Ngalinda, Innocent: Age at First Birth, Fertility, and Contraception in Tanzania 
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The aim of this section is to state the sources of the data used in the analysis and to attempt an assessment of the data quality. Secondly, the methods of analysis applied to the data are described. In the assessment of the data, standard methods of checking data quality are used. The important ones are the extent of heaping of respondent’s ages, the errors in reporting the number of births, birth history and the extent of imputed birth dates. An attempt is also made to assess the accuracy of data in reporting maternity history.
The major sources of data in this study are the Demographic and Health Surveys so far conducted in Tanzania. The first TDHS was conducted between October 1991 and March 1992 under the second phase of the Demographic and Health Survey (DHS) programme. The second TDHS was conducted between July and November 1996 under the third phase of the Demographic and Health Survey (DHS) programme.
The main objective of all two TDHSs was to collect information on fertility, family planning, and general health. The survey was planned to provide estimates for urban and rural areas and of course for the whole country. The two surveys used the 1988 census information as the basic sample frame. The reason given for the choice of the 1988 census frame was that it provided a list of enumeration areas (EAs) that had well defined boundaries and a manageable uniform size (Bureau of Statistics, 1993 and 1997). EAs were used as primary sampling units (PSUs). In each region of Tanzania, the sample was designed to be selfweighted in each region in Tanganyika (20 regions). For the case of Zanzibar, five regions were grouped into two regions for this purpose, i.e. Pemba and Unguja. In each region, the sample of the EAs was proportionally distributed according to its urban and rural size.
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All surveys used a threestage sample. The primary sampling unit were the wards or branches, EAs were systematically selected with the probability proportional to size. In the second sampling stage, two EAs per selected rural ward or branch and one EA per selected urban ward or branch were chosen with probability proportional to size. All surveys selected 357 EAs of which 95 were from urban and 262 in rural areas (Bureau of Statistics, 1996: 178). The survey involved randomly selected women at the age between 1549 in selected households. The target population of the 1991/92 and 1996 TDHS were 7,850 and 9,000 women (1549 years) with completed interviews. By assuming that not more than 20 percent of the households will be uncovered, the total sample of selected households was 9,560 in 199/92 and 9,000 in 1996. The total number of persons in the households was identified before the field work (listing).
The sampling procedure can be obtained in the analysis volume for the 1996 TDHS but mathematically, the first stage sampling was implemented by using the following relationship:
P_{1 }= (w_{h} M_{hi})/M_{h}
Where
P_{1 }= the first stage selection probability
w_{h} = the number of wards or branches selected in a particular region
M_{hi }= the measure of the size of the ith selected ward or branch
M_{h} = the measure of the size for the region under consideration.
P_{2 }= (w_{hi} M_{hij})/M_{hi}
Where
P_{2 }= the second stage selection probability
w_{hi} = the number of EAs selected in a particular ward or branch
M_{hij }= the measure of the size of the jth selected EA
M_{hi} = the measure of the size for the ward or branch under consideration.
Hence P_{3} = b/L_{hij}, where b is either 20 (urban) or 30 (rural) and L_{hij} is the number of households listed in the jth selected EA according to the final analysis of 1991/92 and 1996 TDHS.
Four types of questionnaires were used in the first survey, namely: service available questionnaire, household questionnaire, female and male questionnaires. In the second survey, all types of questionnaire were used except the service available questionnaire which was conducted as a different survey. The household questionnaire listed all usual
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residents of the household as well as visitors who slept in that house a night before the interview day. This questionnaire was used to collect socioeconomic data as well as to identify women and men eligible for the individual interview. Basic information was collected on characteristics of each person in the household including their relationship to the head of household, age, sex, educational background, and place of residence. Socioeconomic data included the source of water, type of toilet facilities, materials used for the floor of the house, and ownership of various durable items like radios, television sets, refrigerators, bicycles, motorcycles and cars. A total of 9,238 women (96 percent of the eligible women identified) aged between 15 and 49 years were successfully interviewed in the 1991/92 TDHS. The household response rate was 97.2 and individual response was 88.9 percent (Bureau of Statistics, 1993). A total of 8,900 households were selected for the 1996 TDHS sample, of which 8,141 houses were occupied at the time of the interview. The household interview was completed in 7,969 households (98 percent of occupied households). In the interviewed households, 8,501 women were identified as eligible (15 to 49 years) for individual interview. A total of 8,120 women (96 percent of the eligible women) were successfully interviewed in all 25 administrative regions of Tanzania (Bureau of Statistics, 1997).
