Ordinary Least Squares Regression of Ordered Categorical Data: Inferential Implications for Practice

Positive public attitudes towards agricultural robots

Robot technologies could lead to radical changes in farming. But what does the public know and think about agricultural robots? Recent experience with other agricultural technologies-such as plant genetic engineering-shows that public perceptions can influence the pace and direction of innovation, so understanding perceptions and how they are formed is important. Here, we use representative data from an online survey (n = 2269) to analyze public attitudes towards crop farming robots in Germany-a country where new farming technologies are sometimes seen with skepticism. While less than half of the survey participants are aware of the use of robots in agriculture, general attitudes are mostly positive and the level of interest is high. A framing experiment suggests that the type of information provided influences attitudes. Information about possible environmental benefits increases positive perceptions more than information about possible food security and labor market effects. These insights can help design communication strategies to promote technology acceptance and sustainable innovation in agriculture.

Similarity-Based Predictive Models: Sensitivity Analysis and a Biological Application with Multi-Attributes

Predictive models based on empirical similarity are instrumental in biology and data science, where the premise is to measure the likeness of one observation with others in the same dataset. Biological datasets often encompass data that can be categorized. When using empirical similarity-based predictive models, two strategies for handling categorical covariates exist. The first strategy retains categorical covariates in their original form, applying distance measures and allocating weights to each covariate. In contrast, the second strategy creates binary variables, representing each variable level independently, and computes similarity measures solely through the Euclidean distance. This study performs a sensitivity analysis of these two strategies using computational simulations, and applies the results to a biological context. We use a linear regression model as a reference point, and consider two methods for estimating the model parameters, alongside exponential and fractional inverse similarity functions. The sensitivity is evaluated by determining the coefficient of variation of the parameter estimators across the three models as a measure of relative variability. Our results suggest that the first strategy excels over the second one in effectively dealing with categorical variables, and offers greater parsimony due to the use of fewer parameters.

Inferential implications of normalizing binomial proportions in a structural equation model: A simulation study motivated by feedlot data

Most commercial software for implementation of structural equation models (SEM) cannot explicitly accommodate outcome variables of binomial nature. As a result, SEM modeling strategies of binomial outcomes are often based on normal approximations of empirical proportions. Inferential implications of these approximations are particularly relevant to health-related outcomes. The objective of this study was to assess the inferential implications of specifying a binomial variable as an empirical proportion (%) in predictor and outcome roles in a SEM. We addressed this objective first by a simulation study, and second by a proof-of-concept data application on beef feedlot morbidity to bovine respiratory disease (BRD). We simulated data on body weight at feedlot arrival (AW), morbidity count for BRD (Mb), and average daily gain (ADG). Alternative SEMs were fitted to the simulated data. Model 1 specified a directed acyclic causal diagram with morbidity fitted as a binomial outcome (Mb) and as a proportion (Mb_p) predictor. Model 2 specified a similar causal diagram with morbidity fitted as a proportion for both outcome and predictor roles within the network. Structural parameters for Model 1 were accurately estimated based on the nominal coverage probability of 95 % confidence intervals. In turn, there was poor coverage for most morbidity-related parameters under Model 2. Both SEM models showed adequate empirical power (>80 %) to detect parameters not equal to zero. Model 1 and Model 2 produced predictions that were reasonable from a management standpoint, as determined by calculating the root mean squared error (RMSE) through cross-validation. However, interpretability of parameter estimates in Model 2 was impaired due to the model misspecification relative to the data generation. The data application fitted SEM extensions, Model 1 * and Model 2 * , to a dataset from a group of feedlots in the Midwestern US. Models 1 * and 2 * included explanatory covariates, specifically percent shrink (PS), backgrounding type (BG), and season (SEA). Lastly, we tested if AW exerted both direct and BRD-mediated indirect effects on ADG using Model 2 * . In Model 1 * , mediation was not testable due to the incomplete path from morbidity as a binomial outcome through Mb_p as a predictor to ADG. Model 2 * supported a minor morbidity-mediated mechanism between AW and ADG, though parameter estimates were not directly interpretable. Our results indicate normal approximation to a binomial disease outcome in a SEM may be a viable option for inference on mediation hypotheses and for predictive purposes, despite limitations in interpretability due to inherent model misspecification.

