.90 0.95 1.00
##
## Mean item complexity = 2.6
## Test of the hypothesis that 6 factors are sufficient.
##
## The degrees of freedom for the null model are 300 and the objective function was 33.7 with Chi Square of 2049.97
## The degrees of freedom for the model are 165 and the objective function was 8.58
##
## The root mean square of the residuals (RMSR) is 0.03
## The df corrected root mean square of the residuals is 0.04
##
## The harmonic number of observations is 71 with the empirical chi square 46.06 with prob < 1
## The total number of observations was 71 with Likelihood Chi Square = 487.83 with prob < 1.2e-33
##
## Tucker Lewis Index of factoring reliability = 0.637
## RMSEA index = 0.165 and the 90 % confidence intervals are 0.15 0.184
## BIC = -215.51
## Fit based upon off diagonal values = 0.99Los resultados obtenidos indican que hay factores para los cuales no hay presencia de cargas factoriales por encima del 0,5 elegido como corte. En tal sentido, se intenta factorizar nuevamente pero realizando una rotación de tipo “varimax”:
ff <- fa(base,nfactors=6,n.obs=20, use="complete.obs",rotate="varimax",fm="pa")## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.print(ff, cut=.50, sort=TRUE)## Factor Analysis using method = pa
## Call: fa(r = base, nfactors = 6, n.obs = 20, rotate = "varimax", fm = "pa",
## use = "complete.obs")
## Standardized loadings (pattern matrix) based upon correlation matrix
## item PA1 PA2 PA3 PA4 PA6 PA5 h2 u2 com
## VSINAGUA 4 0.93 0.90 0.096 1.1
## ESCMEDIO 12 -0.90 0.87 0.133 1.1
## VSINELEC 5 0.79 0.95 0.054 2.0
## VIVPREC 17 0.76 0.64 0.356 1.2
## ASISHTPI 14 0.71 0.79 0.214 2.2
## PURBANA 1 -0.71 0.78 0.218 2.2
## HSINGAS 6 0.68 -0.53 0.96 0.039 2.9
## ANALFAB 13 0.67 0.79 0.210 2.4
## TASDESMU 22 -0.88 0.89 0.111 1.3
## TASDESTO 21 -0.83 0.86 0.140 1.5
## TASACTTO 19 0.69 0.52 0.81 0.195 2.2
## TASACTMU 20 0.69 0.55 0.90 0.104 2.5
## IRRTENVI 18 -0.51 0.68 0.323 4.2
## MIGINTPR 2 0.35 0.654 3.0
## PRECASAL 25 0.81 0.83 0.170 1.6
## ASALPUBL 23 -0.80 0.89 0.112 1.8
## JEFMUJER 16 -0.71 0.88 0.121 2.5
## MIGLIMIT 3 0.66 0.59 0.410 1.7
## MORTNEON 9 0.92 0.91 0.090 1.1
## MORTINF 8 0.83 0.75 0.247 1.2
## CONDESAG 7 -0.64 0.66 0.340 2.1
## NACVIV20 10 0.60 0.54 0.457 2.0
## PRPERHOG 15 0.57 0.53 0.473 2.3
## SINCOBSA 11 0.52 0.70 0.97 0.034 2.7
## CTAPROP 24 0.63 0.55 0.450 1.8
##
## PA1 PA2 PA3 PA4 PA6 PA5
## SS loadings 5.71 3.70 3.65 2.55 1.99 1.64
## Proportion Var 0.23 0.15 0.15 0.10 0.08 0.07
## Cumulative Var 0.23 0.38 0.52 0.62 0.70 0.77
## Proportion Explained 0.30 0.19 0.19 0.13 0.10 0.09
## Cumulative Proportion 0.30 0.49 0.68 0.81 0.91 1.00
##
## Mean item complexity = 2
## Test of the hypothesis that 6 factors are sufficient.
##
## The degrees of freedom for the null model are 300 and the objective function was 33.7 with Chi Square of 2049.97
## The degrees of freedom for the model are 165 and the objective function was 8.58
##
## The root mean square of the residuals (RMSR) is 0.03
## The df corrected root mean square of the residuals is 0.04
##
## The harmonic number of observations is 71 with the empirical chi square 46.06 with prob < 1
## The total number of observations was 71 with Likelihood Chi Square = 487.83 with prob < 1.2e-33
##
## Tucker Lewis Index of factoring reliability = 0.637
## RMSEA index = 0.165 and the 90 % confidence intervals are 0.15 0.184
## BIC = -215.51
## Fit based upon off diagonal values = 0.99Con este nuevo resultado se obtiene que cada factor aporta cargas factoriales superiores a 0,5 (en valor absoluto) a más de una variable. Es en este paso que los autores deciden que de todas manera uno de los factores no aporta en gran medida al análisis. En tal sentido, se procede a quita un factor, quedándonos con 5 de ellos:
# Guardo los scores en un nuevo dataframe
base_scores <- as.data.frame(ff$scores)
base_scores2 <- base_scores[,-6,drop=FALSE]Segunda etapa: Análisis de clusters
En esta etapa los autores deciden realizar cuatro clusters, para lo cual se realiza una aglomeración jerárquica basada en las distancias euclídeas y empleando el método de Ward:
# Agglomerative Nesting (Hierarchical Clustering)
base.agnes <- agnes(x = base_scores2,stand = TRUE,
metric = "euclidean",
method = "ward")
# Se obtienen los números de cluster para luego incorporarlos al dataframe
clust <- cutree(base.agnes, k = 4)
# Se grafica primero el dendrograma y luego el plot de las distancias de los clusters
fviz_dend(base.agnes, cex = 0.6, k = 4)## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.
fviz_cluster(list(data = base_scores2, cluster = clust)) 
Tercera etapa: Análisis de correlación entre los estratos obtenidos y los datos de NBI
Por último, se realiza un análisis de correlación entre los estratos obtenidos y los datos de NBI, efectuando un análisis de varianza entre ellos.
## Le vuelvo a agregar al dataframe las variables de NBI y nombre de provincia
base_cluster <- cbind(base, clust)
base_cluster2 <- base_cluster %>% rownames_to_column(var="DEPTO")
provincias <- basejor3[, c("DEPTO", "PCIA", "HOGNBI")]
base_cluster3 <- merge(base_cluster2, provincias, by = "DEPTO")Se realiza un análisis ANOVA entre las variables HOGNBI y PCIA
anova1 <- aov(base_cluster3$HOGNBI ~ base_cluster3$PCIA)
summary(anova1)## Df Sum Sq Mean Sq F value Pr(>F)
## base_cluster3$PCIA 3 3236 1078.7 8.734 5.72e-05 ***
## Residuals 67 8275 123.5
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# calculo de eta cuadrado
determinacion1 <- 3236/(3236+8275)
determinacion1## [1] 0.2811224Se obtiene un valor de eta cuadrado de 0.2811224, que resulta coincidente con aquél obtenido por los autores.
Luego se realiza un análisis ANOVA entre las variables HOGNBI y el Estrato al que pertenece ese Departamento:
anova2 <- aov(base_cluster3$HOGNBI ~ base_cluster3$clust)
summary(anova2)## Df Sum Sq Mean Sq F value Pr(>F)
## base_cluster3$clust 1 3021 3021 24.55 4.94e-06 ***
## Residuals 69 8490 123
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1determinacion2 <- 3021/(3021+8490)
determinacion2## [1] 0.2624446El valor de eta cuadrado obtenido para este caso es de 0.2624446, lo cual demuestra una homogeneidad interna similar a aquella obtenida a partir del ordenamiento por provincias, aunque sensiblemente menor para el caso de la estructuración en base a la variable compleja de impacto del desarrollo económico en las condiciones de vida (IDECV) propuesta por los autores en la ponencia.