The female questionnaire was used to collect data from women 1549 years old. Information was collected on background characteristics of a woman including reproductive history, knowledge and use of contraceptive methods, fertility preference, antenatal and delivery care. Data was also collected on sexual activities, marital status, employment status, on child survival information, breastfeeding and weaning practices, vaccinations, height, weight and the health status of children under five years. Topics like the awareness of HIV/AIDS and STDs as well as maternal mortality, female circumcision were also included.
The male questionnaire had the same features as the female questionnaire except for questions on reproductive history, maternal and child health. Approximately one third of the households were selected for the male questionnaire, out of which 2,658 eligible men for the individual interview were identified. A total number of 2,256 (85 percent of the eligible men identified) aged between 15 and 60 years were successfully interviewed. In this study we will not deal with the male questionnaire.
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The population census data will supplement the TDHS data particularly in studying fertility trends. The three Tanzanian postindependence population censuses were conducted on August 27 or 28^{<11>} in 1967, 1978 and 1988 respectively for both Tanganyika and Zanzibar. These censuses are the major source of mortality and fertility statistics in the country since registration of births and deaths is very incomplete in Tanzania. Usually the questions asked during the censuses were similar to the TDHS questions with minor modifications. Therefore, the census data are expected to be comparable with the TDHS.Major problems associated with retrospective data that could affect fertility estimates include the accuracy of the respondents’ age, reported on the individual questionnaire and the quality of birth history data. This section deals with these nonsampling errors as reported in the female questionnaire.
The age distribution of women by single years of age is given in Figure 5 , according to the information on age obtained from the female questionnaire. A common feature of such age distributions in censuses and surveys in developing countries is heaping on ages ending with 0, or 5, and to some extent those ending with even numbers. The TDHS is no exception. A marked heaping at ages ending with 0, 5, and even numbers is clearly seen. It can be observed that many women are concentrated particularly on age 16, 20, 28, 30, 32, 38, 40, 42, 45 and 48. But the heaping is not serious although one must be cautious when performing any analysis that involves women's age. The problem of heaping in particular ages can be partly reduced by grouping women in fiveyear age groups as shown in Figure 6 . It can be observed from the figure that age distortions have been smoothened to a large extent compared with Figure 5 . The percentage of women decreases consistently from age group 1519 to age group 4549.
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Figure 5: Percentage distribution of women by current age in single years
Source: calculated from 1996 TDHS
There is some evidence that interviewers ‘displaced’ women at the age of 15 and 49 outside the eligible age range (1549) presumably in order to avoid the need to interview them. The number of women at the age of 15 is substantially lower in both surveys than 14 and 16. The number of women at the age of 16 reported (488) is higher than that reported of women at age 15 (425) in 1991/92. In 1996 too, the number of respondents age 16 exceeds the number of respondents age 15 by 116. At the end of the range, the number of women aged 49 is lower than aged 50 for both surveys which indicates a deliberate move to avoid a backlog of interviewing. In the comparative study of the DHS, Rutstein and Bicego (1990) noted some similar displacements out of the eligible age range.
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Figure 6: Percentage distribution of women by fiveyear age groups
Source: calculated from 1996 TDHS
It is important to look on the completeness and accuracy of information on births as this can also be used to ascertain the quality of data. Figure 6 shows the percentage distribution of births by calendar year to ascertain if any unusual pattern exists which may indicate that births have been omitted or that the ages of children have been displaced. The percentage of surviving children with known month and year of their birth in the 1996 TDHS is 92 percent. For children who died the percentage is 82 percent, bringing the total to 90 percent (table 2).
All in all, in many surveys that include both demographic and health data for children below a specific age, age displacement is common. It is also difficult to measure the extent of displacement but the examination of the year of birth distributions of children helps to identify whether displacement is a significant problem. A close look at Figure 7 shows deficits of births in 1991 and a surplus in 1990. This could be due to a deliberate attempt by some interviewers to reduce their workload, in particular to shorten the interview by skipping the health section that contains extensive questions about children under five. This might have been possibly due to the fact that the cutoff date for asking health and breastfeeding questions was January 1991 (Bureau of Statistics, 1997).
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Figure 7: Distribution of births in calendar year
Source: calculated from 1996 TDHS
Table 1: Percentage distribution of respondents and siblings by years of birth
Year of Birth 
Respondents 
Siblings 
Before 1945 
0.0 
2.7 
194549 
3.9 
3.4 
195054 
8.1 
6.0 
195559 
9.4 
9.3 
196064 
13.4 
12.4 
196569 
16.0 
14.6 
197074 
19.8 
15.6 
1975 or later 
29.4 
36.2 
Total 
100 
100 
Lower range 
1946 
1915 
Upper range 
1981 
1996 
Median year 
1969 
1970 
Number of cases 
8,120 
47,705 
Source: calculated from 1996 TDHS
Another measure of the quality of data is to examine the percentage distribution of respondents and their siblings by year of birth. If there is no bias, the year of birth of siblings should be nearly equivalent to the year of birth of respondents overall ( Table 1 ). This table shows that the distribution of respondents and their siblings by year of birth is very similar. The median year of birth is about the same, 1969 for respondents and 1970 for siblings. This indicates that there was no serious underreporting of siblings.
