Multidimensional analysis of poverty and income poverty in Poland - Principal Component Analysis
Marian Nehrebecki
1/23/2021
1 Introduction
The occurrence of poverty has significant social and economic effects, and the way it is defined and measured poverty affects strategies to combat it. Therefore, this issue is widely discussed both in the literature and in the political arena. It is now believed that it is not merely an inability to meet basic needs essential for physical survival, but rather an involuntary lack of material, social and cultural resources deemed necessary by society as a whole. Thus, simple one-dimensional measures, based only on income, may not be sufficient to correctly identify poor people (Coromaldi, Zoli, 2007; Siani, 2015 ).
Therefore, the aim of this article is to verify the research hypothesis that, in the case of Poland, the multidimensional analysis of poverty cannot be replaced with a measure based solely on income, without significant differences in the identification of the poor. The study is based on an analogous analysis of poverty Italy, presented in the article Coromaldi and Zola (2007).
The first part briefly presents the concept of poverty measurement in economic literature, along with the results of analyzes of empirical articles relevant to the research hypothesis. The research methodology is then described after the data set used has been presented. Then, the results of the analysis and conclusions from the study are presented.
2 Literature review
Currently, it is believed that poverty should be treated as a multidimensional phenomenon, more related to a person’s standard of living, not only to the amount of income. And while traditional methods have the advantage of being easy to compute, the univariate approach has been challenged in recent decades. Mainly due to the fact that they do not include other non-monetary variables relevant to determining the needs of households. In addition, income-based methods often mean that such elements as savings, informal income, family benefits or the consumption of public services are not taken into account or are not very reliable, which may distort the results obtained. It is also worth noting that income is not a measure of real living conditions, but only a resource that enables the achievement of prosperity. In other words, actual poverty can only be determined by means of multivariate analysis, but is related to financial poverty, and therefore income-based measures are still widely used as poverty measures. In this context, the economic literature asks how far such financial measures can replace multidimensional measures (Coromaldi, Zoli, 2007; Dekkers 2003).
3 Methodology
For the analysis of poverty in this study, principal components analysis were used, after prior transformation of categorical variables using the optimal scaling method. The methodology used is analogous to that adopted in the article by Coromaldi and Zola (2007). It is based on the premise that if poverty is defined as a state in which several deficiencies in different areas accumulate, these deficiencies can be seen as a hidden dimension of poverty. One of the statistical techniques used to identify the hidden, invisible structures of a data set is the aforementioned principal components analysis. Each hidden variable is weighted by a function of the original variables. The more the observed variables are correlated with each other, the more likely they are to represent the same dimension of scarcity.
4 Data
The data set used was based on the data from the Social Diagnosis study. The data included in the study refer to 2015.
library(readxl)
library(stats)
#Set working directory
setwd("/Users/nehrebeckiwp.pl/Desktop/UL2")
data <- read_excel("Sondaz_Spol_1.xlsx")## [1] 1161 20The variables used to determine the poverty dimensions concern:
possession of durable goods like computer, internet, mobile phone, CD player, video player, car, satellite dish, color TV, freezer, washer / dryer, dishwasher, microwave oven, washing machine.
satisfaction with the financial situation consists of satisfied, more or less satisfied, hard to say, dissatisfied.
satisfaction with the housing situation covers very satisfied, satisfied, rather satisfied, hard to say, rather dissatisfied, dissatisfied, very dissatisfied.
flat area per person, variable determining whether it happened that there was not enough money for food and clothing, housing, treatment, doctor and education.
The variable used to measure income poverty is monthly per capita household income.
Other variables used in the analysis are the following sociodemographic variables, situation on the labor market, size of the place of residence.
## tibble [1,161 × 20] (S3: tbl_df/tbl/data.frame)
## $ fla_area : num [1:1161] 23.3 20 35 30 50 ...
## $ car : num [1:1161] 0.00985 0.00985 0.00985 0.00985 0.99596 ...
## $ v_colour : num [1:1161] 1 1 1 1 1 1 1 1 1 1 ...
## $ video_player : num [1:1161] 0 0 0 0 0 1 1 0 1 0 ...
## $ saelie : num [1:1161] -3.77e-15 -3.77e-15 -3.77e-15 1.00 -3.77e-15 ...
## $ cd_player : num [1:1161] -6.66e-15 -6.66e-15 -6.66e-15 -6.66e-15 -6.66e-15 ...
## $ compuer : num [1:1161] 4.55e-15 4.55e-15 4.55e-15 4.55e-15 4.55e-15 ...
## $ inerne : num [1:1161] 2.22e-15 2.22e-15 2.22e-15 2.22e-15 2.22e-15 ...
## $ washing : num [1:1161] 1.00 1.00 1.00 2.22e-15 2.22e-15 ...
## $ machine : num [1:1161] -1.62e-15 -1.62e-15 -1.62e-15 -1.62e-15 -1.62e-15 ...
## $ dishwasher : num [1:1161] 2.78e-17 2.78e-17 2.78e-17 2.78e-17 2.78e-17 ...
## $ microwave : num [1:1161] 3.11e-15 3.11e-15 3.11e-15 3.11e-15 3.11e-15 ...
## $ freezer : num [1:1161] 1.17e-15 1.17e-15 1.17e-15 1.00 1.00 ...
## $ el : num [1:1161] -9.55e-15 -9.55e-15 -9.55e-15 -9.55e-15 1.00 ...
## $ no_food_clohes : num [1:1161] 1 1 1 1 1 ...
## $ no_reamen : num [1:1161] 1 1 1 1 1 ...
## $ no_educaion : num [1:1161] 1 1 1 1 1 ...
## $ no_aparmen : num [1:1161] 1 1 1 1 1 ...
## $ siuaion_fin : num [1:1161] 0.0487 0.0487 0.0487 0.0487 0.0487 ...
## $ aparmen_siuaion: num [1:1161] 4.77 2.39 1.83 4.77 4.77 ...The elements of PCA with individual functions is normalization of data.
