ISSN(Print): 2328-7306
ISSN(Online): 2328-7292

Article Versions

Export Article

Cite this article

- Normal Style
- MLA Style
- APA Style
- Chicago Style

Research Article

Open Access Peer-reviewed

Chijioke J. Nweke, George C. Mbaeyi^{ }, Kelechi C. Ojide, Chukwunenye I. Okonkwo

Received October 10, 2019; Revised November 19, 2019; Accepted December 17, 2019

We present an empirical approach to changes in some fertility measures using multivariate profile analysis to determine level, trend and differences in fertility measures in Nigeria. ASFR, TFR and MNCEB was studied with respect to residency for three time points. Results obtained showed strong evidence of mean differences in TFR across zones with both ASFR, TFR and MNCEB showing no interaction with respect to residency. Various profile plots and tests showed evidences of parallelism for all the fertility measures considered. Some implications and suggestions with regards to policy formulation were also given.

Population change results from the interaction of three components namely; fertility, mortality and migration. With improved health facilities, nutrition and environmental conditions, mortality levels in most developing countries have been drastically reduced but fertility levels seem to have remained high due to some several factors responsible for fertility ^{ 1}. It is the combined effects of declining mortality and high fertility rate that has kept the rate of population growth very high in most developing countries. Some of the socio-economic and cultural factors that influence fertility level are place of residence (rural/urban), level of education, occupation, employment status, income, religion and ethnic nationality ^{ 2}. These factors influence fertility through the intermediate variables (proximate determinants). The four main fertility-reducing proximate determinants, according to Bongaarts ^{ 3} are marriage, abortion, contraception and postpartum infecundability while, coital frequency, primary and secondary sterility and separation of spouses are considered secondary proximate determinants ^{ 4}. In a society where marriage is early universal and stable and where contraceptive use is low, fertility level is usually high.

According to ^{ 5}, developing countries of the world accounted for about 81 percent of the world populations in 2017. Among the developing regions, Africa has the highest annual population growth rate of about 2.6 percent. Among the sub-regions in Africa, West Africa has the second highest growth rate of about 2.7 percent per annum. Within the sub-region, Nigeria is one of the most populous countries and has one of the most rapidly growing populations in Africa. The rate of population growth is currently put about 2.6 percent per year. The 2008 and 2013 Nigerian Demographic and Health Survey (NDHS) reported a total fertility rate (TFR) of about 5.7 and 5.5 children per women respectively. The 2008 (and 2013) NDHS also reported the total fertility rate (TFR) for the six geopolitical zones as follows: North Central has about 5.4 (and 5.3)children per women, North East has 7.2 (and 6.3) children per women, North West has 7.3 (and 6.3)children per women, South East has 4.8 (and 4.7) children per women, South South has 4.7 (and 4.3) children per women and South West has 4.5 (and 4.6) children per women respectively.

Many developing countries experiencing the problem of rapid population growth, have adopted a number of measures to control their fertility levels. In 1988, the Nigerian Government inaugurated the National Population Policy (NPP). The policy is aimed at improving the quality of life of the population and achieving lower population growth rates through reduction of birth rates by voluntary fertility regulation methods. Some of the set targets of the policy are: (i) to reduce the proportion of women bearing more than four children by 50 percent by 1995 and by 80 percent by the year 2000 and (ii) to reduce the total fertility rate per woman from over six to four children by the year 2000 and the population growth rate from about 3.3 percent to 2.0 percent per year by the year 2000 among others. To achieve the set goals and targets, some of the strategies adopted are: -making family planning services easily affordable, safe and culturally acceptable, mobilizing relevant agencies both private and public for effective service delivery and pursuing aggressive population information, education and communication programmes among others. The country has also invested a lot of resources towards achieving the set targets. Some non-governmental organizations like International Planned Parenthood Federation (IPPF), Planned Parenthood Federation of Nigeria (PPFN), and the United Nations Fund for Population Activities (UNFPA) have also made a lot of contributions towards achieving these goals.