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Table 2: Percentage distribution of birth with reported year and month of birth by calendar years for surviving, dead and all children
Year 
Percentage with complete birth date 

Surviving 
Dead 
Total 

1996 
98.5 
87.4 
97.4 
1995 
96.3 
88.2 
95.3 
1994 
96.0 
90.0 
95.2 
1993 
97.3 
88.3 
96.2 
1992 
92.7 
85.1 
91.4 
1991 
92.6 
86.7 
91.7 
1990 
91.8 
81.4 
89.9 
1989 
94.7 
81.8 
92.5 
1988 
90.4 
86.8 
89.8 
1987 
92.7 
84.0 
90.9 
199296 
96.1 
87.5 
95.0 
198791 
92.4 
84.0 
90.9 
198286 
90.6 
80.2 
88.7 
197781 
88.7 
77.2 
86.6 
before 1977 
85.8 
75.4 
83.2 
All 
92.0 
81.5 
90.2 
Source: calculated from 1996 TDHS
Table 3: Mean number of children ever born by age group of women
Current age 
MNCEB 
1519 
0.23 
2024 
1.33 
2529 
2.80 
3034 
4.21 
3539 
5.46 
4044 
6.70 
4549 
7.29 
Source: calculated from 1996 TDHS
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Figure 8: Distribution of mean number of children ever born by age
Source: calculated from 1996 TDHS
A general picture of the coverage of the number of live births can indicate whether the information on births contains no serious errors and whether it can be used in the analysis. This can be obtained by looking at the average number of children ever born by fiveyear age groups of women. Figure 8 shows that the mean number of children ever born increases monotonically with age, even at older ages where memory lapse is expected to be higher.
The information on the age at first birth of a respondent is obtained by subtracting the respondent’s date of birth from the date of birth of her first child can be used to asses the quality of data. This is due to the fact that the accuracy of information on the age at first birth depends on the accuracy of the information of the respondent’s birth date and the date of birth of her first child.
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Table 4: Percentage distribution of mothers by completeness of information on date of first birth by age group
Broad age groups of respondents 
Year and month reported, no imputation 
Year reported month imputed 
Age reported, year and month imputed 
No information, year and month imputed 
N 
2029 
90.8 
8.8 
0.1 
0.3 
2,921 
3039 
75.2 
23.9 
0.3 
0.6 
2,096 
4049 
58.2 
39.8 
0.2 
1.8 
1,363 
Total 
80.2 
19.0 
0.2 
0.7 
6,887 
Source: calculated from 1996 TDHS
The completeness of reporting date of first births in Tanzania is 80.2 percent. The reporting of the date of first birth is less complete among older women than among younger women. This pattern probably reflects the difficulty of recalling births that occurred many years ago and the relatively low levels of education of the older respondents (Croft, 1991). Table 4 shows a decrease in the completeness of reporting with age. 58.2 percent of women 4049 reported a complete date of their first birth compared to 90.8 percent of women age 2029. The date of first birth for older women, therefore, required more imputation than that for younger women. In the surveys conducted in subSaharan Africa, with the exception of Kenya (DHSI, II), Malawi, Namibia, Rwanda, and Zambia, more than 25 percent of first births to women aged 4049 required some imputation (Saha and Mboup, 1992).
The quality of data on the date of first birth is further examined by comparing the proportion of women who ever had given birth to a child at the time of the survey to the proportions at 5, 10, and 15 years prior to the survey. It is expected that the proportions would decrease or remain stable over time. A trend towards increasing proportions in intervals close to the survey date would indicate a tendency for older women to shift the date of first birth further back in time than it really occurred, assuming that there has been no differential omission of first births by age group.
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Table 5: Percentage of women who had their first birth at ages 1519 and 2024 for selected years prior to the 1996 TDHS
Years prior to the 1996 TDHS 
0 
5 
10 
15 
Age at first birth 
Percentage of women 

1519 
23.2 
23.8 
27.5 
34.4 
2024 
75.7 
75.5 
79.5 
81.6 
Source: calculated from 1996 TDHS
The proportion of women having a first birth at age 1519 decreases steadily from groups with longer time intervals to those with smaller time intervals between this age and the time of the interview. However, there is a slightly higher proportion of women who have ever given birth in the age group 2024 at the time of the survey than at the fifth year preceding the survey, which is also an indication of displacement or omission errors.
