In Chapter 12 we discussed the modeling and fitting of a logistic regression equation with a dependent variable with three or more ordered categories. In this chapter we discuss the modelling and fitting of a logistic regression equation with a multi-categorical dependent variable, but here the dependent variable will have response categories that are not ordered, that is, they are nominal. The most frequently used method for estimating a nominal categorical dependent variable is the multinomial logistic regression model, the subject of this chapter. This model is a natural extension of logistic regression for a binary dependent variable.

The remains of adults present a significant challenge for age-at-death estimation and dental histology provides most of the methods used in forensic studies of teeth. This chapter critically reviews these methods, including: cement annulation, the Gustafson technique, root dentine sclerosis (transparency) and secondary dentine deposition. It ends with a discussion of the forensic context in which these are employed and questions whether or not they are up to the job required of them.

Many of the dependent variables analyzed in the social sciences involve a time period of nonoccurrence prior to their occurrence. Demographers study death; but one cannot die without being born. Thus, one’s death is preceded by a time period after the person has been born during which time they do not die. Such a dependent variable is referred to as a time-to-event variable because there must be a time period of nonoccurrence before the event occurs. Such analyses have several names. The broadest ones are survival analysis or hazard analysis, owing to their early development in biostatistics and epidemiology, where researchers modeled the occurrence of death. The event of death was referred to as a hazard. Persons over a time interval not experiencing the hazard, that is, not dying, were referred to as surviving the hazard. There are two main types of survival models, continuous-time models and discrete-time methods. We direct most of our attention in this chapter to continuous-time models of survival analysis, and specifically to the Cox proportional hazard model. In the last section of the chapter, we focus on discrete-time survival models.

Cement or cementum is at the centre of current research on the estimation of age in adult remains. Like enamel and dentine, it has a layered structure, known as annulation. These annulae or ring-like structures vary between different types of cement, found in different parts of the root, but some show a more regular spacing. Cement is laid down slowly on the surface of the root throughout life and one established idea is that these regular annulae are deposited yearly. This chapter gives a detailed description of cement structure and the evidence this provides for the changes which took place at the root surface during life.

Dentine is variably preserved, as it has a higher organic component and it is generally a more difficult tissue to work with than enamel. This chapter outlines its development and microscopic anatomy, and shows how its rhythmic pattern of development can be used to amplify the chronology built up from an analysis of enamel histology. Dentine too provides evidence for disruptions to this even progress, which can sometimes be matched with those of enamel (although not always). It also shows several changes during adult life and these accumulate to form the basis of age estimation methods. Secondary dentine formation and root dentine sclerosis (or transparency) are reviewed.

Many dependent variables analyzed in the social sciences are not continuous, but are dichotomous, with a yes/no response. A dichotomous dependent variable takes on only two values; the value 1 represents yes, and the value 0, no. The independent variables in the regression model are then used to predict whether the subjects fall into one of the two dependent variable categories. In this chapter we discuss the modeling of a dichotomous dependent variable and show why ordinary least squares regression is not appropriate. We discuss the logistic regression model. We fit a logistic regression equation and address several statistical concepts and issues: log likelihoods, the likelihood ratio chi-squared statistic, Pseudo R2, model adequacy, and statistical significance. We then discuss the interpretation of logit coefficients, odds ratios, standardized logit coefficients, and standardized odds ratios. We show how to use “margins” in the interpretation of logit models with predicted probabilities. The last sections deal with testing and evaluating nested logit models, and with comparing logit models with probit models.

This preface introduces the subject of dental anthropology and outlines the aims and structure of the book.

Each type of tooth varies considerably in size and shape. Some of these variations can be measured by simple dimensions, whilst others require digitisation of outlines and scans. One well established method is to score different features and variants by eye. This chapter introduces these approaches, compares them and discusses the way in which variation arises during development of the teeth. Differences in body size/shape and tooth size between males and females are pronounced in most primates and the evolution of the much smaller degree of such sexual dimorphism in living humans is a key area of debate. Another focus of research is the reduction in tooth size seen in hominid evolution, together with the evidence that dental morphology provides for the origins and dispersal of modern humans.

Dental tissues, together with dental calculus or tartar which builds up on the tooth surface in life, are mineral/organic composites. This chapter introduces the minerals present in the inorganic component and discusses variation in their chemistry, both through the thickness of tissue and between individual teeth. It goes on to describe the organic component, primarily a mixture of proteins and peptides. One of the main foci of research is in the field of stable isotopes, which have been used to reconstruct past human diet and mobility, dating of remains (and age-at-death for forensic cases) and the history of pollution.