Indmedica Home | About Indmedica | Medical Jobs | Advertise On Indmedica
Search Indmedica Web
Indmedica - India's premier medical portal

Indian Journal of Community Medicine

Some Factors Associated with Number of Children Ever Born in Uttar Pradesh A Comparative Results under Multiple Regression Analysis and Multilevel Analysis

Author(s): S.N. Dwivedi, S. Rajaram*

Vol. 29, No. 2 (2004-04 - 2004-06)


Research Question: Whether education of women and child survival play an important role in limiting the number of children everborn.

Objectives: To study the factors associated with the number of children everborn to currently married women.

Study design: Two stage sample desig : Selection of Census Enumeration Blocks (PSU's) followed by selection of household in each of the selected PSU's.

Setting: Most populous Indian State "Uttar Pradesh" covered under National Family Health Survey, 1992-93.

Participants: All currently married women of age 13 to 49 years.

Sample Size: 10,750.

Study variables: Age, marital, duration, religion, place of residence, wife's education, wife's work status, husband's education, everuse of contraception, number of child loss, type of house. source of lighting, availability of all-weather road, distance of PSU from primary school, and distance of PSU from health facility.

Outcome variable: Number of children everborn.

Statistical Analysis: Multiple regression analysis as well as multilevel analysis and related simulation analysis.

Results: More number of variables are found significantly associated with the number of children everborn under multiple regression analysis in comparison to multilevel analysis. Wife's education especially high-school and above was found to be negatively associated, where as number of child loss was found to be positively associated with the number of children everborn.

Recommendations: Improvements in women's education especially high-school and above, and in facilities regarding child survival may help in limiting number of births.

Keywords: Children everborn; Multiple regression analysis; Multilevel Analysis; National Family Health Survey; Primary Sampling Units (PSU's); Simulation

The demographic literature covers a series of article related to fertility either in relation to recent levels and trends or in relation to understanding of association factors with its various indices, for example, number of children everborn, total fertility rate, crude birth rate and so on. The importance of these types of studies is well known and documented1,2,3. The need for region specific study from time to time regarding issues having regional variation is well understood4. The purpose of this article is to study the factors associated with the number of children everborn to women in Uttar Pradesh, which is the most populous state of Indian5, 6 . The usual procedure to analyse data regarding above mentioned purpose is either to disaggregate higher level variables to the individual level and carry out the analysis at individual level; or aggregate the individual level variables to the higher level and carry out the analysis at higher level'. The first procedure does not use the assumption of independence of observations that is basic for the classical statistical techniques in particular for the multiple regression analysis. On the other hand, the second procedure throws away all the within group information which may be as much as 80% or 90% of the total variation. As a result, relations between aggregated variables are often much stronger giving distorted interpretation at individual level's . Therefore, this study deals with the results under classical procedure multiple regression analysis" as well as relatively new procedure "multilevel analysis" that takes hierarchical structure into account and make its possible to incorporate variables from all levels which leads to correct analysis and proper interpretation of the data. Also, this procedure takes into account the unobserved community effects which are unavoidable because a number of quality/behavioural characteristics may not be either available or adequately measured, particularly the behaviour as perceived by the client/community. Ignorance of this fact in the analysis may produce downward biases in the standard errors of the estimated parameters which leads to erroneous estimates of the impact of individual variables7,8,9,10. In view of above mentioned points, this article deals with comparative results under multiple regression analysis and multilevel analysis in relation to association of some factors with number of children everborn in Uttar Pradesh.

Material and Methods

Data: The data used in the present study are from the National Family Health Survey (NFHS) conducted in Uttar Pradesh in 1992-93. The sample design adopted for the NFHS is a systematic, two-stage stratified random sample of households. The NFHS is a nationally as well as state representative survey of ever married women of age 13 to 49 years. It was undertaken as the principal activity of a collaborative project to strengthen the research capabilities of the Population Research Centres (PRCs) in India. Funding for the survey was provided by the United States Agency for International Development (USAID). The Ministry of Health and Family Welfare (MOHFW), New Delhi, designated the International Institute for Population Sciences (IIPS), Mumbai, as the nodal agency for providing coordination and technical guidance to the NFHS. The East­ West Center/Macro-International, USA also provided technical assistance for all the survey operations. The main objective of the survey was to collect reliable and up-to-date information on fertility, family planning, mortality, and maternal and child health providing state-level and national estimates. Its other important objective was to provide high quality data to academicians and researchers for undertaking analytical research11.