## Loading required package: lattice## Loading required package: ggplot2preproc <- preProcess(data, method=c("center", "scale"))
data.s <- predict(preproc, data)
summary(data.s)## fla_area car v_colour video_player
## Min. :-1.2824 Min. :-4.5385 Min. :-6.3584 Min. :-1.4081
## 1st Qu.:-0.6537 1st Qu.:-1.1958 1st Qu.: 0.1571 1st Qu.:-1.4081
## Median :-0.2709 Median : 0.8135 Median : 0.1571 Median : 0.7095
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.3350 3rd Qu.: 0.8135 3rd Qu.: 0.1571 3rd Qu.: 0.7095
## Max. :10.0626 Max. : 3.0691 Max. : 0.1571 Max. : 0.7095
## saelie cd_player compuer inerne
## Min. :-0.6688 Min. :-1.1885 Min. :-1.1021 Min. :-0.9321
## 1st Qu.:-0.6688 1st Qu.:-1.1885 1st Qu.:-1.1021 1st Qu.:-0.9321
## Median :-0.6688 Median : 0.8407 Median : 0.9066 Median :-0.9321
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 1.4940 3rd Qu.: 0.8407 3rd Qu.: 0.9066 3rd Qu.: 1.0719
## Max. : 1.4940 Max. : 0.8407 Max. : 0.9066 Max. : 1.0719
## washing machine dishwasher microwave
## Min. :-2.6994 Min. :-0.3152 Min. :-0.3425 Min. :-0.9321
## 1st Qu.: 0.3701 1st Qu.:-0.3152 1st Qu.:-0.3425 1st Qu.:-0.9321
## Median : 0.3701 Median :-0.3152 Median :-0.3425 Median :-0.9321
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.3701 3rd Qu.:-0.3152 3rd Qu.:-0.3425 3rd Qu.: 1.0719
## Max. : 0.3701 Max. : 3.1699 Max. : 2.9170 Max. : 1.0719
## freezer el no_food_clohes no_reamen
## Min. :-0.6809 Min. :-1.861 Min. :-1.4791 Min. :-1.5862
## 1st Qu.:-0.6809 1st Qu.: 0.537 1st Qu.:-1.4791 1st Qu.:-1.5862
## Median :-0.6809 Median : 0.537 Median : 0.6755 Median : 0.6299
## Mean : 0.0000 Mean : 0.000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 1.4673 3rd Qu.: 0.537 3rd Qu.: 0.6755 3rd Qu.: 0.6299
## Max. : 1.4673 Max. : 0.537 Max. : 0.6755 Max. : 0.6299
## no_educaion no_aparmen siuaion_fin aparmen_siuaion
## Min. :-2.6994 Min. :-1.8516 Min. :-1.4140 Min. :-2.1066
## 1st Qu.: 0.3701 1st Qu.: 0.5396 1st Qu.:-1.0119 1st Qu.:-0.6883
## Median : 0.3701 Median : 0.5396 Median : 0.5287 Median : 0.2975
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.3701 3rd Qu.: 0.5396 3rd Qu.: 0.5287 3rd Qu.: 0.2975
## Max. : 0.3701 Max. : 0.5396 Max. : 1.5891 Max. : 3.07065 Results
After quantifying the categorical variables through optimal scaling, Principal Component Analysis was performed. The preliminary analysis of the adequacy of the selection of variables indicates that there is a basis for applying PCA.
## [1] "fla_area" "car" "v_colour" "video_player"
## [5] "saelie" "cd_player" "compuer" "inerne"
## [9] "washing" "machine" "dishwasher" "microwave"
## [13] "freezer" "el" "no_food_clohes" "no_reamen"
## [17] "no_educaion" "no_aparmen" "siuaion_fin" "aparmen_siuaion"In this paper two approaches are considered: prcomp() and princomp() for PCA. The procedure prcomp() use the singular value decomposition (SVD).
# prcomp() - PCA basic command from stats:
# centering data around 0 (center=TRUE) by shifting the variables
# rescaling variance to one (unit) (scale.=TRUE)
PCA_sondaz <- prcomp(data.s, center=TRUE, scale=TRUE)
PCA_sondaz## Standard deviations (1, .., p=20):
## [1] 2.2226057 1.5201938 1.1885940 1.0638010 1.0031870 0.9667459 0.9360685
## [8] 0.9026622 0.8813330 0.8547610 0.8480405 0.8243927 0.7926269 0.7648995
## [15] 0.7529300 0.7053451 0.6740203 0.6557288 0.5579307 0.4394618
##
## Rotation (n x k) = (20 x 20):
## PC1 PC2 PC3 PC4 PC5
## fla_area 0.0210327 -0.28029291 0.46443292 -8.951332e-03 0.307329627
## car -0.2812000 0.06478813 0.10813153 -1.378984e-01 -0.067035193
## v_colour -0.1078562 0.08201130 -0.08133650 -5.047907e-01 -0.094713221
## video_player -0.2769384 0.22668227 0.02620493 -1.380239e-01 -0.154436355
## saelie -0.1705138 0.02579958 0.33030848 -1.474442e-01 -0.138505225
## cd_player -0.3069504 0.17282597 -0.05168192 3.936375e-02 -0.109570045
## compuer -0.3168397 0.23745612 -0.12533109 2.208387e-01 0.239097517
## inerne -0.3091436 0.18980458 -0.14672626 3.106617e-01 0.241958643
## washing -0.2081214 0.06538875 0.02101971 -4.100576e-01 0.377833309
## machine -0.1081032 0.01034346 0.27335715 3.551096e-01 -0.557769063
## dishwasher -0.1670237 -0.01730783 0.27067018 3.452405e-01 0.099932535
## microwave -0.2333310 0.10770587 0.19441407 1.587887e-02 0.062734109
## freezer -0.1312643 -0.02389469 0.37780561 -2.879348e-01 -0.289577619
## el -0.2759079 0.27083936 -0.06154688 -5.918334e-02 -0.033266110
## no_food_clohes -0.2660416 -0.37274999 -0.19824810 -1.972604e-02 -0.048420793
## no_reamen -0.2755538 -0.29687753 -0.24508435 -3.375987e-02 0.009219708
## no_educaion -0.1288467 -0.39825078 -0.20285197 8.644942e-05 -0.122628804
## no_aparmen -0.2178961 -0.38221438 -0.15745850 -5.184980e-02 -0.173176561
## siuaion_fin -0.2323404 -0.18333434 0.01611853 1.846580e-01 0.001860157
## aparmen_siuaion -0.1320561 -0.28388824 0.34347538 7.195153e-03 0.348027976
## PC6 PC7 PC8 PC9 PC10
## fla_area -0.02177672 -0.005103380 8.573949e-02 -0.16169895 0.001919977
## car 0.32644850 -0.076563484 -2.781732e-02 -0.08297071 0.268774165
## v_colour -0.70028240 0.004574490 -2.430990e-01 -0.16984226 0.292852351
## video_player 0.01544580 0.021192488 2.052911e-01 0.09425397 -0.300307242
## saelie 0.14371241 -0.676391264 7.304167e-02 -0.41789558 0.015789212
## cd_player 0.04454145 0.074177776 8.367777e-02 -0.01200382 -0.377567826
## compuer 0.04184996 0.018392045 -1.022833e-01 -0.15342601 0.236316732
## inerne -0.05277122 0.003416087 -1.664257e-01 -0.04257539 0.259167100
## washing -0.14931749 0.036948566 2.072252e-01 0.13082873 -0.387735159
## machine -0.37066780 0.200238826 3.231946e-01 -0.11985924 -0.006523110
## dishwasher -0.31480280 -0.368087785 -4.596148e-01 0.38503049 -0.292962432
## microwave -0.02724318 -0.018127711 3.860436e-01 0.50264972 0.428197706
## freezer 0.30375598 0.340184293 -5.045772e-01 0.25206668 0.047822744
## el 0.10011224 0.108772742 3.922493e-02 -0.06219302 -0.046775912
## no_food_clohes 0.03368059 -0.034021800 -1.111572e-03 0.02089511 -0.022399076
## no_reamen 0.03546696 0.003485599 4.268592e-03 -0.07313130 -0.140207753
## no_educaion -0.03916628 -0.168323634 1.016125e-01 0.23047940 0.085168028
## no_aparmen 0.03611721 -0.086679903 -9.548153e-05 0.11241269 0.109584087
## siuaion_fin -0.01449390 0.299826495 -2.000663e-01 -0.38437590 -0.127040031
## aparmen_siuaion -0.08879989 0.313907359 1.611111e-01 -0.10012941 0.079950880
## PC11 PC12 PC13 PC14 PC15
## fla_area 0.59578689 0.26956679 -0.17751585 -0.117686112 0.29891833
## car 0.01206635 -0.19837173 0.49509339 0.094381438 0.44840879
## v_colour 0.02880431 0.16624311 0.04532247 -0.059709227 0.02686918
## video_player 0.04064730 0.36297136 0.07257132 -0.148981966 -0.19196576
## saelie -0.18827759 -0.03330864 -0.18610932 0.058536788 -0.24532354
## cd_player 0.12314439 0.29117904 0.03432883 0.005321009 -0.11925727
## compuer 0.19239346 -0.08424490 -0.11105140 0.073011986 -0.20744724
## inerne 0.18903586 -0.09758353 -0.14997048 0.092919381 -0.18604133
## washing -0.02811856 -0.51804270 -0.18225118 0.259041025 0.11240032
## machine 0.17219854 -0.36750323 -0.01579886 0.091550027 0.03038090
## dishwasher -0.09526121 -0.01502780 0.21693362 -0.057316631 0.12986883
## microwave -0.30714100 0.15106852 -0.31609117 -0.197444726 0.15616836
## freezer 0.10838654 -0.08894968 -0.24491527 0.095518326 -0.21743605
## el 0.09753180 0.15268795 0.24917209 0.051922086 0.27482974
## no_food_clohes 0.05537781 -0.18142595 -0.01771316 -0.213458994 -0.04930351
## no_reamen 0.08271029 -0.06599411 -0.14473974 -0.334705314 0.02653340
## no_educaion 0.11736886 0.28901047 -0.02274629 0.743491912 -0.01326024
## no_aparmen 0.02714326 -0.09677663 0.13728128 -0.278721879 -0.06428452
## siuaion_fin -0.52831949 0.18775711 -0.29420710 0.116358164 0.35331445
## aparmen_siuaion -0.24574976 0.05446858 0.46445385 0.053768247 -0.45832031
## PC16 PC17 PC18 PC19 PC20
## fla_area 0.05330408 -0.09649605 -0.019275919 0.04346068 0.002576881
## car 0.39170432 0.17788938 0.005876287 -0.09297635 0.029156607
## v_colour 0.04602592 0.08434368 -0.049761848 0.02244782 -0.009938797
## video_player 0.36053172 -0.27685674 0.526419192 -0.07023873 0.005925266
## saelie -0.15096255 0.00391472 -0.021086903 0.01541977 0.059669942
## cd_player 0.13433822 0.30140422 -0.680533163 0.11749075 0.036015563
## compuer 0.03545689 -0.05088874 0.022822276 -0.02515199 -0.720995823
## inerne 0.10009440 -0.10870669 0.031546632 -0.03066927 0.676447705
## washing 0.03040881 -0.14098867 -0.057761475 -0.02736735 0.002553528
## machine -0.02221873 0.01808360 0.046909428 -0.04764629 -0.019061929
## dishwasher -0.04071345 0.03098437 0.054147073 -0.02315631 -0.082797669
## microwave -0.05290758 0.11880224 -0.083784822 0.03006894 -0.024082605
## freezer -0.07995603 0.03088850 0.020936940 -0.02083593 0.004392615
## el -0.76441495 -0.15979857 0.101103406 0.12519997 0.061418442
## no_food_clohes 0.03257162 0.17182423 0.210431545 0.76540415 -0.003324991
## no_reamen -0.18893474 0.45606199 0.186180003 -0.56966017 0.024617665
## no_educaion -0.02381444 0.04623275 0.084882692 -0.07533830 -0.040991823
## no_aparmen -0.01299417 -0.65659558 -0.377365944 -0.17231185 -0.036722598
## siuaion_fin 0.12102183 -0.17084304 0.011478823 0.02055660 -0.018379291
## aparmen_siuaion -0.10380037 0.09103052 0.008896862 -0.04122395 0.033980606## PC1 PC2 PC3 PC4 PC5
## fla_area 0.0210327 -0.28029291 0.46443292 -8.951332e-03 0.307329627
## car -0.2812000 0.06478813 0.10813153 -1.378984e-01 -0.067035193
## v_colour -0.1078562 0.08201130 -0.08133650 -5.047907e-01 -0.094713221
## video_player -0.2769384 0.22668227 0.02620493 -1.380239e-01 -0.154436355
## saelie -0.1705138 0.02579958 0.33030848 -1.474442e-01 -0.138505225
## cd_player -0.3069504 0.17282597 -0.05168192 3.936375e-02 -0.109570045
## compuer -0.3168397 0.23745612 -0.12533109 2.208387e-01 0.239097517
## inerne -0.3091436 0.18980458 -0.14672626 3.106617e-01 0.241958643
## washing -0.2081214 0.06538875 0.02101971 -4.100576e-01 0.377833309
## machine -0.1081032 0.01034346 0.27335715 