Although fertility reduction is speculated in some quarter, there is no empirical evidence of fertility decline. It is equally not clear whether the rapid population growth is the result of the decline in mortality levels accompanied by constant fertility or a tendency to over –estimate fertility levels. The questions that follow are; what level of achievement has Nigeria made on fertility reduction? Is there enough evidence to show that fertility level is reducing or will reduce? Are there differences in the fertility level among the regions (geo-political zones) of the country? This work therefore seeks to adopt a multivariate profile analysis approach to address these questions objectively.

The data used for this study are secondary data obtained from ^{ 13}, ^{ 14} and ^{ 15} Nigeria Demographic and Health survey (NDHS). The fertility level measures used are Total Fertility Rate (TFR), Age Specific Fertility Rate (ASFR) and Mean Number of Child Ever Born (MNCEB). The fertility trend was examined within the years under study while the differentials were made between residence (Urban and Rural) and Region (the six geo-political zones). The age group as well as states of the nations including Federal Capital Territory(FCT) served as experimental subjects.

The data was analyzed using Profile Analysis, where each region/residence area serves as profile. The term profile comes from the practice in applied work in which scores on a test battery are plotted in terms of graph or profile ^{ 6}. It has found wide application in psychology and education, often such that profile analysis at a point was considered by educationist as simply the practice of depicting scores. Profile analysis is primarily used to identify patterns, and, some techniques have been employed in this situation. Examples include cluster analysis approach ^{ 7}, model profile analysis ^{ 8}, factor analysis ^{ 9}, profile analysis via multidimensional scaling ^{ 10}, and criterion-related profile analysis ^{ 11}. It is a multivariate equivalent of mixed ANOVA most commonly used in (i) comparing same dependent variable between groups over several time points, and (ii) when there are several measures of the same dependent variable, as such, it makes same assumption as those of the MANOVA. Data used in profile analysis must be on the same scale, otherwise, z-score or any other transformation may be required. Since sample size can affect power and homogeneity of variance/covariance test, it is required that there be more subjects than the number of dependent variables. The major tests of Profile Analysis includes (i) Parallelism Test, (ii) Level or Separation Test, and (iii) Flatness Test. These enable us to ascertain if there is a significant trend in the mean value of the variable under study.

Let the data matrix for n observation vectors be given by

(1) |

where,

Ÿ the column represents the p variables or the same variable at p time points.

Ÿ The rows are the units (objects or subjects) upon which the measurement are carried out.

Assuming that **Y** in Equation (1.1) is partitioned into K independent groups with each group having n_{i} observations such that, then **Y** could be represented thus:

(2) |

Given a k independent groups each with n_{i} observations with *p* variables or the same variables at p time point, the null hypothesis for the test of parallelism for the k groups is given by:

Where µ_{k} is k^{th} group mean vector, and C is any (p-1)×p matrix of rank p-1 such that Cj = 0 ( i.e each row of C sums to zero). Example of such matrix thus:

(3) |

If Y are one variable at p time points and the time points are equal or approximately equal, C in Eq. (3) can be replaced with an orthogonal polynomial contrast which are often test for linear, quadratic, cubic and higher-order trend line. Example of such can be found in ^{ 12} which is given by:

(4) |

The four rows of C in Eq. (4) are orthogonal polynomial that test for linear, quadratic, cubit and quartic trend line in the mean of the profiles. ^{ 13} had shown that the test statistic for the null hypothesis (H_{01}) is given by:

(5) |

The test statistic is distributed as

Where, Λ is Wilks statistic, C is contrast matrix given in Eq. (3), λ_{i} is i^{th }eigen values of the matrix

(6) |

(7) |

Besides the test statistic given in Eq. (5), other equivalent multivariate test statistic that can achieve the purpose can be derived using the Eigen value of the matrix . Three of such test statistic are:

(8) |

(9) |

(10) |

For k profiles (groups) the null hypothesis for testing difference in mean level is stated thus:

Where, µ_{i }is i^{th} group mean vector and J is an identity vector.

The test statistic is given by:

(11) |

Where E and H retain its definition in Eq. (6) and Eq. (7), while j is an identity vector. The test statistic in (11) has a relationship with the other equivalent test as shown in Eq. (8), Eq. (9) and Eq. (10), and the rejection of the null hypothesis (H_{02}) would suggest a significant mean difference.