The NFHS in Uttar-Pradesh was conducted between 10th October, 1992 and 22nd February, 1993, selecting 242 rural area Primary Sampling Units (PSU's) and 96 urban PSU's. In rural areas, the 1981 Census list of villages served as the sampling frame, and a two stage sample design was adopted with the selection of villages (PSU's) in the first stage and households in selected villages in the next stage. On the other hand, in urban areas, the list of Census Enumeration Blocks provided by the Registrar General of India for 1991 served as the sampling frame. Accordingly, a two-stage sample design was adopted: selection of Census Enumeration Blocks (PSU's), followed by selection of households in each of the selected PSU's. The households to be interviewed were selected from the household lists using systematic sampling with equal probability. On an average, in rural areas, 30 households were selected from each selected PSU with fewer than 300 households and 40 households from larger PSU's with 300 households or more. In urban areas on an average, 20 households per PSU were selected. A total of 11,438 ever-married women of age 13-49 from 10,110 households were interviewed. More details are available in the state level report for Uttar Pradesh released in October, 199412.

For the present study, a total of 10,750 currently married women of age 13 to 49 years were considered. Accordingly, a total of 10750 women were considered for the analysis. As mentioned above, number of children everborn was considered as dependent variable. Taking into account theoretical consideration as well as the results from a series of exploratory analysis, women level variables considered in the analysis were: age; duration of marriage; religion (Hindu/non-Hindu); place of residence (rural/urban); wife's education (illiterate/primary school completed/middle school completed/ high school and above); wife's work status (working/not-working); husband's education (illiterate/l-4 years-years of study/5-7 years/8-10 years/1 l years and above); ever use of contraceptive (not used/used); number of child loss (0/1/2/3 and above); type of house (kaccha/semi puccalpucca); source of lighting in house (non-electrified l electrified).

The survey, in addition to the standard set of questions on individual level socio-demographic and other variables, included questions on higher level viz., households/PSU/districtlstate. Since data at higher levels were yet to be finalized by the Macro International, available data did not allow to consider district level variables. However, PSU level data could be organized and considered in the analysis. These were: availability of all weather road in the PSU (No/Yes); distance of PSU from primary school (2 kms. and Above / less than 2 kms.) and distance of PSU from health centre (2 kms. and Above/less than 2 kms).

After much exploration with alternative forms, it was decided that these forms of the variables were more appropriate. In this study, household­level characteristics were not considered because the sample sizes within each household were too small to permit meaningful estimates.


Suppose we have data as:

J=1 J=2 J=3            
Z1 Z2 Z3            
i=1 i=2 i=3 i=1 t=2 i=1 i=2 i=3 i=4
Y11 Y21 Y31 Y12 Y22 Y13 Y23 Y33 43
X11 X21 X31 X12 X22 X13 X23 X33 X43


Yij are individual level response variable (number of children everborn); Xij are individual level predictors; and

Zj are area lever (multilevel) predictors.

Thus, data are of two level

(Yij, Xij, Zj) ; j =1, ..., Ji; i =1 ...n,.

Under ordinary multiple regression analysis, there are two choices

(a) at individual level, we could have observations:

Yij ; Xij ; Zij = Zij = Zj [same for everyone in area j] ij ll V ~.I J

Then, Yij = fn (Xij, Zij = Zj)

which is used to predict individual level number of children ever born.


(b) at area level, we look at means

1 nj 1 nj

Yj= Yij; Xj=Xij; Zj

nj i=1

Then, Yj = fn (Xj, zj)

which is used to predict area level average number of children everborn. Thus, for individual level analysis, ordinary multiple linear regression becomes:

Yij = A+b1X..+b2Zj +eij ............. (1)

Where, a is constant, b1 and b2 are the respective coefficients for each of the independent variables; and eij are random errors. The most straight forward way to estimate these parameters is ordinary least squares14,15 Under multilevel multiple regression analysis, to predict number of children everborn (Yij), we have the model 14 as follows