Spatial regression and geostatistics discourse with empirical application to precipitation data in Nigeria

In this study, we propose a robust approach to handling geo-referenced data and discuss its statistical analysis. The linear regression model has been found inappropriate in this type of study. This motivates us to redefine its error structure to incorporate the spatial components inherent in the data into the model. Therefore, four spatial models emanated from the re-definition of the error structure. We fitted the spatial and the non-spatial linear model to the precipitation data and compared their results. All the spatial models outperformed the non-spatial model. The Spatial Autoregressive with additional autoregressive error structure (SARAR) model is the most adequate among the spatial models. Furthermore, we identified the hot and cold spot locations of precipitation and their spatial distribution in the study area.

Smoothing in Ordinal Regression: An Application to Sensory Data

The so-called proportional odds assumption is popular in cumulative, ordinal regression. In practice, however, such an assumption is sometimes too restrictive. For instance, when modeling the perception of boar taint on an individual level, it turns out that, at least for some subjects, the effects of predictors (androstenone and skatole) vary between response categories. For more flexible modeling, we consider the use of a ‘smooth-effects-on-response penalty’ (SERP) as a connecting link between proportional and fully non-proportional odds models, assuming that parameters of the latter vary smoothly over response categories. The usefulness of SERP is further demonstrated through a simulation study. Besides flexible and accurate modeling, SERP also enables fitting of parameters in cases where the pure, unpenalized non-proportional odds model fails to converge.

Overwintering, Host-Plant Selection, and Insecticide Susceptibility of Systena frontalis (Coleoptera: Chrysomelidae): A Major Insect Pest of Nursery Production Systems

Systena frontalis (F.) is a major insect pest of nursery production systems in the Midwest and Northeastern regions of the United States with the adults feeding on plant leaves, which reduces salability. However, there is conflicting information on overwintering, and no information on host-plant selection or insecticide susceptibility of S. frontalis adults. Therefore, we conducted a series of experiments under greenhouse, laboratory, and field conditions from 2015 to 2019. The overwintering experiment was isolated in a greenhouse to assess adult emergence from growing medium of containerized plants collected from a wholesale nursery. We found that S. frontalis overwinters in growing medium based on adults captured on yellow sticky cards and the presence of adults on new plant growth. Host-plant selection experiments were conducted at the wholesale nursery and under laboratory conditions to determine feeding selection based on S. frontalis adult feeding damage on whole plants using a foliar damage ranking scale for different cultivars of Itea virginica L., Hydrangea paniculata Siebold, Weigela florida (Bunge), and Cornus sericea L., plants. We found that S. frontalis adults exhibited no preference for the leaves of the plant species or cultivars tested in the field or laboratory. Insecticide efficacy experiments were conducted under field and laboratory conditions. In the field experiments, the insecticides acetamiprid, dinotefuran, and Isaria fumosorosea (Wize) (Hypocreales: Clavicipitaceae) provided better protection of plants from S. frontalis adult feeding than the untreated check. In the laboratory experiments, the acetamiprid and pyrethrins with canola oil treatments provided the highest percent S. frontalis adult mortality.