To examine if there is a significant trend in the mean level within the year under review, the null hypothesis is stated thus:

Where, C retain its meaning in Eq. (3) or Eq. (4), µ_{k} is the k^{th} group mean vector and k is the number of groups.

The test statistic for the hypothesis (H_{03}) is given by:

(12) |

Where, T^{2} is the Hotelling test statistic, K is the number of groups, n is the number of observations,is the estimate of the ground mean for the entire groups (µ) and the estimate of the pooled variance (**Σ**). C and E retain its definition in equations Eq. (3) or Eq. (4) and Eq. (5) respectively. The test statistic in equation (11) is distributed with . Using the C in (1.4) will enable us to detect the pattern of the trend line that most appropriately fits that study data.

As in a univariate case where we can formally test the null hypothesis that the mean of our observations are equivalent, same can be performed in a multivariate profile analysis using the Hotelling’s T^{2} test. Literatures have identified two basic hypotheses to be tested in this case. The first is the null hypothesis that the ratio of mean over a hypothesized means is equal to one, and the second is, the null hypothesis that these ratios are the same. The second is mostly important when the first is rejected. This test start by assuming the vector of means is equal to a hypothesized one, i.e

Thus, the first hypothesis is equivalent to testing the null hypothesis

Rejection of this hypothesis implies that at least one of the ratios is not equal to one thereby leading to testing of a second one which is equivalent to testing the null hypothesis

To carry out these two tests, as in ^{ 10}, the differences between successive ratios are computed. Let this ratio be represented by for each observation, thus, testing the null hypothesis that all the ratios are equal to one another is same as testing the null hypothesis that all mean differences are equal to zero. That is,

The Hotteling T^{2} is then applied to this test. Details on Hotelling T^{2} test is given in ^{ 12}.

This section presents the results of analysis and discussion under various sub-headings for age specific fertility rate (ASFR) collected for Urban and Rural areas over three time periods (2003, 2008, 2013), total fertility rate (TFR) and Mean number of children ever born (MNCEB) collected for the six geopolitical zones of Nigeria over three time periods (2003, 2008, 2013).

Table 2 and Table 3 present significant values for various hypothesis tested. Except for the ASFR_URBAN, other datasets had results that led to rejection of the null hypothesis In essence, only ASFR for the urban residence had ratio of means over hypothesize mean value equal to one. Thus, the null hypothesis was not rejected in the case of ASFR_URBAN. Consequent upon the rejection of in the datasets (excluding ASFR_URBAN), was tested. Results in third column of Table 2 showed that was rejected in the case of TFR for South-East, South-South and North-East and MNCEB for North-Central, North-East and South-South. Thus, for these datasets, rejection of the both and could be an indication that the TFR and MNCEB values for these zones are significantly different from both each other and some hypothesized values. Reasons for this may not be far from those identified in the introduction.

**Figure 2**. Profile plot of TFR for the six geopolitical zones observed over three periods (1=North-Central, 2=North-East, 3=North-West, 4=South-West, 5=South-South, 6=South-West)

**Figure 3**. Profile plot of MNCEB for the six geopolitical zones observed over three periods (1=North-Central, 2=North-East, 3=North-West, 4=South-West, 5=South-South, 6=South-West)

In Table 3, testing for parallelism of ASFR gave evidence for non-rejection of the null hypothesis of parallelism, thus, there is no significant interaction between group memberships and the time points. ASFR may not be associated to residency (Rural or Urban) with respect to the various years considered. Same was the case for TFR in which situation we infer that TFR also is not associated with residency (geopolitical zone) over the years considered. For the MNCEB, test statistics gave different values in which case none presented enough evidence that could warrant rejection of the null hypothesis of parallelism. Profile plots presented in Figure 1, Figure 2, and Figure 3 further buttress the result of test for parallelism. For each plot, the lines are clearly seen parallel to each other over the three time points for the various residencies, as such, ASFR, TFR and MNCEB collected and analyzed has shown independence with respect to years and residency.