Yij= A + b1Xij + b2Zij + eij...................... (2)

here a is constant; bl and b2 are fixed estimated regression coefficients; and uj and eij are random errors at area and individual levels, that is uj N (0, 02) not 0.2 it's 0-2

eij - N (0, 02) not 0.2 it's 0-2

This model assumes that individuals in the same area are correlated which is not true in ordinary multiple linear regression model. This model is

As reported in Table IV, adjusted mean number of children everborn are not comparable with those reported as unadjusted. This clearly indicates the role of other variables in assessing the association of a particular factor with the mean number of children everborn. However, adjusted means reported under ordinary multiple regression were comparable with those reported under multilevel regression, which may be attributed to the fact that comparatively larger sample size was available under data analysis. These results, further, reveal that there is positive relationship between the number of child loss and number of mean children everborn. However, wife's education shows inverse relationship with the mean number of children everborn.

Table I: Mean number of children ever born by selected characteristics

Factors Mean Standard Number of
Deviation Women
Religion 3.54 2.62 8968
Non-Hindus 3.82 2.80 1782
Place of residence 3.66 2.71 8578
Urban 3.30 2.40 2172
Wife's education 3.90 2.74 8079
Primary school completed 3.16 * 2.33 1082
Middle school completed 2.60 * 2.05 617
High school and above 2.09* 1.61 972
Wife's work status 3.44 2.62 9369
Not working
Working 4.53 * 2.65 1381
Husband's education 4.27 2.87 3636
1-4 years of study 4.30 2.73 505
5-7 years of study 3.93 2.65 1418
8-10 years of study 3.13* 2.45 2997
11 ± years of study 2.67* 2.06 2194
Everuse of contraception 3.36 2.76 7933
Not used
Used 4.22* 2.21 2817
Number of child loss 2.37 1.96 6646
No loss
1 4.38 * 2.01 2186
2 5.98 * 1.93 1003
3+ 7.86 * 2.01 915
Type of house 3.75 2.73 5610
Semi-pucca 3.66 2.68 2909
Pucca 3.06 * 2.31 2231
Source of lighting 3.76 2.72 7094
Not electrified
Electrified 3.25 2.47 3656
PSU has all-weather road 3.66 2.75 5217
Yes 3.51 2.55 5533
Distance of
PSU from primary school
3.62 2.71 1200
2+ Kms.
< 2 Kms. 3.58 2.64 9550
Distance of PSU from health facility 3.69 2.68 4646
2+ Kms.
< 2 Kms. 3.50 2.62 6104
Total 3.58 2.65 10750

Table II: Estimate from multiple and multilevel regression models.

Factors Multiple
Fixed Part
Constant 0.3121 0.1184 0.3161 0.1302
Age 0.0227* 0.0062 0.0206* 0.0063
Marriage duration 0.1284* 0.0061 0.1315* 0.0062
Non-Hindus 0.5284* 0.0419 0.4500* 0.0461
Place of residence
Urban 0.0773 0.0495 0.0622 0.0648
Wife's education
Primary school -0.1044* 0.0507 -0.0775 0.0506
Middle school -0.1493* 0.0662 -0.1169 0.0661
High School and above -0.4240* 0.0659 -0.3493* 0.0671
Wife's work status
Working -0.0076 0.0389 0.0533 0.0419
Husband's education
1-4 Years -0.0338 0.0704 -0.0265 0.0702
5-7 Years 0.0333 0.0461 0.0300 0.0459
8-10 Years 0.0854* 0.0396 -0.0783* 0.0398
11+ Years -0.1753* 0.0499 -0.1615* 0.0503
Everuse of contraception
Used 0.3805* 0.0338 0.3844* 0.0341
Number of child loss
1 1.1128* 0.0380 1.0980* 0.0378
2 2.0634* 0.0541 2.0470* 0.0538
3+ 3.4031* 0.0583 3.3760* 0.0581
Type of house
Semi-pucca 0.0585 0.0349 0.0391 0.0368
Pucca -0.1022* 0.0486 -0.0918 0.0501
Source of lighting
Electrified 0.0534 0.0386 0.0375 0.0401
PSU has all-weather road
Yes 0.0043 0.0356 0.0297 0.0523
Distance of PSU from primary school
<2 Kms. 0.0091 0.0492 0.0235 0.0727
Distance of PSU from health facility
<2 Kms. -0.0377 0.0346 -0.0427 0.0516
Random Part
PSU Level (Level II) 0.0692aa 0.0107    
Individual Level (Level I) 2.0600a 0.0286    
Adj. R2 0.6955b        
-2 log likelihood 38217.2        
* Significant (p<0.05)

(a): The extent to which women's actual number of everborn children vary from those predictedby the average line for their PSU. (aa) : The variation of individual PSU's lines around the average line predicted by the fixed part of the model. (b) : Proportion of variance explained.

