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Fish photolocomotor behavioral response (PBR) studies have become increasingly prevalent in pharmacological and toxicological research to assess the environmental impact of various chemicals. There is a need for a standard, reliable statistical method to analyze PBR data. The most common method currently used, univariate analysis of variance (ANOVA), does not account for temporal dependence in observations and leads to incomplete or unreliable conclusions. Repeated measures ANOVA, another commonly used method, has drawbacks in its interpretability for PBR study data. Because each observation is collected continuously over time, we instead consider each observation to be a function and apply functional ANOVA (FANOVA) to PBR data. Using the functional approach not only accounts for temporal dependency but also retains the full structure of the data and allows for straightforward interpretation in any subregion of the domain. Unlike the traditional univariate and repeated measures ANOVA, the FANOVA that we propose is nonparametric, requiring minimal assumptions. We demonstrate the disadvantages of univariate and repeated measures ANOVA using simulated data and show how they are overcome by applying FANOVA. We then apply one-way FANOVA to zebrafish data from a PBR study and discuss how those results can be reproduced for future PBR studies. 

Abstract Predicting dissolved oxygen (DO) in lakes is important for assessing environmental conditions as well as reducing water treatment costs. High levels of DO often precede toxic algal blooms, and low DO causes carcinogenic metals to precipitate during water treatment. Typically, DO is predicted from limited data sets using hydrodynamic modeling or data‐driven approaches like neural networks. However, functional data analysis (FDA) is also an appropriate modeling paradigm for measurements of DO taken vertically through the water column. In this analysis, we build FDA models for a set of profiles measured every 2 hours and forecast the entire DO percent saturation profile from 2 to 24 hours ahead. Functional smoothing and functional principal component analysis are applied first, followed by a vector autoregressive model to forecast the empirical functional principal component (FPC) scores. Rolling training windows adapt to seasonality, and multiple combinations of window sizes, model variables, and parameter specifications are compared using both functional and direct root mean squared error metrics. The FPC method outperforms a suite of comparison models, and including functional pH, temperature, and conductivity variables improves the longer forecasts. Finally, the FDA approach is useful for identifying unusual observations. 

Abstract The joint analysis of spatial and temporal processes poses computational challenges due to the data's high dimensionality. Furthermore, such data are commonly non-Gaussian. In this paper, we introduce a copula-based spatiotemporal model for analyzing spatiotemporal data and propose a semiparametric estimator. The proposed algorithm is computationally simple, since it models the marginal distribution and the spatiotemporal dependence separately. Instead of assuming a parametric distribution, the proposed method models the marginal distributions nonparametrically and thus offers more flexibility. The method also provides a convenient way to construct both point and interval predictions at new times and locations, based on the estimated conditional quantiles. Through a simulation study and an analysis of wind speeds observed along the border between Oregon and Washington, we show that our method produces more accurate point and interval predictions for skewed data than those based on normality assumptions.