Cross-sectional and longitudinal designs (child development)

 

Introduction

If developmental psychology is quintessentially the study of ‘change within organisms over time,’ then which methods should it employ? This is an old question, but is one that remains in want of a complete answer. Measuring change is very difficult for both conceptual and statistical reasons. This entry divides into four sections. The first compares cross-sectional and longitudinal designs. The second section focuses upon the latter to highlight their centrality in studying change. The third part examines the controversies that have prevented longitudinal methods from becoming more evident within developmental psychology. Finally, the fourth section briefly reviews attempts to overcome some of the interpretative problems in longitudinal research.

Cross-sectional and longitudinal studies: different beginnings, different ends

The term ‘cross-section’ is used in the biological sciences to refer to the process of cutting through one or more dimensions of an organism, usually by identifying layers of tissue types within such a section. The analogy transfers into psychology to apply to different groups within the same sample. These groupings might include divisions by gender or social class, but usually involve comparisons between different age periods. In such designs, individuals within different age groups are studied just once, and any difference on a dependent measure is attributed to the hypothesized process of change between them.

It is not difficult to criticize the cross-sectional approach. Differences between age groups reveal just that – differences – and not the process of developmental change within the child. However, there is also much to commend in the cross-sectional approach. For example, it allows us to identify the developmental issues confronting individuals within a particular age range. There is no point in undertaking a longitudinal study unless we know something about the timing of changes. Cross-sectional studies help us to identify the age-demarcated transitions during which one or more changes take place, and individual differences in the ages at which an ability is acquired. For example, several hundred cross-sectional studies over the past twenty years have identified the period around the child’s fourth birthday as the age when the false belief test is passed for the first time, suggesting that the understanding of the mind undergoes an important shift at 4 years of age. However, these age differences have led to many contrasting accounts of the nature of change.

As a number of commentators have long pointed out, the tensions between cross-sectional and longitudinal approaches have centered on deeper philosophical divisions. For example, Overton (1998) contrasts the essentialism associated with cross-sectional designs – the attempt to identify crucial causal variables – with the attempts to explore weaker causal links in the longitudinal approach.

Longitudinal research: one paradigm or many?

Two broad traditions of longitudinal research are subsumed within one methodology. Firstly, longitudinal investigations chart the dynamics of change. There are a number of possible patterns. The most simple is a linear function in which change in an individual is constant (i.e., the individual maintains her/his rank relative to others over age). More complex are functions in which there are dramatic or step-like progressions, as typified in stage models, or exponential patterns in which there is an accelerated period of change that continually slows toward an asymptote. Even more complex are U-shaped developmental trajectories in which the development of a particular function seems to disappear and then to reappear. Researchers who explore the dynamics of change in this way tend to examine the developmental function (Wohlwill, 1973), defined as the average change of a group of individuals over time. Secondly, the longitudinal approach has been used to examine individual differences and their stability over time (McCall, 1977). Such research designs are used mainly to examine issues related to personality or intelligence, but which have developmental implications in terms of whether individuals with different abilities (e.g., children with autism versus typically developing children, or preterm versus fullterm infants) develop in the same way and at equivalent rates.

Baltes & Nesselroade (1979) suggested five fundamental goals of longitudinal research. The first three are to identify and describe the key developmental trends: (1) change within individuals; (2) differences between individuals in their patterns of change; (3) interrelationships between the factors that change in development. The final two are about the determinants of change and analyze (4) the causes of change within individuals; (5) the causes of changes in individual differences. Goals 4 and 5 are the gold standard of longitudinal research, but they are hard to realize. An additional goal is whether individual differences in one domain of functioning predict those in another domain (Schneider, 1993).

Issues in longitudinal research

That longitudinal data require repeated measures imposes practical constraints. To begin with, it is necessarily costly, in that it involves research time and efforts to collect data. This could be solved by reducing the sample or the number of test visits required. However, most statistical techniques for longitudinal data analysis require large samples for sufficient statistical power (and this is only one of a legion of problems in conducting such research). Longitudinal studies, particularly those which cover greater periods of time, are renowned for participant attrition through mobility and morbidity. This causes massive headaches in terms of the generalizability of the research, its cost in efforts to maintain contact with the sample, and the statistical headache of coping with missing data. However, general mixed linear models provide some compensation for lost data.

Psychologists have been relatively unsophisticated about a related issue – the influence of repeated contact upon the participants and the resulting data. This has been shown in some studies to lead to Hawthorne effects (positive change), but in other projects to ‘screw you’ effects (decrements in performance), simply as a result of the researcher’s interest. Another problem concerns the equivalence of measures over time. For example, crying may not serve the same function in a

3-month-old and a 12-month-old, let alone a 4-year-old. Partly as a result, we must be cautious about the nature of correlations over time as they do not necessarily indicate causal relationships. Research I conducted with John and Elizabeth Newson (C. Lewis, Newson, & Newson, 1982) found that one of two predictors of success at national school exams at 16 and avoiding a criminal record by age 21 was reported father involvement at ages 7 and 11. However, we were at pains to point out possible explanations other than a naive belief in paternal influences (e.g., an involved father might be a marker of a closer family).

