Mixed distribution analysis identifies saltation and stasis growth

A maximum likelihood method of mixed distribution analysis is investigated for its utility as a method for the identification of saltation and stasis in longitudinal growth data. Daily infant growth data that have been previously identified to follow a saltatory growth process are employed. This is a novel application of the finite mixed distribution analysis (MDA), a method designed to objectively identify the presence of one or more Gaussian populations. The null hypothesis is that a single Gaussian distribution best describes the incremental growth data. This would be compatible with smooth, slowly varying daily growth patterns. This study explores whether or not two distinctive populations are evident in incremental saltatory growth data, as postulated by the saltation and stasis observations. The analysis is important in providing a growth model-independent test for the presence of saltation and stasis by a separate statistical assessment with none of the saltatory algorithm assumptions. The finite mixed distribution analysis identifies that each individual's incremental growth data is statistically best described as a mixture consisting of two components, or two populations of increments (chi-square, p < 0.05). For each individual, one of these populations is centred about a zero increment, and is compatible with the previous evidence of stasis intervals. The second population of data points is characterized by unique distributions for each individual, compatible with the previous observation that infants grow by unique patterns of growth saltations in both amplitude and frequency. The percentage of data points that fall within each of the two unique finite mixture distributions (FMDs) is similar to the proportions of discrete saltation and stasis intervals previously identified by the saltation and stasis method. Thus, the FMD analysis lends support to the nature of growth as a saltatory process characterized by two states in the daily growth of these infants. By contrast with the saltatory algorithm, which is applied to the original serial growth measurements, the mixed distribution analysis employs increments removed from their time relationships. The lack of time series sequence information precludes the mixed distribution method from reconstructing specific temporal patterns of saltatory growth. The present analysis reiterates that individual growth patterns are statistically unique and cannot be reconstructed or identified from group data.