Testing for equality of levels showed that for ASFR, the null hypothesis of equal levels is not rejected implying that the group (residency) levels are not significantly different from another. But for TFR and MNCEB, the null hypothesis of equal levels was rejected, an indication that there is significant difference in TFR and MNCEB over the various geopolitical zones. It suffices to say that, there is a significant difference in the means of TFR and MNCEB for the various geopolitical zones of Nigeria. Differences and variations in vital statistics across regions as shown by the results obtained in this study informs a need to further identify why the differences.

In testing for flatness given that the profiles are parallel, the null hypothesis of flatness is not rejected for ASFR. For TFR, the null hypothesis of flatness was rejected while MNCEB fail to produce enough strong evidence as to reject the null hypothesis of flatness. Thus, within each residency (Rural and Urban), there is no difference between mean response of ASFR. In each of the geopolitical zones, average TFR is shown to exhibit differences while MNCEB does not.

[1] | Liu, J.E., Chai, L., and Xu., Z.N, “Forecast of China population under different fertility policy”. Open Journal of Social Sciences, 7(4), 213-229. 2016. | ||

In article | View Article | ||

[2] | Adogu, P., Udigwe, I., Udigwe, G., and Ubajaka, G, “Review of problems of adolescent sexual behavior and the role of millennium development goals 4, 5 and 6 in Nigeria”. International Journal of Clinical Medicine, 15(5), 940-948. 2014. | ||

In article | View Article | ||

[3] | Bongaarts, J, “A framework for analyzingthe proximate determinants of fertility”.Population and Development Review, 1(4), 105-132. 1978. | ||

In article | View Article | ||

[4] | Loubaki, D, “Marriages, polygamous, early fertility and development in Congo”. Journal of Human Resource and Sustainability Studies, 3(5), 193-213. 2017. | ||

In article | View Article | ||

[5] | Population Reference Bureau, World Population Data Sheet of the Population. 2018. Available: http://www.dhsprogram.com. | ||

In article | |||

[6] | Ding, C.S, “Profile analysis: multidimensional scaling approach”. Practical Assessment, Research and Evaluation, 7(16), 1-6. 2001. | ||

In article | |||

[7] | Konald, T.R., Glutting, J.J., McDermott, P.A., Kush, J.C., and Watkins., M.M, “Structure and diagnostic benefits of a normative subtest taxonomy developed from the WIS-II standardization sample.” Journal of School of Psychology, 1(37), 29-48. 1999. | ||

In article | View Article | ||

[8] | Moses, J.A., and Pritchard, D.A, “Model profiles for the wechsler adult intelligence scale-revised”. Archives of Clinical Neuropsychology, 1(11), 61-68. 1996. | ||

In article | View Article | ||

[9] | Davison, M.L., Kim, S.K., and Close, C.W, “Factor analytic modeling of within person variation in score profiles”. Multivariate Behavioral Research5(44), 668-687. 2009. | ||

In article | View Article | ||

[10] | Bulut, O, Between-person and within-person subscore reliability: comparison of unidimensional and multidimensional IRT models. (Ph.D thesis). University of Minnesota. 2013. | ||

In article | |||

[11] | Davison, M.L., and Davenport, E.C, “Identifying criterion-related patterns of predictor scores using multiple regression”. Psychological Methods, 7(4), 468-484. 2002. | ||

In article | View Article PubMed | ||

[12] | Rencher, A.C, Methods of Multivariate Analysis. Second Edition. USA: Wiley. 2002. | ||

In article | View Article | ||

[13] | National Population Commission Nigeria Demographic and Health Survey. 2003. Available http://www.dhsprogram.com. | ||

In article | |||

[14] | National Population Commission (2008). Nigeria Demographic and Health Survey. 2008. Available http://www.dhsprogram.com. | ||

In article | |||

[15] | National Population Commission, Nigeria Demographic and Health Survey. 2013. Available http://www.dhsprogram.com. | ||

In article | |||

Published with license by Science and Education Publishing, Copyright © 2019 Chijioke J. Nweke, George C. Mbaeyi, Kelechi C. Ojide and Chukwunenye I. Okonkwo

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

Chijioke J. Nweke, George C. Mbaeyi, Kelechi C. Ojide, Chukwunenye I. Okonkwo. Fertility Level, Trend and Differentials in Nigeria: A Multivariate Analysis Approach. *American Journal of Applied Mathematics and Statistics*. Vol. 7, No. 6, 2019, pp 231-236. http://pubs.sciepub.com/ajams/7/6/5

Nweke, Chijioke J., et al. "Fertility Level, Trend and Differentials in Nigeria: A Multivariate Analysis Approach." *American Journal of Applied Mathematics and Statistics* 7.6 (2019): 231-236.