It is expected that the median age at first birth would either remain stable or increase from the older to the younger age groups, with the expansion in female education over time. The measurement of the time of first births may be affected by errors in the reporting of the date of the birth of the respondent or her oldest child, or by the omission of the first birth, especially for those who died at an early age. These reporting errors might be more prevalent among older women and might lead, in some cases, to an apparent increase of age at first birth. Figure 8 shows that the trimean age at first birth for the age group 4549 is 0.5 years higher than the trimean for women age 4044. This is an indication that there was some degree of forward displacement of the date of first birth or an omission of first births of children who died in early infancy among the oldest cohort.
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Figure 9: Mean age at first intercourse, first marriage, and first birth by current age
Source: calculated from 1996 TDHS
Figure 9 also show the trimean for age at first sexual intercourse, marriage and birth for successive cohorts of women in the 1996 TDHS. The patterns of these indicators show the same trend of increase in the age group 2024 and a stability or a slight decrease in older ages. The pattern in age at first birth indicates that there are cases of memory lapse among older women as we expected the pattern to be decreasing as the age increases. However, some of the errors in the dating of the first birth are unavoidable in largescale retrospective surveys that are conducted in settings where there is poor knowledge and documentation of the dates of events. However, the result of age at first sexual intercourse may be affected by the sensitivity of the question. There is a lot of error in the data concerning this variable. For example, two women aged 16 are recorded as having their sexual experience at age 17, two other women who are currently 17 years are categorised as they had their first sexual intercourse at age 18. One woman in each of the ages 18, 21 and 22 seems to have started sexual intercourse one year ahead of her current age. Either the age was recorded wrongly or they gave false answers regarding this question. Therefore, caution must be exercised in using this data because of errors of recalling, heaping, and displacement.
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Most of the characteristics used in the study are duration variables measured in terms of the time elapsed before a particular event is experienced. For example, age at entry into sexual union is recorded as the time elapsed between the date of the birth of an individual woman and the date of the first sexual intercourse. However, for some individuals the time elapsed to the day of the interview may not have been sufficient for the event to occur. In these cases the information on duration has been censored by the interview.
For censored information, classic life table methods and use of current status data are found to be the most suitable analytic methods and will thus be employed for the duration analysis in Chapter 4. To show the distribution of these duration variables, the study will present a series of quartiles T_{x} i.e. the time elapsed before x percent of the persons concerned have experienced the event. The study will present T_{10}, T_{25}, T_{50}, T_{75} and T_{90} as the time elapsed before 10, 25, 50, 75 and 90 percent of the persons have experienced the event.
Trimean (T) as a summary index of birth functions will be calculated. The trimean is a more sensitive measure of location and contains some information about the shape of the distribution (Rodriguez and Hobcraft, 1980). The trimean is the weighted average of the quartiles that give twice as much weight to the median as to the other two quartiles. As a measure of central tendency the trimean, which is defined as ((T_{25} + 2*T_{50} + T_{75})/4) will be used.
In this study therefore, the life table technique takes into account the problem of truncation and censoring which can create biases in the estimates. For example since the current age of a person remains the same over a period of 12 months after the person’s birthday (complete years), there are women in the sample classified as childless although they still might give birth within the reference age. That means if the survey had been taken at a later point, a number of these previously childless women would have to be classified as mothers.
Selectivity stems from the fact that the transition from, for example marriage to first birth can only be studied for only the evermarried women at the time of the survey.
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Censoring results from the fact that at the time of the survey some of the evermarried women who have been selected for analysis have not yet had the first birth but will eventually do so. Ignoring the fact that some of these open intervals will eventually be closed would lead to serious bias. Thus the life table technique allows the study to control censoring biases.
Percentages and measure of central tendencies as well as multiple regression analysis will also be employed in this study. Multiple regression analysis is a multivariate technique which takes care of the fact that the assessment of the possible dependent variable on the independent variable encounters complications arising from influences of other variables, of which all are interrelated. It allows the study to single out the net effect of each independent variable when the impact of the variables is controlled.
The general form of a multiple regression equation is Y = +B_{1}X_{1} + B_{2}X_{2} +... + B_{n}X_{n} where Y is the estimated value of the dependent variable. While being the constant term, B_{I }is the regression coefficients for each of the independent variables X_{i} (for i = 1,2,3,...,n).
Due to the fact that in Chapter 5 we will estimate proximate determinants of fertility, it is important to elaborate the methodology used. A framework for analysing the proximate determinants of fertility was developed by Bongaarts (1978) and later elaborated by Bongaarts and Potter (1983). The framework shows that group variation in fertility is due to four main factors: the proportion of married women, practice of contraception, induced abortion, and the period of lactation infecundability. Further, the model (sometimes referred to as Bongaarts' model) has quantified the contribution of these four factors to the observed fertility level.