Table III : PSU level (Level-II) and Individual level (Level-I) variances under various multilevel models.

Multilevel models Variance
Level II Level I
age only 0.3727 3.0750
+ Marriage duration 0.2083 2.8610
+ Number of child loss 0.1279 2.0910
+ Ever use of. contraceptive 0.1362 2.0710
+Education of women 0.1145 2.0660
+Religion 0.0709 2.0630
+Work status of women 0.0732 2.0620
+ Husband's education 0.0719 2.0600
+-Type of house 0.0703 2.0600
+ Source of lighting 0.0697 2.0600
+ Place of residence 0.0693 2.0600
+ Distance of health facility 0.0692 2.0600
+All weather road availability 0.0692 2.0600
+Distance of Primary school 0.0692 2.0600

Table IV: Unadjusted and adjusted mean number of children ever born

Factors Unadjusted Adjusted
Hindu 3.54 3.47 3.48
Non-hindus 3.82 4.00 3.93
Place of residence
Rural 3.66 3.54 3.54
Urban 3.30 3.62 3.60
Wife's education
Illiterate 3.90 3.61 3.60
Primary school completed 3.16 3.46 3.48
Middle school completed 2.60 3.42 3.44
High school and above 2.09 3.17 3.24
Wife's work status
Not working 3.44 3.56 3.55
Working 4.53 3.55 3.60
Husband's education
Illiterate 4.27 3.62 3.61
1-4 Years 4.30 3.52 3.53
5-7 Years 3.93 3.53 3.53
8-10 Years 3.13 3.49 3.50
11 +Years 2.67 3.42 3.43
Everuse of contraception
Not used 3.36 3.46 3.45
Used 4.22 3.84 3.84
Number of child loss
No loss 2.37 2.85 2.85
1 4.38 4.44 4.43
2 5.98 5.43 5.41
3+ 7.86 6.67 6.64
Type of house
Kuccha 3.75 3.56 3.56
Semi-pucca 3.66 3.60 3.58
Pucca 3.06 3.48 3.48
Source of lighting
Not electrified 3.76 3.54 3.54
Electrified 3.25 3.59 3.58
PSU has all-weather road
No 3.66 3.55 3.54
Yes 3.51 3.56 3.57
Distance of PSU from primary school
2+ Kms. 3.62 3.55 3.53
< 2 Kms. 3.58 3.56 3.56
Distance of PSU from health facility
2+ Kms. 3.69 3.58 3.58
< 2 Kms. 3.50 3.54 3.54
Total 3.58 3.56 3.55

Discussion and Summary

The differential association of religion, wife's working status, everuse of contraception and number of children loss with the total number of children everborn is documented through various studies16,17. The positive association of ever use of contraception with the number of children everborn is obvious from the fact that a small proportion of couples use contraception in Uttar Pradesh. Further, majority of them go for sterilization. It is also reported that the couples who go for sterilization already had an average of four children18. Wife's education had negative association while number of child loss had positive association with the number of children everborn. These findings emphasize the importance of wife's education in reducing fertility16. Also, the positive impact of the number of child loss on number of children everborn clearly implies either unavailability of appropriate health facility or under utilization of the same. This may indicate the need of making sure that the children who are born, survive. This may encourage the couple to go for contraceptive adoption in view of spacing birth and/or limiting the births. The multivariate analysis clearly reveals that more number of factors are found significantly associated with number of children everborn under ordinary multiple regression analysis in comparison to those under multilevel regression analysis. These findings are on the lines already reported earlier 7,8,9,10Since the standard error of the coefficients under ordinary multiple regression analysis is generally underestimated, in case data has got hierarchical structure, it leads to more number of factors being reported as significantly associated14. In view of this, it is always necessary to use more appropriate procedure in data analysis taking into account the type of data being used under the study, which may provide important valid clues related to ensuing public health programs. Consideration of the value of coefficient of determination under ordinary multiple regression analysis indicates that this set of variables is adequate to explain the variation (70%) in number of children everborn. The value of log likelihood ratio under multilevel analysis also confirms this finding. In summary, improvement i n educating women especially high school and above and utilization of facilities regarding child survival may strengthen the overall performance of the family welfare programme resulting into lesser mean number of children everborn.


