Sideline demographic methods and data

The level of infant and child mortality is taken as indicator of health condition and also be regarded as general indicator of development of society. Decline in mortality has been quite rapid in India, but the rate of infant and child mortality is still very high. Thus, primary concern is to further reduce the level of infant as well as child mortality by exploring the high risk group. In this paper, death under age five year is termed as child death i.e. the sum of infant and child mortality. In this paper we have tried to simulate the distribution of risk of child death (p) for all parity, which can not be observed directly. Since p is affected by many factors, so it seems more logical to consider the p as a random variable and have a distribution. Beta-binomial probability distribution is considered as a model for number of child death to women for fixed parity to estimate the risk of child death. The suitability of model is checked by using National Family Health Survey (NFHS-III, 2005-06) for the two states of north India i.e. Uttar Pradesh and Bihar.

Every researcher while doing any socio demographic project or even in the censuses of many countries, especially in the developing world at an initial stage use to focus on the data quality. As per the present context of the paper, obviously age reporting error is significant to manifest either in the census or project report based on the data either from census or sample. Usually Myers’ index (1940), to a large extent, has been given in those records and reports. Sometimes Whipple’s index (1920) has also been presented in some reports. An attempt has been made to control the many kind of flaws in Myers’ method which were proposed by Bachi (1951), Ramachandran, (1965) and others at different time. The current technique solely is an exercise to show how the many defects at a single attempt and time point are eradicated by utilization of some mathematical model. The corrected Indices are then compared with the original Myers’. The disparity indices for male and female populations are then estimated by forming disparity coefficients in order to have the quantity of error committed while calculating Myers’ index and final discussion has been made.

If today Hajnal would have had to use proportions single from census data to characterize marriage regimes of countries in terms of marriage timing and intensity, he would be faced with the widespread phenomenon of non-marital cohabitation which is increasingly dissociating relationship status from legal marital status. The main objective of the paper is therefore to document how historically and currently censuses have dealt with the issue of cohabitation. To do so, we have exhaustively analyzed of 900+ census questionnaires, representing about 200 countries, covering most of the world's population from 1970 to 2010. The inventory showed that direct ways in which cohabitation is captured include using the question on marital status (e.g. common-law marriage), a separate question on consensual unions (if available) and on the relationship to the head of household (e.g. spouse). Indirect way include the presence, or existence, of own children (mainly asked to women). As the spread of cohabitation has increased the proportion single in many countries, the census measure ‘legal marital status’ is losing its validity and practical use as an indicator of union status. While some censuses now capture current cohabitation, capturing the ‘ever in cohabitation’ is still a challenge.

In the study of human fertility, the models of random length of intervals have been found to be useful in studying the dynamics of birth intervals in a better fashion and estimating certain fertility parameters of interest. Vast literature is available where modelling for duration between $i^{th}$ and $(i + 1)^{th}$ births has been done. Apart from other considerations these models assume that consecutive birth intervals are independently distributed. This assumption may be quite reasonable if the population of females is homogeneous with respect to fertility parameters involved in the model. However, if population is heterogeneous with respect to these parameters, then the consecutive intervals are likely to be dependent. In this paper, the behaviour of closed and open birth intervals under the condition of heterogeneity in the population with respect to certain fertility parameters is investigated.

In this paper, we explore the application of the Lee-Carter type models to forecast migration. The Lee-Carter model and its variants are considered to be a flexible approach to modelling age-specific mortality and fertility. However, its usefulness for forecasting migration is unknown. For application, we forecast age-specific immigration counts and emigration rates for the United Kingdom. To overcome irregularities exhibited in the sample-based migration data, we include smoothing in the model. Various specifications are presented to show the differences in predicted levels and measures of uncertainty.

Demographic events have characteristic age-specific patterns of occurrence. Finding model schedules to summarize the age-pattern of demographic rates has a long tradition, however, parametric models are predominantly used. Many demographic rates shows complex shape in their overall age-pattern. However such pattern can be attributed to different distinct components.