The general form of the Bongaarts' model is given as follows:
TFR = C_{m} x C_{c} x C_{a} x C_{i} x TF 
(3.1) 
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WhereC_{m} = index of the proportion of married women
C_{c} = index of contraception
C_{a} = index of induced abortion
C_{i} = index of postpartum infecundability
TF = total fecundity rate
TFR = observed total fertility rate
The indices take values between 0 and 1 depending on the magnitude of the fertilityinhibiting effect. The index of marriage equals 1 if all women of reproductive age are married and 0 in the absence of marriage. The index of contraception equals 1 in the absence of contraception and 0 if all fecund women use 100 percent effective contraception. If all pregnancies are interrupted, the index of induced abortion becomes 0 and in the absence of abortions the index is 1. Finally, the index of postpartum infecundability equals 1 in the absence of lactation and postpartum abstinence and 0 if the duration of infecundability is infinite. The total fecundity rate is the maximum number of children a woman can have in her reproductive years in the absence of lactation, abstinence, and contraception, and if she remains married during the entire reproductive period.
The index of the proportion of married women is calculated as the weighted average of the agespecific proportions of married women by using the formula:
C_{m} = {m(a)g(a)}/g(a) 
(3.2) 
where m(a) is the proportion of currently married among women aged a years. While g(a) is the agespecific marital fertility rate. g(a) can be computed by dividing the agespecific fertility rate by the proportion of women that is currently married in each age group.
The index of postpartum infecundability is estimated by using the formula:
C_{i} = 20/(18.5+i) 
(3.3) 
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where i is the average duration of postpartum infecundability caused by breastfeeding or postpartum abstinence. The estimate of i is taken as the sum of the postpartum amenorrhea and the portion of postpartum abstinence beyond amenorrhea. The constant 20 in equation (3.3) represents the average birth interval length (in months) if neither breastfeeding nor postpartum abstinence is practised. In the presence of breastfeeding and postpartum abstinence, the average birth interval is estimated to be 18.5 months plus the duration of postpartum infecundability.
The index of contraception is given by the equation:
C_{c} = 1.00  (1.08 x u x e) 
(3.4) 
where u is the average proportion of married women currently using contraception and e is the average contraceptive effectiveness. The value of e is computed using the weighted average of the methodspecific useeffectiveness, e(m), by the proportion of women using a given method, u(m).
By using the following formula:
e = {e(m)u(m)} / u 
(3.5) 
where u(m)=u. Bongaarts and Potter (1983) give the values of e(m) used in the computation of e. The constant 1.08 given in equation (3.4) is an adjustment for the fact that women or couples do not use contraception if they know or believe that they are sterile (Bongaarts and Potter, 1983).
The index of abortion can be computed by using the formula:
C_{a} = TFR/(TFR + b x TA) 
(3.6) 
where TA is the total abortion rate equal to the average number of induced abortions per woman at the end of the reproductive period if induced abortion rates remain at prevailing levels throughout the reproductive period. b is the number of births averted per induced abortion, which may be approximated by the equation:
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b = 0.4 (1+u) 
(3.7) 
It has been suggested that in the absence of contraception, an induced abortion averts about 0.4 births, while about 0.8 births are averted when moderately effective contraception is practised (Bongaarts and Potter, 1983). Equation (3.7) yields b=0.4 when u=0, and b=0.8 when u=1.0. Generally, the index of induced abortion can be defined as the ratio of the observed total fertility rate (TFR) to the estimated TFR without induced abortion (TFR + b x TA).
The Bongaarts' model has been very useful in estimating the proximate determinants of fertility. However several factors have been noted to affect the reliability of the estimates from this model. The reporting errors for the variables: current age, age at marriage, duration of breastfeeding, duration of postpartum abstinence, use of contraception and abortion is one of the problems that make the model give biased estimates. Obviously, this problem will not only affect the Bongaarts' model but any model that estimates the proximate determinants of fertility.
The index of the proportion of married women C_{m}, assumes that all fertility occurs within marriage or consensual union. But a substantial number of nonmarital births particularly in Africa can make the value of C_{m} fail to capture the full ‘risk’ of exposure to sexuality. In order to circumvent this problem, some analysts have introduced a variable (M_{o}) which captures the effect on the total fertility of births outside stable unions (Jolly and Gribble, 1993). That is, if __{m} captures the effect on total fertility of the observed specific union pattern under the assumption that no births occur outside unions, the product of M_{o} and __{m} gives C_{m}. It should be noted, however, that M_{o} is not a fertilityreducing parameter of the model but a correction factor for __{m}.