  1. Srinivasan K. Natural fertility and nuptiality patterns in India. In: Singh SN, Premi MK, Bhatia PS, Bose Ashish, ed, Population transition in India, Vol. 1., New Delhi; B.R. Publishing Corporation, 1989 : 171-192.
  2. Pathak KB. Some approaches to estimate levels and tempo of fertility from the data on surviving siblings. In: Singh SN, Premi MK, Bhatia PS, Bose Ashish, ed, Population transition in India, Vol. 1. New Delhi; B.R. Publishing Corporation, 1989: 305-317.
  3. Arora YL. Condition of fertility decline in India through Path Analysis. In: Singh SN, Premi MK, Bhatia PS, Bose Ashish, ed, Population transition in India, Vol. 1, New Delhi; B.R. Publishing Corporation, 1989; 353-356.
  4. Dwivedi SN. Contribution of some socio-economic variables towards explaining the level of adoption of various family planning devices in
  5. India during 1987. Demography India, 1992; 21(2): 239-245. PERFORM Survey. A final report on the performance indicators for the innovations in family planning services project-1995. The evaluation Project, Carolina Population Center, Chapel Hill, USA, 1996.
  6. Health information of India. An annual publication of the Directorate General of Health Services, Government of India 1994; ISSN 0971­ 0159.
  7. Bryk Anthony S, Raudenbush Stephen W. Hierarchical linear models Application and data Analysis Methods, New Delhi : Sage Publication, 1992.
  8. Harvey G. "Multilevel Statistical Models". London : Edward Arnold, 1995.
  9. Steele F, Diamond I. Immunization uptake in rural Bangladesh : A multilevel analysis. J. Roy. Statist. Soc. A (1996): 159 (2) : 289-299.
  10. Steele F, Diamond I, Wang D. The determinants of contraceptive use in China : A multilevel multinominal discrete hazards modelling approach. demography, 1996; 33(1) : 12-24.
  11. NFHS.: A final report of the "National Family Health Survey, 1992-93". International Institute for Population Sciences, Mumbai, India, 1995.
  12. UP-NFHS : Uttar Pradesh : National Family Health Survey 1992-93 International Institute for Population Sciences, Mumbai, India, 1994.
  13. Hennekens Charles H, Buying Julie E. Epidemiology in Medicine. Boston : Little Brown and Company, 1987.
  14. Woodhouse G. Multilevel Modelling Applications : A guide for users of MLn. London : Institute of Education, 1996.
  15. Stata Corp. Stata Statistical Software. Release 4.0. College Station, Texas Stata Corporation, 1995.
  16. Nag Moni. Alternative routes of fertility and mortality decline : A study of Kerala and Punjab. In : Singh SN, Premi MK, Bhatia PS, Bose Ashish, ed, Population transition in India, Vol. 1. New Delhi, B.R. Publication Corporation, 1989: 143-157.
  17. Gulati SC. Role of Contraception and development factors in fertility transition in the Asian Region : A cross-country analysis. In : Singh SN, Premi MK, Bhatia PS, Bose Ashish, ed, Population transition in India. Vol. l. New Delhi; B.R. Publishing Corporation, 1989 : 161-172.
  18. Pathak KB, Feeney G and Luther NY. Alternative contraceptive methods and fertility decline in India. National Family Health Survey Subject Reports, No. 7. Mumbai, USA : International Institute for Population Sciences; and Honolulu, Hawaii East-West Center, 1998 : 5-28.

Department of Biostatics, All India Institute of Medical Science, Ansari Nagar, New Delhi -110029

Access free medical resources from Wiley-Blackwell now!

About Indmedica - Conditions of Usage - Advertise On Indmedica - Contact Us

Copyright © 2005 Indmedica