Nweke, C. J. , Mbaeyi, G. C. , Ojide, K. C. , & Okonkwo, C. I. (2019). Fertility Level, Trend and Differentials in Nigeria: A Multivariate Analysis Approach. *American Journal of Applied Mathematics and Statistics*, *7*(6), 231-236.

Nweke, Chijioke J., George C. Mbaeyi, Kelechi C. Ojide, and Chukwunenye I. Okonkwo. "Fertility Level, Trend and Differentials in Nigeria: A Multivariate Analysis Approach." *American Journal of Applied Mathematics and Statistics* 7, no. 6 (2019): 231-236.

Share

[1] | Liu, J.E., Chai, L., and Xu., Z.N, “Forecast of China population under different fertility policy”. Open Journal of Social Sciences, 7(4), 213-229. 2016. | ||

In article | View Article | ||

[2] | Adogu, P., Udigwe, I., Udigwe, G., and Ubajaka, G, “Review of problems of adolescent sexual behavior and the role of millennium development goals 4, 5 and 6 in Nigeria”. International Journal of Clinical Medicine, 15(5), 940-948. 2014. | ||

In article | View Article | ||

[3] | Bongaarts, J, “A framework for analyzingthe proximate determinants of fertility”.Population and Development Review, 1(4), 105-132. 1978. | ||

In article | View Article | ||

[4] | Loubaki, D, “Marriages, polygamous, early fertility and development in Congo”. Journal of Human Resource and Sustainability Studies, 3(5), 193-213. 2017. | ||

In article | View Article | ||

[5] | Population Reference Bureau, World Population Data Sheet of the Population. 2018. Available: http://www.dhsprogram.com. | ||

In article | |||

[6] | Ding, C.S, “Profile analysis: multidimensional scaling approach”. Practical Assessment, Research and Evaluation, 7(16), 1-6. 2001. | ||

In article | |||

[7] | Konald, T.R., Glutting, J.J., McDermott, P.A., Kush, J.C., and Watkins., M.M, “Structure and diagnostic benefits of a normative subtest taxonomy developed from the WIS-II standardization sample.” Journal of School of Psychology, 1(37), 29-48. 1999. | ||

In article | View Article | ||

[8] | Moses, J.A., and Pritchard, D.A, “Model profiles for the wechsler adult intelligence scale-revised”. Archives of Clinical Neuropsychology, 1(11), 61-68. 1996. | ||

In article | View Article | ||

[9] | Davison, M.L., Kim, S.K., and Close, C.W, “Factor analytic modeling of within person variation in score profiles”. Multivariate Behavioral Research5(44), 668-687. 2009. | ||

In article | View Article | ||

[10] | Bulut, O, Between-person and within-person subscore reliability: comparison of unidimensional and multidimensional IRT models. (Ph.D thesis). University of Minnesota. 2013. | ||

In article | |||

[11] | Davison, M.L., and Davenport, E.C, “Identifying criterion-related patterns of predictor scores using multiple regression”. Psychological Methods, 7(4), 468-484. 2002. | ||

In article | View Article PubMed | ||

[12] | Rencher, A.C, Methods of Multivariate Analysis. Second Edition. USA: Wiley. 2002. | ||

In article | View Article | ||

[13] | National Population Commission Nigeria Demographic and Health Survey. 2003. Available http://www.dhsprogram.com. | ||

In article | |||

[14] | National Population Commission (2008). Nigeria Demographic and Health Survey. 2008. Available http://www.dhsprogram.com. | ||

In article | |||

[15] | National Population Commission, Nigeria Demographic and Health Survey. 2013. Available http://www.dhsprogram.com. | ||

In article | |||