Another factor which usually causes a problem in applying Bongaarts' model (at least in Africa) is the failure to incorporate the incidence of induced abortion. Although the assumption that abortion is insignificant is valid in some countries, in others this assumption can create serious bias in the estimation of the model. In many African countries, induced abortion is permitted only to save a mother's life. So people practise illegal induced abortion, of which data cannot easily be collected, to terminate unwanted
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pregnancies. The extent of the problem used to be minimal, but as Justesen et al. (1992) shows, the number of induced abortions is growing very fast particularly among young and unmarried women residing in urban areas.It has been argued that Bongaarts' model produces very good estimates under the assumption of random use of contraception and induced abortion. Reinis (1992) finds that with nonrandom use of contraception, which is more likely, given that women tend to use contraception depending on their familybuilding plans, the estimates produced (except for C_{i}) are less accurate. For instance, if the use of contraception is concentrated at the later ages, C_{c} is a poor estimator of the fertilityreducing impact of contraception because women who have become sterile dominate use. Reinis (1992) has concluded that the Bongaarts' model performs poorly when women use contraception to stop rather than to space births, when there is delayed marriage, and when contraceptive use is most prevalent at the oldest ages. These problems, however, seem to be minimal in a country like Tanzania where women use contraception at all ages and mainly for spacing purposes.
Logistic regression, also called logit regression is used when the response variable may be quantitative, categorical, or a mixture of the two.
In a study of determinants of contraceptive use, for example, the response variable may be use or nonuse of contraception at the time of the survey. In a situation like this, the standard multiple regression analysis becomes inappropriate as the response and predictors cannot be related through a linear relationship. One important method that can be used in such a situation is logistic regression. Logistic regression has been widely used in a functional relationship where the response variable is categorical, often either a success or failure.
Suppose that y_{i} is a binomial random variable, with n_{i} trials, and with a probability of success on any trial equal to _{i} (with 0_{i}1 unknown). In logistic regression, we model _{i} as a functional form relating _{i }to X_{i} known to be Sshaped (Weisberg, 1985). This can be done by using the logit transformation of _{i}, defined to be
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logit (_{i}) = ln[_{i}/(1_{i})] 
(3.8) 
The logit is the logarithm of the odds of success, the ratio of the probability of success to the probability of failure. The properties of the logit function include:
The logistic regression model can then be expressed in two equivalent ways. First, we can fit a linear model in the logit scale,
logit (_{i}) = ß_{0} + ß_{1}X_{i} 
(3.9) 
solving (3.9)for i, using (3.8), we get the form
(y_{i}/n_{i}) = _{i} = exp(ß_{0} + ß_{1}X_{i}) / 1 + exp(ß_{0} + ß_{1}X_{i}) 
(3.10) 
Equation (3.10) expresses the model as an Sshaped curve in the original probability scale. It can be noted also that equation (3.9) and (3.10) are equivalent.
In logistic regression, the deviance is useful in some goodness of fit tests, and changes in deviance between various models are used in significance testing. The deviance is defined as

(3.11) 
with N degrees of freedom, where is the number of ß in the linear form and N is number of binomials. To compare two nested models, compute the changes in deviance and degree of freedom, compare the results with the pvalue of the chisquare distribution.
Retherford and Choe (1993) have shown that the most convenient way to present the effects of the predictor variables on the response variable in multinomial logit
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regression is in the form of a Multiple Classification Analysis (MCA) table. This section reproduces (from Retherford and Choe, 1993) the procedure used to construct an MCA table by using an example of a response variable with three categories and two predictor variables.
Suppose that the response variable is unmet need for family planning:
P_{1} = estimated probability of having unmet need for spacing births
P_{2} = estimated probability of having unmet need for limiting births
P_{3} = estimated probability of having a met need (that is, no unmet need).
Suppose also that the predictor variables are education (low, medium and high) and ethnicity (Indian and Fiji):
M: 1 if medium education, 0 otherwise
H: 1 if high education, 0 otherwise
I: 1 if Indian, 0 otherwise
The interest is to examine how education and ethnicity influence unmet need for family planning. The multinomial logit model then consists of two equations plus a constraint:
log (P_{1}/P_{3}) = a_{1} + b_{1}M + c_{1}H + d_{1}I 
(3.12) 
log (P_{2}/P_{3}) = a_{2} + b_{2}M + c_{2}H + d_{2}I 
(3.13) 
P_{1} + P_{2} + P_{3} = 1 
(3.14) 
where a_{1}, b_{1}, c_{1}, d_{1}, a_{2}, b_{2}, c_{2}, and d_{2} are coefficients.