3.551096e-01 -0.557769063
## dishwasher -0.1670237 -0.01730783 0.27067018 3.452405e-01 0.099932535
## microwave -0.2333310 0.10770587 0.19441407 1.587887e-02 0.062734109
## freezer -0.1312643 -0.02389469 0.37780561 -2.879348e-01 -0.289577619
## el -0.2759079 0.27083936 -0.06154688 -5.918334e-02 -0.033266110
## no_food_clohes -0.2660416 -0.37274999 -0.19824810 -1.972604e-02 -0.048420793
## no_reamen -0.2755538 -0.29687753 -0.24508435 -3.375987e-02 0.009219708
## no_educaion -0.1288467 -0.39825078 -0.20285197 8.644942e-05 -0.122628804
## no_aparmen -0.2178961 -0.38221438 -0.15745850 -5.184980e-02 -0.173176561
## siuaion_fin -0.2323404 -0.18333434 0.01611853 1.846580e-01 0.001860157
## aparmen_siuaion -0.1320561 -0.28388824 0.34347538 7.195153e-03 0.348027976
## PC6 PC7 PC8 PC9 PC10
## fla_area -0.02177672 -0.005103380 8.573949e-02 -0.16169895 0.001919977
## car 0.32644850 -0.076563484 -2.781732e-02 -0.08297071 0.268774165
## v_colour -0.70028240 0.004574490 -2.430990e-01 -0.16984226 0.292852351
## video_player 0.01544580 0.021192488 2.052911e-01 0.09425397 -0.300307242
## saelie 0.14371241 -0.676391264 7.304167e-02 -0.41789558 0.015789212
## cd_player 0.04454145 0.074177776 8.367777e-02 -0.01200382 -0.377567826
## compuer 0.04184996 0.018392045 -1.022833e-01 -0.15342601 0.236316732
## inerne -0.05277122 0.003416087 -1.664257e-01 -0.04257539 0.259167100
## washing -0.14931749 0.036948566 2.072252e-01 0.13082873 -0.387735159
## machine -0.37066780 0.200238826 3.231946e-01 -0.11985924 -0.006523110
## dishwasher -0.31480280 -0.368087785 -4.596148e-01 0.38503049 -0.292962432
## microwave -0.02724318 -0.018127711 3.860436e-01 0.50264972 0.428197706
## freezer 0.30375598 0.340184293 -5.045772e-01 0.25206668 0.047822744
## el 0.10011224 0.108772742 3.922493e-02 -0.06219302 -0.046775912
## no_food_clohes 0.03368059 -0.034021800 -1.111572e-03 0.02089511 -0.022399076
## no_reamen 0.03546696 0.003485599 4.268592e-03 -0.07313130 -0.140207753
## no_educaion -0.03916628 -0.168323634 1.016125e-01 0.23047940 0.085168028
## no_aparmen 0.03611721 -0.086679903 -9.548153e-05 0.11241269 0.109584087
## siuaion_fin -0.01449390 0.299826495 -2.000663e-01 -0.38437590 -0.127040031
## aparmen_siuaion -0.08879989 0.313907359 1.611111e-01 -0.10012941 0.079950880
## PC11 PC12 PC13 PC14 PC15
## fla_area 0.59578689 0.26956679 -0.17751585 -0.117686112 0.29891833
## car 0.01206635 -0.19837173 0.49509339 0.094381438 0.44840879
## v_colour 0.02880431 0.16624311 0.04532247 -0.059709227 0.02686918
## video_player 0.04064730 0.36297136 0.07257132 -0.148981966 -0.19196576
## saelie -0.18827759 -0.03330864 -0.18610932 0.058536788 -0.24532354
## cd_player 0.12314439 0.29117904 0.03432883 0.005321009 -0.11925727
## compuer 0.19239346 -0.08424490 -0.11105140 0.073011986 -0.20744724
## inerne 0.18903586 -0.09758353 -0.14997048 0.092919381 -0.18604133
## washing -0.02811856 -0.51804270 -0.18225118 0.259041025 0.11240032
## machine 0.17219854 -0.36750323 -0.01579886 0.091550027 0.03038090
## dishwasher -0.09526121 -0.01502780 0.21693362 -0.057316631 0.12986883
## microwave -0.30714100 0.15106852 -0.31609117 -0.197444726 0.15616836
## freezer 0.10838654 -0.08894968 -0.24491527 0.095518326 -0.21743605
## el 0.09753180 0.15268795 0.24917209 0.051922086 0.27482974
## no_food_clohes 0.05537781 -0.18142595 -0.01771316 -0.213458994 -0.04930351
## no_reamen 0.08271029 -0.06599411 -0.14473974 -0.334705314 0.02653340
## no_educaion 0.11736886 0.28901047 -0.02274629 0.743491912 -0.01326024
## no_aparmen 0.02714326 -0.09677663 0.13728128 -0.278721879 -0.06428452
## siuaion_fin -0.52831949 0.18775711 -0.29420710 0.116358164 0.35331445
## aparmen_siuaion -0.24574976 0.05446858 0.46445385 0.053768247 -0.45832031
## PC16 PC17 PC18 PC19 PC20
## fla_area 0.05330408 -0.09649605 -0.019275919 0.04346068 0.002576881
## car 0.39170432 0.17788938 0.005876287 -0.09297635 0.029156607
## v_colour 0.04602592 0.08434368 -0.049761848 0.02244782 -0.009938797
## video_player 0.36053172 -0.27685674 0.526419192 -0.07023873 0.005925266
## saelie -0.15096255 0.00391472 -0.021086903 0.01541977 0.059669942
## cd_player 0.13433822 0.30140422 -0.680533163 0.11749075 0.036015563
## compuer 0.03545689 -0.05088874 0.022822276 -0.02515199 -0.720995823
## inerne 0.10009440 -0.10870669 0.031546632 -0.03066927 0.676447705
## washing 0.03040881 -0.14098867 -0.057761475 -0.02736735 0.002553528
## machine -0.02221873 0.01808360 0.046909428 -0.04764629 -0.019061929
## dishwasher -0.04071345 0.03098437 0.054147073 -0.02315631 -0.082797669
## microwave -0.05290758 0.11880224 -0.083784822 0.03006894 -0.024082605
## freezer -0.07995603 0.03088850 0.020936940 -0.02083593 0.004392615
## el -0.76441495 -0.15979857 0.101103406 0.12519997 0.061418442
## no_food_clohes 0.03257162 0.17182423 0.210431545 0.76540415 -0.003324991
## no_reamen -0.18893474 0.45606199 0.186180003 -0.56966017 0.024617665
## no_educaion -0.02381444 0.04623275 0.084882692 -0.07533830 -0.040991823
## no_aparmen -0.01299417 -0.65659558 -0.377365944 -0.17231185 -0.036722598
## siuaion_fin 0.12102183 -0.17084304 0.011478823 0.02055660 -0.018379291
## aparmen_siuaion -0.10380037 0.09103052 0.008896862 -0.04122395 0.033980606
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 2.223 1.5202 1.18859 1.06380 1.00319 0.96675 0.93607
