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In this paper we use a statistical mechanical model as a paradigm for educational choices when the reference population is partitioned according to the socioeconomic attributes of gender and residence. We study how educational attainment is influenced by socioeconomic attributes of gender and residence for five selected developing countries. The model has a social and a private incentive part with coefficients measuring the influence individuals have on each other and the external influence on individuals, respectively. The methods of partial least squares and the ordinary least squares are, respectively, used to estimate the parameters of the interacting and the noninteracting models. This work differs from the previous work that motivated this work in the following sense: (a) the reference population is divided into subgroups with unequal subgroup sizes, (b) the proportion of individuals in each of the subgroups may depend on the population size

Education provides people with the knowledge and skills that can lead to better employment opportunities and a better quality of life. The educational level attained by an individual explicitly determines the occupational choice of that individual. All these attainments and choices of individuals are made under certain socioeconomic conditions such as peers, neighbours, family members, wealth quintile of the individual, gender, residence, etc. Those who reside in the rural areas with the poorest wealth quintile are more likely to have low education [

The collective behaviour of a large group of individuals may undergo sudden changes due to slight variations in the socioeconomic structure of the group. For instance a change in the pronunciation of a language due to a small immigrant population and a substantial decrease in crime rate is a result of actions taking by the authorities [

The above and the works in [

The authors of [

The rest of the paper is organized as follows: Section

The Curie-Weiss model is made up of an energy function (Hamiltonian) that assigns interaction energies to spin configurations. This energy function takes the form

This work uses partial least squares estimation procedure developed in [

Therefore a population of size

A representation of the interaction network for our model. Population is divided into four groups

Suppose the spins

For any choice of the parameters

The

In this work we will consider the attributes of gender and residence, i.e.,

The

This allows us, in particular, to write the probability that the

In the case

Due to the factorization property of the model in the thermodynamic limit, it follows from (

Therefore, it follows from (

In the interacting case, the independent variables are correlated. Due to this the least squares method is not appropriate. The partial least squares estimation is used in that case.

The data used in this case study is taken from five different developing countries, namely, Ghana, Kenya, Egypt, Dominican Republic, and Indonesia. Our choice of these countries is based on our desire to compare how interaction influences choices made by individuals from countries with similar characteristics and on availability of data. Our data was taken over a six-year period from reports gathered by the Demographic and Health Surveys Program. These reports are national representative surveys of individuals in the various countries sponsored by USAID, UNICEF, UNFPA, UNDP, TheGlobalFund, ILO, Daninda, and other national bodies. Our interest is in how place of residence and gender influence educational choices of individuals.

Under this section we will be looking at data coming from Ghana Demographic and Health Survey, Egypt Demographic and Health Survey, Kenya Demographic and Health Survey, Encuesta Demográficay De Salud República Dominicana, and Indonesia Demographic and Health Survey [

Note that if

Data for the selected countries grouped according to residence and gender. Taken from [

Country | Ghana | |||||||||||

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Year | 1988 | 1993 | 1998 | 2003 | 2008 | 2014 | ||||||

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Residence/Gender | Female | Male | Female | Male | Female | Male | Female | Male | Female | Male | Female | Male |

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Urban | 1523 | 226 | 3096 | 2621 | 1739 | 547 | 4841 | 3865 | 8830 | 7385 | 9063 | 7763 |

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Rural | 2965 | 717 | 5784 | 5493 | 3104 | 999 | 5944 | 5511 | 10453 | 9743 | 8715 | 8005 |

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Egypt | ||||||||||||

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Year | 1992 | 1995 | 2000 | 2005 | 2008 | 2014 | ||||||

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Residence/Gender | Female | Male | Female | Male | Female | Male | Female | Male | Female | Male | Female | Male |

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Urban | 12096 | 11886 | 16079 | 15703 | 16659 | 16573 | 19850 | 19289 | 16648 | 16290 | 18918 | 18676 |

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Rural | 13638 | 13110 | 19032 | 18023 | 20927 | 20994 | 26480 | 25259 | 21244 | 20267 | 29818 | 28632 |