Equations (3.12) and (3.13) can be written as
P_{1} = P_{3} exp(a_{1} + b_{1}M + c_{1}H + d_{1}I) 
(3.15) 
P_{2} = P_{3} exp(a_{2} + b_{2}M + c_{2}H + d_{2}I) 
(3.16) 
Also, we have the identity
P_{3} = P_{3} 
(3.17) 
Recall that P_{1} + P_{2} + P_{3} = 1, we get
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1 = P_{3} {exp(a_{j} + b_{j}M + c_{j}H + d_{j}I) + P_{3} 
(3.18) 
Solving (3.18) for P_{3}, we obtain
P_{3} = 1 / 1 + {exp(a_{j} + b_{j}M + c_{j}H + d_{j}I)} 
(3.19) 
Substituting (3.19) into (3.15) and (3.16) and repeating (3.17), we obtain
P_{1} = exp(a_{1} + b_{1}M + c_{1}H + d_{1}I)/1 + {exp(a_{j} + b_{j}M + c_{j}H + d_{j}I)} 
(3.20) 
P_{2} = exp(a_{2} + b_{2}M + c_{2}H + d_{2}I)/1 + {exp(a_{j} + b_{j}M + c_{j}H + d_{j}I)} 
(3.21) 
P_{3} = 1/1 + {exp(a_{j} + b_{j}M + c_{j}H + d_{j}I)} 
(3.22) 
where the summations range from j=1 to j=2.
Equation (3.20), (3.21), and (3.22) are calculation formulae for P_{1}, P_{2}, and P_{3} respectively. A shortcut for calculating P_{3} is to calculate P_{1} and P_{2} from (3.20) and (3.21) and then obtain P_{3} as 1(P_{1}+P_{2}). The MCA tables are constructed by substituting appropriate combinations of ones, zeros, and mean values in equation (3.20), (3.21), and (3.22). For example, the formulae for P_{1}, P_{2}, and P_{3} for those with high education are obtained by substituting M=0, H=1 and I=1 in (3.20), (3.21), and (3.22). The formulae for P_{1}, P_{2}, and P_{3} are obtained by substituting I=0, M=M, and H=H in (3.20), (3.21), and (3.22).
The knowledge of the socioeconomic characteristics of the respondents facilitates the interpretation of the findings in this study. Figure 10 presents the distribution of respondents by current age in two TDHSs.
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Figure 10: Percentage distribution of respondents by current age
Source: calculated from 1991/92 and 1996 TDHSs
From Figure 10 it is clear that in both surveys more than half of the interviewed population is under age 30. The respondents in this category (age 1530) are around 60 percent of the total sampled population. With a distribution of 23.6 and 21.3 percent for 1991/92 and 1996 respectively, the 1519 age group has the highest representation in the sampled population for all the surveys. But in this age group the dominant age was 16 years as Figure 5 shows. The reason for this domination was due to the fact that most of the women at age 15 might be underrepresented because the interviewers tried to avoid to include them in the sample in order to minimise workload. This sort of distribution reflects the youthful age structure of Tanzania’s population. It is well known that most of child bearing occurs between ages 15 and 34, therefore this youthful population has implications on fertility. Figure 10 also shows that 73.5 percent of the respondents are in this category, further evidence of the high representation of reproductive potentials in the TDHSs. The age group 4549 had the lowest proportion of respondents. This will affect the results of sterility as the estimation of infertility involves women who have reached their menopause. Therefore this study will have to use indirect measure of infertility.
78
Table 6: Percentage Distribution of respondents by background characteristics
Characteristics 
1991/92 
1996 
Place of residence: 


Urban 
19.9 
23.5 
Rural 
80.1 
76.5 
Education: 


No education 
33.9 
28.7 
Incomplete primary 
19.8 
19.9 
Complete primary 
41.6 
45.4 
Secondary + 
4.8 
6.0 
Religion: 


Moslem 
30.7 
31.2 
Catholic 
30.1 
31.4 
Protestant 
25.0 
25.5 
Other 
14.2 
11.8 
Marital Status: 


Never married 
24.5 
23.2 
Married 
65.4 
66.7 
Widowed 
2.9 
3.1 
Divorced 
7.3 
7.0 
Source: calculated from 1996 TDHS
As reflected in Table 6 , the majority of the respondents were found to be living in rural areas, while less than a quarter of the respondents came from urban areas. It was found in the 1988 Population Census that more than 80 percent of the population reside in rural areas, hence the TDHS surveys match well with that census result. The table further shows a recent rapid increase in the proportion of Tanzanian women living in urban areas as the proportion of female respondents residing in urban areas increased from 20 percent in 1992 to 24 percent in 1996. There has also been a slight increase in the education of women between 1992 and 1996. While 46 percent of women 1549 at the time of the 1991/92 TDHS reported that they had completed primary school or higher, it was found that 51 percent in the 1996 TDHS had completed primary education and above. The distribution of women by marital status is similar in both TDHSs.