## Proportion of Variance 0.247 0.1155 0.07064 0.05658 0.05032 0.04673 0.04381
## Cumulative Proportion 0.247 0.3625 0.43319 0.48977 0.54009 0.58682 0.63063
## PC8 PC9 PC10 PC11 PC12 PC13 PC14
## Standard deviation 0.90266 0.88133 0.85476 0.84804 0.82439 0.79263 0.76490
## Proportion of Variance 0.04074 0.03884 0.03653 0.03596 0.03398 0.03141 0.02925
## Cumulative Proportion 0.67137 0.71021 0.74674 0.78270 0.81668 0.84809 0.87734
## PC15 PC16 PC17 PC18 PC19 PC20
## Standard deviation 0.75293 0.70535 0.67402 0.6557 0.55793 0.43946
## Proportion of Variance 0.02835 0.02488 0.02272 0.0215 0.01556 0.00966
## Cumulative Proportion 0.90569 0.93057 0.95328 0.9748 0.99034 1.00000This table presents the eigenvalues of successive components, the percentage of the total variance explained by the successive components and the cumulative percentage of explained variance. Eigenvalues greater than 1 allow the identification of five principal components. Using the scree test to select the number of factors, it makes sense to leave 3 components (the scree plot shows that there is a slight decrease in eigenvalues to the right of the third component). A sensible interpretation of the main components as dimensions of poverty is possible in the case of 3 components. They account for 43.3% of the total variance. Therefore, the principal components analysis for 3 components was performed.
The procedure princomp() uses the spectral decomposition approach.
##
## Loadings:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9
## fla_area 0.280 0.464 0.307 0.162
## car -0.281 0.108 0.138 -0.326
## v_colour -0.108 0.505 0.700 -0.243 0.170
## video_player -0.277 -0.227 0.138 -0.154 0.205
## saelie -0.171 0.330 0.147 -0.139 -0.144 0.676 0.418
## cd_player -0.307 -0.173 -0.110
## compuer -0.317 -0.237 -0.125 -0.221 0.239 -0.102 0.153
## inerne -0.309 -0.190 -0.147 -0.311 0.242 -0.166
## washing -0.208 0.410 0.378 0.149 0.207 -0.131
## machine -0.108 0.273 -0.355 -0.558 0.371 -0.200 0.323 0.120
## dishwasher -0.167 0.271 -0.345 0.315 0.368 -0.460 -0.385
## microwave -0.233 -0.108 0.194 0.386 -0.503
## freezer -0.131 0.378 0.288 -0.290 -0.304 -0.340 -0.505 -0.252
## el -0.276 -0.271 -0.100 -0.109
## no_food_clohes -0.266 0.373 -0.198
## no_reamen -0.276 0.297 -0.245
## no_educaion -0.129 0.398 -0.203 -0.123 0.168 0.102 -0.230
## no_aparmen -0.218 0.382 -0.157 -0.173 -0.112
## siuaion_fin -0.232 0.183 -0.185 -0.300 -0.200 0.384
## aparmen_siuaion -0.132 0.284 0.343 0.348 -0.314 0.161 0.100
## Comp.10 Comp.11 Comp.12 Comp.13 Comp.14 Comp.15 Comp.16 Comp.17
## fla_area 0.596 0.270 0.178 0.118 0.299
## car 0.269 -0.198 -0.495 0.448 0.392 -0.178
## v_colour 0.293 0.166
## video_player -0.300 0.363 0.149 -0.192 0.361 0.277
## saelie -0.188 0.186 -0.245 -0.151
## cd_player -0.378 0.123 0.291 -0.119 0.134 -0.301
## compuer 0.236 0.192 0.111 -0.207
## inerne 0.259 0.189 0.150 -0.186 0.100 0.109
## washing -0.388 -0.518 0.182 -0.259 0.112 0.141
## machine 0.172 -0.368
## dishwasher -0.293 -0.217 0.130
## microwave 0.428 -0.307 0.151 0.316 0.197 0.156 -0.119
## freezer 0.108 0.245 -0.217
## el 0.153 -0.249 0.275 -0.764 0.160
## no_food_clohes -0.181 0.213 -0.172
## no_reamen -0.140 0.145 0.335 -0.189 -0.456
## no_educaion 0.117 0.289 -0.743
## no_aparmen 0.110 -0.137 0.279 0.657
## siuaion_fin -0.127 -0.528 0.188 0.294 -0.116 0.353 0.121 0.171
## aparmen_siuaion -0.246 -0.464 -0.458 -0.104
## Comp.18 Comp.19 Comp.20
## fla_area
## car
## v_colour
## video_player -0.526
## saelie
## cd_player 0.681 0.117
## compuer -0.721
## inerne 0.676
## washing
## machine
## dishwasher
## microwave
## freezer
## el -0.101 0.125
## no_food_clohes -0.210 0.765
## no_reamen -0.186 -0.570
## no_educaion
## no_aparmen 0.377 -0.172
## siuaion_fin
## aparmen_siuaion
##
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9
## SS loadings 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
## Proportion Var 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05
## Cumulative Var 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45
## Comp.10 Comp.11 Comp.12 Comp.13 Comp.14 Comp.15 Comp.16 Comp.17
## SS loadings 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
## Proportion Var 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05
## Cumulative Var 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85
## Comp.18 Comp.19 Comp.20
## SS loadings 1.00 1.00 1.00
## Proportion Var 0.05 0.05 0.05
## Cumulative Var 0.90 0.95 1.005.1 Visualization and Interpretation
## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa5.1.1 Correlation circle
The correlation between the variable and the main component (PC) is used as the coordinates of the variable on the PC.