Such theoretical issues concerning correlation-causation confounds are echoed in the problems in designing statistical procedures for analyzing longitudinal data. In the 1970s, it was fashionable to analyze possible mutual forms of influence using cross-lagged correlations in which the relative strengths of variables a and b at times 1 and 2 were assessed. If, for example, the correlation of a1 and b2 was significantly stronger than that between b1 and a2, then it was thought that causal inferences could be made (Fig. 1). However, authors like Rogosa (1988) have been very critical of the assumptions behind such inferences. He points out that false statistical assumptions have to be made, and that such analyses often single out pairs of variables from a range of possible influences, thus inflating the likelihood of Type 1 errors. More importantly, they hypothesize simple causal effects, when such reciprocal influences are notoriously complex and difficult.

Recent advances have been made by means of structural equation models in which covariance matrices are explored, particularly those involving the latent factors underlying manifest variables. Rogosa (1988) was equally critical of these because they do not provide us with an analysis of the mechanisms of development. He favored more simple models that are built up by examining the growth curves for each individual followed by a broader comparison of collections of the developmental patterns across a sample.

An example of a cross-lagged correlation showing the relative influence of the two key variables upon each other over time.

Figure 1. An example of a cross-lagged correlation showing the relative influence of the two key variables upon each other over time.

Cross-sequential (.............), time-sequential (----) and cohort-sequential (—) designs. After W. K. Schaie, 1965. A general model for the study of developmental problems.

Figure 2. Cross-sequential (………….), time-sequential (—-) and cohort-sequential (—) designs. After W. K. Schaie, 1965. A general model for the study of developmental problems.  

A third issue concerns theoretical confounds that inspired so much writing on longitudinal methods in the 1960s. This is between developmental processes that are the focus of the study and three other factors: age, time of assessment, and cohort. The problem here is that these are not clearly independent of one another, and getting to the heart of developmental processes is impeded by them. Any well-designed study that charts a developmental trajectory cannot rule out the possibility of this pattern of change being a feature of this particular cohort, which itself is susceptible to unique genetic and environmental influences. The lessons to learn are that:

(1) the three other factors are not part of the causal story that the developmentalist wants to tell about changes in psychological functioning, they are just possible confounds that have to be taken into consideration;

(2) they have to be treated as non-experimental features of a research design since they cannot be manipulated. The end result is that only replication of a change in more than one population will identify a generalizable developmental effect.

Conclusions

Hoppe-Graff (1989) argues that whether and how we can observe change relies upon both one’s concept of change, and thus on the theoretical stance one takes. He claims first that only a complete theoretical account of the dynamics of change has a hope of being tested, and that the differences between cross-sectional and longitudinal designs are trivial by comparison. Others, like Rogosa (1988), contend that if longitudinal studies are to gain the advantage they must first develop closer ways of analyzing within-participant growth and development curves and subsequent comparisons of different individuals. However, such modeling processes remain relatively uncommon.

There are three shortcuts that can be used to redress the imbalance between cross-sectional and longitudinal studies. Firstly, researchers can combine cross-sectional and longitudinal designs, using techniques originally proposed to overcome the confounds between age, time, and cohort (Wohlwill, 1973). These condense the research period and allow for replication so that cohorts can be compared. Figure 2 shows these techniques in a hypothetical design in which children are studied once a year within the age period 2-6. In the cross-sequential design, represented in the dotted rectangle, the researcher starts with three cohorts and studies them at three time points, covering the age-span of 2-6 years involving 4-year-olds in each group and one comparison between two samples at ages 4-5. The problem here is that cross-age comparisons cannot fully be made. The time-sequential design, in the dashed parallelogram, is essentially three cross-sectional studies of 2- to 4-year-olds with extra longitudinal data so that 2-3 and 3-4 transitions can be explored, each in two cohorts. However, this design does not allow cohort effects to be completely explored. In the black parallelogram, the cohort-sequential design is the successive comparison of three cohorts over three years. The problem with this design is that it takes two years longer to complete, but it does allow for cohort and age effects to be untangled, at least partially. None of the designs in Figure 2 is the solution to the problems of confounds and the time limitations on research, but they can be used to good effect.

Secondly, there are ways of examining the dynamics of change. While there are various techniques, including intensive case studies, the most used is the microgenetic method (Granott & Parziale, 2002) in which a known transition phase is studied in depth and the individual is subjected to intensive trial-by-trial analysis over that period. Such research allows for the examination of an individual’s developmental trajectory, and for the possibility that different individuals reach the same end at different rates or via different routes. Indeed, some authors using this method search for the possibility that we may use a diversity of old and new skills to varying degrees when making a developmental transition (Siegler in Granott & Parziale, 2002).

The third means of condensing the longitudinal study is to carry out an intervention to effect change through training or by experimental manipulation. Where there are competing explanations for a developmental change, training studies can manipulate both sets of precursors to see whether one is more effective. As with micro-genetic studies, there is always the danger of teaching skills that do not develop spontaneously. Indeed, the term ‘microgenetic’ was coined to describe such studies, in part because the training aspect might effect change that does not spontaneously occur in development. However, the training study is an important research tool as it condenses the period in which change might occur. Studying the relationship between different types of intervention and different outcomes allows us to make theoretical claims about the nature of change in general. The bottom line is that no research technique provides all the answers, but a healthy combination of the techniques described here is the solution in most developmental studies.

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