Quantitative Ordinal Scale Estimates of Plant Disease Severity: Comparing Treatments Using a Proportional Odds Model

Studies in plant pathology, agronomy, and plant breeding requiring disease severity assessment often use quantitative ordinal scales (i.e., a special type of ordinal scale that uses defined numeric ranges); a frequently used example of such a scale is the Horsfall-Barratt scale. Parametric proportional odds models (POMs) may be used to analyze the ratings obtained from quantitative ordinal scales directly, without converting ratings to percent area affected using range midpoints of such scales (currently a standard procedure). Our aim was to evaluate the performance of the POM for comparing treatments using ordinal estimates of disease severity relative to two alternatives, the midpoint conversions (MCs) and nearest percent estimates (NPEs). A simulation method was implemented and the parameters of the simulation estimated using actual disease severity data from the field. The criterion for comparison of the three approaches was the power of the hypothesis test (the probability to reject the null hypothesis when it is false). Most often, NPEs had superior performance. The performance of the POM was never inferior to using the MC at severity <40%. Especially at low disease severity (≤10%), the POM was superior to using the MC method. Thus, for early onset of disease or for comparing treatments with severities <40%, the POM is preferable for analyzing disease severity data based on quantitative ordinal scales when comparing treatments and at severities >40% is equivalent to other methods.

Assigning scores for ordered categorical responses

Deciding on the best statistical method to apply when the response variable is ordinal is essential because the way the categories are ordered in the data is relevant as it could change the results of the analysis. Although the models for continuous variables have similarities to those for ordinal variables, this paper presents the advantages of the use of the ordering information on the outcomes with methods developed for modeling ordinal data such as the ordered stereotype model. The novelty of this article lies in showing the dangers of assigning equally spaced scores to ordered response categories in statistical analysis, which are illustrated with a simulation study and a case study. We propose a new way to use the score parameters, which incorporates the fitted spacing dictated by the data. Additionally, this article uses score parameter estimates in the ordered stereotype model to propose a new measure to calculate continuous medians in the raw data: the adjusted c-median. It benefits the general audience who can easily understand the median as a summary statistic. Supplementary materials for this article are available online.

Robustness of statistical methods when measure is affected by ceiling and/or floor effect

GOALS AND METHODS

A simulation study investigated how ceiling and floor effect (CFE) affect the performance of Welch's t-test, F-test, Mann-Whitney test, Kruskal-Wallis test, Scheirer-Ray-Hare-test, trimmed t-test, Bayesian t-test, and the "two one-sided tests" equivalence testing procedure. The effect of CFE on the estimate of group difference and on its confidence interval, and on Cohen's d and on its confidence interval was also evaluated. In addition, the parametric methods were applied to data transformed with log or logit function and the performance was evaluated. The notion of essential maximum from abstract measurement theory is used to formally define CFE and the principle of maximum entropy was used to derive probability distributions with essential maximum/minimum. These distributions allow the manipulation of the magnitude of CFE through a parameter. Beta, Gamma, Beta prime and Beta-binomial distributions were obtained in this way with the CFE parameter corresponding to the logarithm of the geometric mean. Wald distribution and ordered logistic regression were also included in the study due to their measure-theoretic connection to CFE, even though these models lack essential minimum/maximum. Performance in two-group, three-group and 2 × 2 factor design scenarios was investigated by fixing the group differences in terms of CFE parameter and by adjusting the base level of CFE.

RESULTS AND CONCLUSIONS

In general, bias and uncertainty increased with CFE. Most problematic were occasional instances of biased inference which became more certain and more biased as the magnitude of CFE increased. The bias affected the estimate of group difference, the estimate of Cohen's d and the decisions of the equivalence testing methods. Statistical methods worked best with transformed data, albeit this depended on the match between the choice of transformation and the type of CFE. Log transform worked well with Gamma and Beta prime distribution while logit transform worked well with Beta distribution. Rank-based tests showed best performance with discrete data, but it was demonstrated that even there a model derived with measurement-theoretic principles may show superior performance. Trimmed t-test showed poor performance. In the factor design, CFE prevented the detection of main effects as well as the detection of interaction. Irrespective of CFE, F-test misidentified main effects and interactions on multiple occasions. Five different constellations of main effect and interactions were investigated for each probability distribution, and weaknesses of each statistical method were identified and reported. As part of the discussion, the use of generalized linear models based on abstract measurement theory is recommended to counter CFE. Furthermore, the necessity of measure validation/calibration studies to obtain the necessary knowledge of CFE to design and select an appropriate statistical tool, is stressed.