This part of analysis present the variable correlation plots. Positively correlated variables are grouped together. Otherwise negatively correlated variables are positioned on opposite sides of the plot origin (opposed quadrants).
In sum, two approarch are given the similar results.
5.1.2 Visusalisation of quality
In order to verify the number of major components, the eigenvalues should be analyzed. Based on the graph above and the table below, we choose the third principal component.
## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 4.9399762 24.6998810 24.69988
## Dim.2 2.3109893 11.5549467 36.25483
## Dim.3 1.4127558 7.0637790 43.31861
## Dim.4 1.1316726 5.6583632 48.97697
## Dim.5 1.0063842 5.0319209 54.00889
## Dim.6 0.9345976 4.6729878 58.68188
## Dim.7 0.8762241 4.3811207 63.06300
## Dim.8 0.8147991 4.0739953 67.13699
## Dim.9 0.7767478 3.8837390 71.02073
## Dim.10 0.7306164 3.6530821 74.67382
## Dim.11 0.7191726 3.5958631 78.26968
## Dim.12 0.6796234 3.3981170 81.66780
## Dim.13 0.6282574 3.1412870 84.80908
## Dim.14 0.5850712 2.9253561 87.73444
## Dim.15 0.5669035 2.8345176 90.56896
## Dim.16 0.4975117 2.4875584 93.05651
## Dim.17 0.4543034 2.2715170 95.32803
## Dim.18 0.4299803 2.1499015 97.47793
## Dim.19 0.3112867 1.5564335 99.03437
## Dim.20 0.1931266 0.9656332 100.00000
The most significant variables are analyzed that constitute PC1.
loading_scores_PC_1<-PCA_sondaz$rotation[,1]
fac_scores_PC_1<-abs(loading_scores_PC_1)
fac_scores_PC_1_ranked<-names(sort(fac_scores_PC_1, decreasing=T))
PCA_sondaz$rotation[fac_scores_PC_1_ranked, 1]## compuer inerne cd_player car video_player
## -0.3168397 -0.3091436 -0.3069504 -0.2812000 -0.2769384
## el no_reamen no_food_clohes microwave siuaion_fin
## -0.2759079 -0.2755538 -0.2660416 -0.2333310 -0.2323404
## no_aparmen washing saelie dishwasher aparmen_siuaion
## -0.2178961 -0.2081214 -0.1705138 -0.1670237 -0.1320561
## freezer no_educaion machine v_colour fla_area
## -0.1312643 -0.1288467 -0.1081032 -0.1078562 0.0210327loading_scores_PC_2<-PCA_sondaz$rotation[,2]
fac_scores_PC_2<-abs(loading_scores_PC_2)
fac_scores_PC_2_ranked<-names(sort(fac_scores_PC_2, decreasing=T))
PCA_sondaz$rotation[fac_scores_PC_2_ranked, 2]## no_educaion no_aparmen no_food_clohes no_reamen aparmen_siuaion
## -0.39825078 -0.38221438 -0.37274999 -0.29687753 -0.28388824
## fla_area el compuer video_player inerne
## -0.28029291 0.27083936 0.23745612 0.22668227 0.18980458
## siuaion_fin cd_player microwave v_colour washing
## -0.18333434 0.17282597 0.10770587 0.08201130 0.06538875
## car saelie freezer dishwasher machine
## 0.06478813 0.02579958 -0.02389469 -0.01730783 0.01034346loading_scores_PC_3<-PCA_sondaz$rotation[,3]
fac_scores_PC_3<-abs(loading_scores_PC_2)
fac_scores_PC_3_ranked<-names(sort(fac_scores_PC_3, decreasing=T))
PCA_sondaz$rotation[fac_scores_PC_3_ranked, 3]## no_educaion no_aparmen no_food_clohes no_reamen aparmen_siuaion
## -0.20285197 -0.15745850 -0.19824810 -0.24508435 0.34347538
## fla_area el compuer video_player inerne
## 0.46443292 -0.06154688 -0.12533109 0.02620493 -0.14672626
## siuaion_fin cd_player microwave v_colour washing
## 0.01611853 -0.05168192 0.19441407 -0.08133650 0.02101971
## car saelie freezer dishwasher machine
## 0.10813153 0.33030848 0.37780561 0.27067018 0.273357155.1.3 Graph of individuals
The above analysis provides a list of matrices containing all scores for persons (coordinates, correlations between persons and axes, cosine squared and contributions).