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Kenya | ||||||||||||

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Year | 1989 | 1993 | 1998 | 2003 | 2008 | 2014 | ||||||

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Residence/Gender | Female | Male | Female | Male | Female | Male | Female | Male | Female | Male | Female | Male |

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Urban | 1236 | 157 | 2253 | 2108 | 2726 | 2931 | 3099 | 3051 | 3257 | 2997 | 19931 | 19729 |

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Rural | 5914 | 1013 | 12420 | 14207 | 12667 | 11567 | 12316 | 11774 | 12805 | 11884 | 38677 | 35652 |

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Dominican Republic | ||||||||||||

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Year | 1991 | 1996 | 1999 | 2002 | 2007 | 2013 | ||||||

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Residence/Gender | Female | Male | Female | Male | Female | Male | Female | Male | Female | Male | Female | Male |

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Urban | 9207 | 7697 | 10435 | 9338 | 1682 | 1486 | 30726 | 29026 | 37934 | 35686 | 13185 | 12418 |

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Rural | 4969 | 5731 | 5701 | 6374 | 853 | 942 | 15249 | 16971 | 15576 | 16560 | 4399 | 4854 |

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Indonesia | ||||||||||||

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Year | 1991 | 1994 | 1997 | 2002 - 2003 | 2007 | 2012 | ||||||

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Residence/Gender | Female | Male | Female | Male | Female | Male | Female | Male | Female | Male | Female | Male |

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Urban | 17560 | 16989 | 21216 | 20919 | 19951 | 19390 | 29786 | 29377 | 30740 | 31502 | 38557 | 37583 |

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Rural | 38338 | 37672 | 46540 | 45964 | 46529 | 45873 | 33159 | 32889 | 40461 | 41714 | 39024 | 36901 |

Here we are looking at groups of individuals that have been partitioned according to these two binary attributes of gender

Tables

Educational Attainment: Estimates for the interacting model.

Estimates | |||||
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Parameter | Ghana | Kenya | Egypt | Dominican R. | Indonesia |

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| -0.03 | -0.03 | -0.00 | 0.05 | -0.11 |

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| 0.12 | 0.10 | 0.12 | -0.06 | -0.01 |

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| -0.01 | 0.00 | 0.01 | -0.01 | -0.004 |

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| 0.20 | 0.13 | -0.15 | 0.49 | -0.67 |

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| 0.08 | 0.11 | 0.02 | 0.23 | -0.19 |

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| 0.06 | 0.03 | 0.14 | 0.23 | 0.07 |

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| -0.01 | 0.00 | -0.03 | 0.23 | -0.03 |

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| -0.20 | 0.03 | -0.33 | 0.92 | -0.28 |

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| -0.14 | -0.10 | 0.18 | -0.70 | 0.34 |

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| -0.17 | 0.03 | -0.01 | -0.41 | 1.19 |

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| -0.03 | -0.07 | -0.27 | 0.05 | -0.31 |

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| 0.37 | 0.13 | -0.29 | 1.11 | 0.02 |

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| -0.47 | -0.72 | 0.27 | 0.25 | 0.82 |

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| 0.21 | -0.01 | -0.59 | -0.72 | 0.71 |

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| 0.66 | -0.88 | -0.56 | 0.65 | -1.58 |

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| 0.95 | -0.04 | -0.72 | -3.52 | 0.49 |

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| -0.13 | -0.09 | 1.01 | -0.25 | -0.73 |

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| 1.25 | 0.11 | -0.02 | 0.55 | 0.72 |

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| 0.55 | 0.93 | 0.63 | 0.97 | 1.08 |

Educational Attainment: Estimates for the non-interacting model.

Estimates | |||||
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Parameters | Ghana | Kenya | Egypt | Dominican R. | Indonesia |

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| -0.29 | -0.26 | -0.41 | 0.04 | -0.36 |

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| 0.52 | 0.43 | 0.44 | 0.39 | 0.42 |

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| 0.43 | 0.84 | 0.62 | 0.75 | 1.05 |

The estimates for the noninteracting model will be followed by discussion on the interacting model. In the above case study there are four groups and these groups are explained in Table

Groups and their interpretations.