Model-based goodness-of-fit tests for the ordered stereotype model

This paper presents two new model-based goodness-of-fit tests for the ordered stereotype model applied to an ordinal response variable. The proposed tests are based on the Lipsitz test, which partitions the subjects into G groups following the popular Hosmer-Lemeshow test for binary data. The tests construct an alternative model where group effects are added into the null model. If the model fits the data well then the null model is correct, and there should be no group effects. One of the main advantages of the ordered stereotype model is that it allows us to determine a new uneven spacing of the ordinal response categories, dictated by the data. The two proposed tests use this new adjusted spacing. One test uses the form of the original ordered stereotype model, and the other uses an ordinary linear model. We demonstrate the performance of both tests under a variety of scenarios. Finally, the results of the application in three examples are presented.

Conceptual framework for investigating causal effects from observational data in livestock

Understanding causal mechanisms among variables is critical to efficient management of complex biological systems such as animal agriculture production. The increasing availability of data from commercial livestock operations offers unique opportunities for attaining causal insight, despite the inherently observational nature of these data. Causal claims based on observational data are substantiated by recent theoretical and methodological developments in the rapidly evolving field of causal inference. Thus, the objectives of this review are as follows: 1) to introduce a unifying conceptual framework for investigating causal effects from observational data in livestock, 2) to illustrate its implementation in the context of the animal sciences, and 3) to discuss opportunities and challenges associated with this framework. Foundational to the proposed conceptual framework are graphical objects known as directed acyclic graphs (DAGs). As mathematical constructs and practical tools, DAGs encode putative structural mechanisms underlying causal models together with their probabilistic implications. The process of DAG elicitation and causal identification is central to any causal claims based on observational data. We further discuss necessary causal assumptions and associated limitations to causal inference. Last, we provide practical recommendations to facilitate implementation of causal inference from observational data in the context of the animal sciences.

Invited review: Reproducible research from noisy data: Revisiting key statistical principles for the animal sciences

Reproducible results define the very core of scientific integrity in modern research. Yet, legitimate concerns have been raised about the reproducibility of research findings, with important implications for the advancement of science and for public support. With statistical practice increasingly becoming an essential component of research efforts across the sciences, this review article highlights the compelling role of statistics in ensuring that research findings in the animal sciences are reproducible-in other words, able to withstand close interrogation and independent validation. Statistics set a formal framework and a practical toolbox that, when properly implemented, can recover signal from noisy data. Yet, misconceptions and misuse of statistics are recognized as top contributing factors to the reproducibility crisis. In this article, we revisit foundational statistical concepts relevant to reproducible research in the context of the animal sciences, raise awareness on common statistical misuse undermining it, and outline recommendations for statistical practice. Specifically, we emphasize a keen understanding of the data generation process throughout the research endeavor, from thoughtful experimental design and randomization, through rigorous data analysis and inference, to careful wording in communicating research results to peer scientists and society in general. We provide a detailed discussion of core concepts in experimental design, including data architecture, experimental replication, and subsampling, and elaborate on practical implications for proper elicitation of the scope of reach of research findings. For data analysis, we emphasize proper implementation of mixed models, in terms of both distributional assumptions and specification of fixed and random effects to explicitly recognize multilevel data architecture. This is critical to ensure that experimental error for treatments of interest is properly recognized and inference is correctly calibrated. Inferential misinterpretations associated with use of P-values, both significant and not, are clarified, and problems associated with error inflation due to multiple comparisons and selective reporting are illustrated. Overall, we advocate for a responsible practice of statistics in the animal sciences, with an emphasis on continuing quantitative education and interdisciplinary collaboration between animal scientists and statisticians to maximize reproducibility of research findings.