A smoothing-based goodness-of-fit test of covariance for functional data.

Functional data methods are often applied to longitudinal data as they provide a more flexible way to capture dependence across repeated observations. However, there is no formal testing procedure to determine if functional methods are actually necessary. We propose a goodness-of-fit test for comparing parametric covariance functions against general nonparametric alternatives for both irregularly observed longitudinal data and densely observed functional data. We consider a smoothing-based test statistic and approximate its null distribution using a bootstrap procedure. We focus on testing a quadratic polynomial covariance induced by a linear mixed effects model and the method can be used to test any smooth parametric covariance function. Performance and versatility of the proposed test is illustrated through a simulation study and three data applications.

Spine and dine: A key defensive trait promotes ecological success in spiny ants.

A key focus of ecologists is explaining the origin and maintenance of morphological diversity and its association with ecological success. We investigate potential benefits and costs of a common and varied morphological trait, cuticular spines, for foraging behavior, interspecific competition, and predator-prey interactions in naturally co-occurring spiny ants (Hymenoptera: Formicidae: Polyrhachis) in an experimental setting. We expect that a defensive trait like spines might be associated with more conspicuous foraging, a greater number of workers sent out to forage, and potentially increased competitive ability. Alternatively, consistent with the ecological trade-off hypothesis, we expect that investment in spines for antipredator defense might be negatively correlated with these other ecological traits. We find little evidence for any costs to ecological traits, instead finding that species with longer spines either outperform or do not differ from species with shorter spines for all tested metrics, including resource discovery rate and foraging effort as well as competitive ability and antipredator defense. Spines appear to confer broad antipredator benefits and serve as a form of defense with undetectable costs to key ecological abilities like resource foraging and competitive ability, providing an explanation for both the ecological success of the study genus and the large number of evolutionary origins of this trait across all ants. This study also provides a rare quantitative empirical test of ecological effects related to a morphological trait in ants.

Correlation models for monitoring fetal growth.

Ultrasound growth measurements are monitored to evaluate if a fetus is growing normally compared with a defined standard chart at a specified gestational age. Using data from the Fetal Growth Longitudinal Study of the INTERGROWTH-21st project, we have modelled the longitudinal dependence of fetal head circumference, biparietal diameter, occipito-frontal diameter, abdominal circumference, and femur length using a two-stage approach. The first stage involved finding a suitable transformation of the raw fetal measurements (as the marginal distributions of ultrasound measurements were non-normal) to standardized deviations (Z-scores). In the second stage, a correlation model for a Gaussian process is fitted, yielding a correlation for any pair of observations made between 14 and 40 weeks. The correlation structure of the fetal Z-score can be used to assess whether the growth, for example, between successive measurements is satisfactory. The paper is accompanied by a Shiny application, see https://lxiao5.shinyapps.io/shinycalculator/.