## Principal Component Analysis Results for individuals
## ===================================================
## Name Description
## 1 "$coord" "Coordinates for the individuals"
## 2 "$cos2" "Cos2 for the individuals"
## 3 "$contrib" "contributions of the individuals"The coordinates of individuals is below:
## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 Dim.6 Dim.7
## 1 2.330862 -2.2128044 -1.0617138 -0.5363029 0.3414520 -0.8215527 -0.2756493
## 2 2.533416 -1.7254566 -1.6713366 -0.5460945 -0.2502165 -0.6796196 -0.7642926
## 3 2.596719 -1.8229552 -1.4634524 -0.5551447 -0.1567322 -0.6628280 -0.8825546
## 4 2.325629 -2.4984437 0.5478922 -0.2179283 -1.6419308 0.5931932 -1.1227701
## 5 1.487973 -2.0428552 0.3475797 -0.3265893 -1.2627780 1.1575150 0.4421925
## 6 -3.101770 0.2826362 1.7220626 1.9671891 -1.0041789 -1.9032591 -1.9347156
## Dim.8 Dim.9 Dim.10 Dim.11 Dim.12 Dim.13
## 1 0.1324714 0.39434590 -0.1631445 -0.04821283 -1.1876731 -0.02812483
## 2 -0.1324122 0.57625748 -0.2881133 0.23996169 -1.3155898 -0.72401231
## 3 -0.1297029 0.49677657 -0.3159236 0.75721732 -1.1420330 -1.02095878
## 4 -1.4022466 -0.42111562 1.1645062 0.05375411 0.2253103 -0.45397101
## 5 -1.4400269 0.01214875 1.5600895 1.28910456 0.5227832 1.37092907
## 6 0.8644046 0.67212984 -0.2271571 1.05308094 -1.1095689 0.73838222
## Dim.14 Dim.15 Dim.16 Dim.17 Dim.18 Dim.19
## 1 -0.3123004 -0.71577795 0.1161038 0.3793659 -0.08269062 -0.12289320
## 2 -0.3773709 -0.04881389 0.2694533 0.2528153 -0.09348909 -0.06554570
## 3 -0.4814523 0.33301217 0.3455994 0.1503365 -0.11056958 -0.01930835
## 4 -0.8131632 -1.96314136 -0.4584987 0.8561781 0.08783230 -0.03643922
## 5 -0.7382323 0.41339559 -1.1267882 0.7296678 0.36921875 0.08516950
## 6 -0.2006754 -0.04394799 -0.2219509 0.3925125 0.12556805 -0.14510895
## Dim.20
## 1 -0.01671272
## 2 -0.07010760
## 3 -0.08066389
## 4 0.11475997
## 5 0.19402104
## 6 -0.07133706The contributions of individuals to PC:
## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 Dim.6
## 1 0.09472752 0.182497062 0.068725141 0.021891086 0.009978456 0.06220338
## 2 0.11190663 0.110962936 0.170305443 0.022697735 0.005358409 0.04256718
## 3 0.11756902 0.123857358 0.130574356 0.023456296 0.002102423 0.04048972
## 4 0.09430263 0.232653164 0.018301679 0.003614715 0.230735102 0.03242915
## 5 0.03860404 0.155541036 0.007365622 0.008118033 0.136476530 0.12347992
## 6 0.16774983 0.002977318 0.180800051 0.294536549 0.086303049 0.33384046
## Dim.7 Dim.8 Dim.9 Dim.10 Dim.11 Dim.12
## 1 0.007469064 0.001855076 1.724417e-02 0.003137784 0.0002783941 0.178769433
## 2 0.057421153 0.001853418 3.682315e-02 0.009785996 0.0068963368 0.219351420
## 3 0.076565959 0.001778348 2.736591e-02 0.011766371 0.0686713706 0.165293866
## 4 0.123917950 0.207857684 1.966484e-02 0.159868145 0.0003460653 0.006433711
## 5 0.019220974 0.219209039 1.636631e-05 0.286930955 0.1990265102 0.034637190
## 6 0.367948310 0.078986236 5.009497e-02 0.006083184 0.1328183683 0.156029966
## Dim.13 Dim.14 Dim.15 Dim.16 Dim.17 Dim.18
## 1 0.0001084451 0.014358333 0.0778422295 0.002333765 0.027285904 0.001369720
## 2 0.0718657691 0.020965050 0.0003620307 0.012569890 0.012117936 0.001750818
## 3 0.1429047246 0.034124441 0.0168491827 0.020678091 0.004284999 0.002449010
## 4 0.0282544206 0.097345179 0.5855470250 0.036394912 0.138979257 0.001545353
## 5 0.2576677945 0.080231534 0.0259651193 0.219810844 0.100942064 0.027307800
## 6 0.0747468053 0.005928535 0.0002934517 0.008528608 0.029209813 0.003158476
## Dim.19 Dim.20
## 1 0.0041789093 0.0001245718
## 2 0.0011887640 0.0021920769
## 3 0.0001031567 0.0029019102
## 4 0.0003674052 0.0058736282
## 5 0.0020071297 0.0167889392
## 6 0.0058263368 0.0022696348To visualize the total contributions of individual variables to PC1, PC2 and PC3:
5.2 Rotated PCA
In order to obtain the simplest possible structure a rotation should be made. This is a way of maximizing high loads and minimizing light loads.
There are two types of rotation methods, orthogonal and oblique. In orthogonal rotation, the factors after rotation will remain uncorrelated, while in oblique rotation, the factors resulting from the rotation will be correlated.
The most common orthogonal method is called varimax rotation.
##
## Attaching package: 'psych'## The following objects are masked from 'package:ggplot2':
##
## %+%, alpha## Principal Components Analysis
## Call: principal(r = data, nfactors = 3, rotate = "varimax")
## Standardized loadings (pattern matrix) based upon correlation matrix
## RC1 RC2 RC3 h2 u2 com
## fla_area -0.41 0.13 0.55 0.488 0.51 2.0
## car 0.52 0.18 0.34 0.417 0.58 2.0
## v_colour 0.28 0.05 -0.02 0.082 0.92 1.1
## video_player 0.68 0.01 0.21 0.499 0.50 1.2
## saelie 0.23 0.02 0.49 0.299 0.70 1.4
## cd_player 0.70 0.14 0.16 0.538 0.46 1.2
## compuer 0.79 0.11 0.07 0.648 0.35 1.1
## inerne 0.75 0.17 0.05 0.586 0.41 1.1
## washing 0.42 0.14 0.18 0.224 0.78 1.6
## machine 0.12 -0.01 0.38 0.164 0.84 1.2
## dishwasher 0.20 0.09 0.44 0.242 0.76 1.5
## microwave 0.45 0.04 0.38 0.349 0.65 2.0
## freezer 0.11 0.02 0.53 0.288 0.71 1.1
## el 0.74 0.00 0.10 0.551 0.45 1.0
## no_food_clohes 0.19 0.82 0.10 0.726 0.27 1.1
## no_reamen 0.29 0.76 0.04 0.664 0.34 1.3
## no_educaion -0.07 0.71 -0.01 0.507 0.49 1.0
## no_aparmen 0.09 0.77 0.11 0.607 0.39 1.1
## siuaion_fin 0.24 0.47 0.26 0.345 0.66 2.1
## aparmen_siuaion -0.11 0.35 0.55 0.439 0.56 1.8
##
## RC1 RC2 RC3
## SS loadings 3.89 2.84 1.94
## Proportion Var 0.19 0.14 0.10
## Cumulative Var 0.19 0.34 0.43
## Proportion Explained 0.45 0.33 0.22
## Cumulative Proportion 0.45 0.78 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 3 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0.06
## with the empirical chi square 1757.88 with prob < 2.1e-281
##
## Fit based upon off diagonal values = 0.93##
## Factor analysis with Call: principal(r = data, nfactors = 3, rotate = "varimax")
##
## Test of the hypothesis that 3 factors are sufficient.
## The degrees of freedom for the model is 133 and the objective function was 1.06
## The number of observations was 1161 with Chi Square = 1216.34 with prob < 2.8e-174
##
## The root mean square of the residuals (RMSA) is 0.06##
## Loadings:
## RC1 RC2 RC3
## car 0.519
## video_player 0.675
## cd_player 0.701
## compuer 0.795
## inerne 0.745
## el 0.736
## no_food_clohes 0.825
## no_reamen 0.762
## no_educaion 0.708
## no_aparmen 0.767
## fla_area -0.406 0.554
## freezer 0.526
## aparmen_siuaion 0.553
## v_colour
## saelie 0.495
## washing 0.415
## machine
## dishwasher 0.438
## microwave 0.450
## siuaion_fin 0.470
##
## RC1 RC2 RC3
## SS loadings 3.888 2.835 1.940
## Proportion Var 0.194 0.142 0.097
## Cumulative Var 0.194 0.336 0.433On the basis of the obtained result, it should be noted that after applying the varimax rotation, the charges of the components are very clear.