Group Number | Interpretation |
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1 | Females in urban area |

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2 | Males in urban area |

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3 | Females in rural area |

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4 | Males in rural area |

When the sum of the

The sum of the

All the selected countries have positive estimates for the private incentive of residence

The base private incentive

The interacting model has a utility function that consists of both social and private incentives. Whenever the coefficient of the social incentive

Note that

For

The estimate

Under this section our interest is to look at how well our interacting model fits the data. The partial least squares (PLS) method was used to estimate the parameters of the interacting model found in (

Our results and analyses are performed in the R statistical software, version 3.5.2. Tables

Variance of

Latent | Percentage of Explained Variances for | Cumulative Percentage of Explained Variances for | Percentage of Explained Variances for | Cumulative | RMSEP |
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1 | 33.4 | 33.34 | 82.7 | 82.7 | 0.1772 |

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2 | 6.13 | 39.53 | 12.18 | 94.88 | 0.1549 |

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3 | 25.89 | 65.42 | 1.57 | 96.45 | 0.1081 |

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4 | 28.21 | 93.63 | 0.15 | 96.60 | 0.0860 |

It is observed from Table

Variance of

Latent Vectors | Percentage of Explained Variances for | Cumulative Percentage of Explained Variances for | Percentage of Explained Variances for | Cumulative Percentage of Explained Variances for | RMSEP |
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1 | 49.37 | 49.37 | 87.07 | 87.07 | 0.1347 |

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2 | 33.1 | 82.47 | 0.35 | 87.42 | 0.1362 |

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3 | 16.73 | 99.20 | 0.73 | 88.15 | 0.3740 |

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4 | 0.62 | 99.82 | 10.64 | 98.79 | 0.4133 |

Variance of

Latent Vectors | Percentage of Explained Variances for | Cumulative Percentage of Explained Variances for | Percentage of Explained Variances for | Cumulative Percentage of Explained Variances for | RMSEP |
---|---|---|---|---|---|

1 | 33.60 | 33.60 | 82.06 | 82.06 | 0.1794 |

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2 | 10.64 | 44.24 | 12.99 | 95.05 | 0.1337 |

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3 | 18.29 | 62.53 | 4.24 | 99.29 | 0.08637 |

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4 | 20.86 | 83.39 | 0.13 | 99.42 | 0.06150 |

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5 | 11.54 | 94.93 | 0.14 | 99.56 | 0.04821 |

Variance of

Latent Vectors | Percentage of Explained Variances for | Cumulative Percentage of Explained Variances for | Percentage of Explained Variances for | Cumulative Percentage of Explained Variances for | RMSEP |
---|---|---|---|---|---|

1 | 38.36 | 38.36 | 51.38 | 51.38 | 0.2401 |

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2 | 23.28 | 61.64 | 6.80 | 58.18 | 0.2291 |

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3 | 24.13 | 85.77 | 14.71 | 72.89 | 0.1619 |

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4 | 13.09 | 98.86 | 22.26 | 95.15 | 0.1041 |

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5 | 0.45 | 99.31 | 2.93 | 98.08 | 0.07877 |

Variance of

Latent Vectors | Percentage of Explained Variances for | Cumulative Percentage of Explained Variances for | Percentage of Explained Variances for | Cumulative Percentage of Explained Variances for | RMSEP |
---|---|---|---|---|---|

1 | 28.06 | 28.06 | 82.7 | 59.24 | 0.2275 |

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2 | 43.05 | 71.11 | 12.18 | 61.36 | 0.2128 |

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3 | 20.56 | 91.67 | 1.57 | 72.27 | 0.1835 |

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4 | 8.03 | 99.70 | 0.15 | 98.17 | 0.06593 |

The above study gives credence to the potential of statistical mechanical models to socioeconomic applications, as has been suggested by the authors of [

The data used in this study are survey data carried out by the Demographic and Health Survey program in developing countries. The data used are found in [

The authors declare that they have no conflicts of interest.

The authors thank the staff at the Mathematics and Statistics Department of University of Energy and Natural Resources for their support and kindness during the period this paper was written.