While some of the components can be described by a parametric model, such as the Gompertz hazard for adult mortality, many others cannot. Additional complication arises if data are provided in age groups, which is still the case in many official statistics and historical data.

In the article we propose a model that allows to specify rates across a wide range of ages as the sum of several components, which are modelled on the log scale and are assumed to be smooth, but do not have to follow a particular parametric form. A penalized composite link model is used to decompose complex trajectories into smooth additive components.

Parametric and non-parametric forms can be used. Data can be given in age-groups which can eventually be of variable lengths. Furthermore, monotonicity or shape constraints on the components can be incorporated and the model can cope with two-dimensional settings in which age-patterns change over time.

Reproduction measures were most popular between the two World Wars, before various methodological remarks produced a general negative opinion about them. Those measures were essentially developed from one-sex population models with no migration; however, since the second half of past century, immigration has become a relevant component of population change in Europe, and nowadays is the most important one in several European countries. With the acknowledged primary contribution of migration to the population dynamics, scholars have tried to incorporate its effects in the traditional reproduction measures, or they have proposed new indicators, which were then taking more a wider meaning of measures of population replacement. This study makes a comparative assessment, both analytically and empirically, of old and new measures proposed in literature. Further, it uses these demographic tools for a revision of the population replacement dynamics in Europe over the last 50 years. It is shown the similarity between some of the existing measures, as well as their different sensitivity to migration changes. A few additional measures of population replacement, variation of existing indicators, are also proposed for illustrative purposes.

Short Abstract: Age is an important variable in the anthropometric investigation of nutritional status of children. Bias and random error are common in children’s age data. We assess the effect of bias and random error in age on (i) estimates of malnutrition; and on (ii) the mortality discriminating power of age dependent anthropometric indicators. Accurate age, weight, height and mortality data were collected for 1,571 Bangladeshi children under five years of age. We introduce systematic bias and random error into the age variable and compute anthropometric indicators using both the correct original data and the data with errors. Results from different data sets are compared. Positive age bias over estimates while negative bias under estimates malnutrition. It is shown statistically and empirically in the paper that if malnutrition in the population is less than 50%, random error in age overestimates malnutrition; if it is more than 50%, it underestimates malnutrition; and if it is 50%, there will be no effect. Both bias and random error affect the mortality discriminating power of anthropometric indices. Errors in age data of young children deserve serious attention to make anthropometric investigation of young children meaningful and useful.

India’s National Family Health Survey datasets are hierarchical (subjects nested in groups) in nature. NFHS 3 datasets apart from providing information on Households and Individuals characteristics also gave information on couple’s characteristics. Couple’s dataset pose a particular challenge for statistical analysis as each group consists of two subjects’ male or female, or the hierarchy being couple/dyads. Challenge in analysing such data is that the variations may occur at the individual or dyadic level. Secondly the dyadic data are not independent, violating the assumption of independent observations. Also as the group size is small (male and female) it poses analytical challenges. Hierarchical Linear Models are used for analysing couples data using SAS PROC GLMMIX procedure. The challenge of correlated observations/response in couple’s dataset is taken care of using the GLMMIX procedure.

Short Abstract: The role of random error in age on estimate of malnutrition measured by anthropometric indicators of nutritional status for young children is not clear. This study demonstrates statistically and empirically that random error can over estimate severe malnutrition and at the same time it can underestimate severe and moderate malnutrition combined. But this depends on the level of malnutrition in the population. If malnutrition in the population is less than 50%, random error in age overestimates malnutrition; if it is more than 50%, it underestimates malnutrition; and if it is 50%, there will be no effect. Both bias and random error in age deserve attention in estimating malnutrition for young children using anthropometric indices.

**This tiny paper (having only 10 pages with statistical derivation, figures and references) is ready for submission, if needed.