Table 6 reveals that more than one quarter of the women in the 1996 TDHS sample (28.7 percent) has never attended school. Only 6 percent have secondary education and above. It is therefore evident that out of the women who enrol in primary school, a good number have completed seven years of schooling but most of them could not reach secondary school. Data from Trends in Demographic Family Planning, and Health Indicators in Tanzania of the Bureau of Statistics (1997) also show that there has been a
79
declining trend in the proportion of women (7 years and above) with no education from 46.1 percent in the 1991/92 TDHS to 41.7 percent in the 1996 TDHS.
The women interviewed in the survey were classified into four categories by religion as shown in Table 6 , including those who responded as none believers and traditional believers. The TDHS data suggest that the majority of Tanzanian women (56.9 percent) are Christians with the highest proportion comprising Catholics who represent 31.4 percent of the sampled population. The ‘others’ form the lowest group of all: less than 12 percent.
Table 7: Percentage distribution of women by current marital status and current age
Age group 
Never married 
Married 
Widowed 
Divorced 
Not living together 
N 
1519 
74.6 
23.2 
0.1 
1.2 
0.9 
1,732 
2024 
24.5 
67.5 
1.2 
4.5 
2.3 
1,676 
2529 
7.4 
82.2 
1.5 
6.5 
2.5 
1,440 
3034 
4.5 
84.7 
3.5 
4.8 
2.4 
1,118 
3539 
1.7 
83.3 
5.3 
8.0 
1.7 
888 
4044 
1.5 
82.5 
8.1 
5.6 
2.4 
680 
4549 
0.7 
76.5 
11.1 
7.5 
4.1 
584 
1549 
23.2 
66.7 
3.1 
4.9 
2.1 
8,119 
Source: calculated from 1996 TDHS
In this study, the terms ‘living together with a male partner’ and ‘married’ are combined and referred to as ‘currently married’. Women who are currently married, widowed, divorced or not living together are referred to as ‘ever married’. Table 6 shows that only 23.2 percent of women of child bearing age have never been married. This proportion of the never married women falls sharply from 74.6 percent in the age group 1519 to 7.4 percent in the age group 2529. It then declines to 0.7 percent in the age group 4549, reinforcing earlier findings that most women in Tanzania marry early. At the age of 25 more than 90 percent have been married ( Table 7 ). It is also evident that a large proportion of women (66.7 percent) are currently married and only a small proportion (10.1 percent) are either widowed, divorced or are not living together with male partners. The proportion of women who are currently divorced and not remarried is small (4.9 percent) indicating that in general marital unions in Tanzania seem to be stable. However, there is no consistency in the pattern of marital stability across the
80
cohorts. The striking point is the percentage of divorces in the age group 1519 (1.2 percent). We do not expect to find divorcees at this tender age. Widowhood increases steadily with age, varying from an insignificant proportion of 1.2 percent for women aged 1519 years and reaching a maximum at 26.4 percent for those aged 4549.
Table 8: Percentage distribution of adolescent women by current marital status
Age 
Never married 
Currently married 
Widowed 
Divorced 
Not living together 
N 
15 
78.8 
3.8 
0.0 
0.3 
0.0 
288 
16 
88.5 
11.0 
0.0 
0.5 
0.0 
408 
17 
80.2 
18.7 
0.0 
1.2 
0.0 
343 
18 
65.0 
33.3 
0.0 
1.1 
2.0 
354 
19 
44.5 
48.7 
0.6 
3.3 
2.7 
335 
Source: calculated from 1996 TDHS
As noticed in Table 8 , the same situation prevails with the adolescents, as the proportion of the never married adolescent women decreases with age. The proportion of the currently married increases with age, while we find widowed adolescent women already at age 19. But divorce starts as early as age 15, with 0.3 percent, and increases with age to 3.3 percent by age 19. Women who agreed to have partners but are not living together with them are found from age 18 onwards. However, these women who admitted to have partnership although not living with them under the same roof may be equated with ‘nyumba ndogo’.^{<12>}
Fußnoten:  

<11>  The choice of the date depended on the day it was Sunday around 28 of August. 
<12>  Nyumba ndogo means concubine whereby a married man secretly keeps a household with another woman. This is also a type of polygamous behaviour but in a different way. With nyumba ndogo, the ‘official’ wife does not have any knowledge of the informal wife. Usually the informal wife is younger than the formal wife. 
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