This above table presents the factor loadings after orthogonal rotation (Varimax), which allows for the interpretation of individual components as subsequent dimensions of poverty. The variables were grouped in such a way as to assign them to the appropriate components (the highest values of loads for each variable were marked).
Ultimately, the next dimensions can be interpreted as follows: the first dimension - “endowment with durable goods”, the second - “livelihood”, and the third - “housing situation”.
The first dimension of poverty relates to the scarcity in terms of equipping a home with durable goods. This dimension consists of 9 variables that determine the possession of such goods as: a computer and related Internet access, a mobile phone, a CD player, a video player, a car, a microwave oven, an automatic washing machine, and a color TV set. These goods are now owned by the vast majority of households, so their forced absence constitutes a significant type of exclusion.
The second poverty dimension includes 5 variables that relate to the ability to meet basic needs and the general financial situation. This dimension consists of variables determining whether it happened that there was a shortage of money for food and clothing, housing, treatment, doctor, education, and a variable describing the overall level of satisfaction with the financial situation. This dimension defines the basic standard of living because a lack of resources for food, housing and other basic expenses can be considered a serious indicator of poverty.
The third dimension of poverty determines the standard of housing. The elements included in this dimension are the living area per person, general satisfaction with the housing situation, and the possession of other less common durable goods such as a dishwasher, separate freezer or washer / dryer or separate dryer. This dimension is not as important an indicator of poverty as the other two, but it does refer to an important element of the overall standard of living, namely the housing situation.
5.3 Quality measures
5.3.1 SCREE PLOTS
The explained variance with consecutive principal components (PC) can be verified.
5.3.2 Analisys of the variables used
## Loading required package: sp## Checking rgeos availability: TRUE
plot(PCA_sondaz3$complexity, pch=".", xlim=c(-20, 110), main="Factors complexity", sub="Number of variables consists of component factor", xlab=" ", ylab="complexity")
pointLabel(PCA_sondaz3$complexity, labels=names(PCA_sondaz3$complexity), cex=0.8) 
plot(PCA_sondaz3$uniqueness, pch=".", xlim=c(-20, 110), main="Uniqueness of factors", sub="Percentage of variance", xlab=" ", ylab="complexity")
pointLabel(PCA_sondaz3$uniqueness, labels=names(PCA_sondaz3$uniqueness), cex=0.8)
plot(PCA_sondaz3$complexity, PCA_sondaz3$uniqueness, xlim=c(0, 4))
pointLabel(PCA_sondaz3$complexity, PCA_sondaz3$uniqueness, labels=names(PCA_sondaz3$uniqueness), cex=0.8)
abline(h=c(0.38, 0.75), lty=3, col=2)
abline(v=c(1.8), lty=3, col=2)
set<-data.frame(complex=PCA_sondaz3$complexity, unique=PCA_sondaz3$uniqueness)
set.worst<-set[set$complex>1.8 & set$unique>0.78,]
set.worst## [1] complex unique
## <0 rows> (or 0-length row.names)Based on the analysis there are no “Worst variables” which are problematic in analysis.
After defining the poverty dimensions, it is possible to proceed to the assessment of the level of poverty of individuals in subsequent dimensions. The method of defining the variables allows for the interpretation of the values of individual principal components for each unit as its individual indicator of the degree of deficiency in a given dimension (the lower the value of the indicator, the more poor in this dimension a person may be). Comparing the set of poor people in the context of a given dimension with the set of poor people in the context of income will allow to verify the research hypothesis. If these sets overlap it will mean that income can replace multidimensional measures in detecting poor people. However, if these collections differ significantly, the income may be considered insufficient to correctly identify the poor. The value of 60% of the median was adopted as the income poverty line income in the study population. In this case, 20.5% of individuals are counted among the poor. In the case of the designated dimensions, the poverty line was set in such a way that the group of poor people was the same percentage as in the case of income poverty, which would allow for comparison.
Data on the percentage of people in the population of poor people in terms of income, who are also below the poverty line in a given dimension (DIM 1: 15.5%; DIM 2:37.39%; DIM 3: 28.99%). In all dimensions, these values are less than 40% with the highest value for the second dimension. This means that income cannot replace multivariate analysis in identifying poverty. However, it identifies poor people to a slightly better extent in terms of their ability to meet their basic needs (the second poverty dimension).
Therefore, in the future, it is interesting to investigate what characteristics of people, among those above the income poverty line, contribute to the greater likelihood of living in poverty in the context of each poverty dimension.
6 Conclusion
The aim of the above study was to verify the hypothesis that in the case of Poland, the multidimensional analysis of poverty cannot be replaced by a measure based solely on income, without significant differences in the identification of poor people. The study was based on the data contained in the Social Diagnosis study. The multidimensional analysis with the use of principal components analysis, after optimal scaling of categorical variables, allowed to distinguish three main dimensions of poverty.
On the basis of comparing the set of poor people in each poverty dimension, and the set of poor people in terms of income, it can be concluded that these sets do not overlap to a large extent. This means that the classification using only the poverty income index is not sufficient to properly identify the poor, which means that there are no grounds for rejecting the hypothesis.
7 Bibliography
Coromaldi M., Zoli M. (2007), “A Multidimensional Poverty Analysis.Evidence from Italian Data”
Dekkers G. (2003), Financial and multidimensional poverty in european countries: can the former be used as a proxy of the latter?
Siani J. (2015), “A Multidimensional Analysis of Poverty using the Fuzzy Set Approach. Evidence from Cameroonian data,” Economics Bulletin, AccessEcon, vol. 35(3), pages 2012-2025.