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# Comparison of linear model and Poisson model. Note: The red line shows how expected y depends on x and how observations are distributed at x ¼ 1, 2, 3, 4, and 5 (conditional distribution). Axes show kernel density plots of x and y (unconditional distribution).

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Transforming variables before analysis or applying a transformation as a part of a generalized linear model are common practices in organizational research. Several methodological articles addressing the topic, either directly or indirectly, have been published in the recent past. In this article, we point out a few misconceptions about transformat...

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... were the most common way to apply transformations, and therefore it is important to understand what GLMs do. 2 To this end, we take linear regression, shown in the first plot of Figure 1, as a starting point. In linear regression, the mean (or more precisely, the expected value) of the dependent variable depends linearly on the independent variables, and the data are assumed to be normally distributed around the population regression line. ...
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... the distribution is a conditional distribution specified for a specific combination of independent variables, not an unconditional distribution of the dependent variable overall. In the linear regression model shown in the first plot of Figure 1, the observations are always normally distributed around the regression line. That is, if we only look at observations that have the same x value (e.g., x ¼ 1), that subset will be normally distributed (conditional distribution). ...
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... specification of a GLM involves two key decisions: choosing the link function for the relationship between the independent variable and the expected value of the dependent variable and the (conditional) distribution for the dependent variable. Importantly, the distribution concerns the conditional distribution for a specific set of predictor variables, not the unconditional distribution that one would analyze in the data preparation and screening stage of research (see Figure 1). Of these, the first decision is much more important because it determines which functional form is estimated; the second decision only influences whether the chosen form is estimated correctly. ...
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... example, fitting a parabola to a data set where y ¼ log(x) would erroneously indicate the presence of a U-shape (first up, then down, or the other way) effect. An opposite incorrect conclusion of an increasing trend could be made if y first increases gradually but then decreases steeply (Simonsohn, 2018, Figures 2, 3). We show this effect in the first panel of Figure 8, which shows a binned scatterplot and second-order polynomial curve produced by the binsreg command and an exponential curve fitted with Poisson QML regression for reference. ...
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... bands can be included to accomplish the first task (Mize, 2019). To support the chosen functional form, we recommend that researchers not only visualize the predicted curves but also indicate where their data are in the same plot (Fife, 2020), either by plotting the cases (as done in, e.g., Figure 3) or, if not possible due to their large number, by using rug and contour plots, as shown in the first plot of Figure 10. A contour plot shows which parts of the plot the observations are located in (have higher density) using a set of nested simple closed curves. ...
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... demonstrate, we add prestige as a control variable in Model 4 in Table 7, causing the effect of education to disappear. 18 The second plot of Figure 10 shows that the adjusted prediction curve does not explain the pattern in the data well. To better visualize this kind of effect, we can divide the data set into five quantiles by prestige and plot the prediction curves separately for each subsample. ...
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... linear Model 5 has a significant interaction term, whereas in the nonlinear Model 6, the interaction term is nonsignificant. Nevertheless, Figure 11 shows a clear moderation effect if absolute income is considered: The effect of education is much stronger for men-dominated occupations in both plots. It also shows why plotting the data is helpful in choosing a model: The linear model clearly extrapolates the data and underpredicts the incomes of higher education occupations, particularly those with more women, and hence does not fit as well as the nonlinear model. ...
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... reason is that in the exponential model, the effects are multiplicative instead of additive, as noted before. The lack of a significant interaction term thus does not mean a moderation effect would not exist in absolute terms (Russell & Dean, 2000); it is simply presented in an alternative form, as Figure 11 shows. Similarly, if the appropriate model for the data is an exponential model, then fitting a linear model can produce significant interactions that did not exist in the exponential model. ...
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... we interpret Figure 11 as supporting a moderation effect? Ideally, moderation hypotheses should be stated in a way that leaves no room for ambiguity (see also Gardner et al., 2017). ...
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... results shown in Table 7 and Figure 11 would not support Hypothesis 2a. Even though the absolute increase of income is greater for men-dominated occupations, the results do not demonstrate that education would increase income differently between men and women. ...

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... Common mistake: Researchers often log-transform non-negative and skewed variables to make them "more normally distributed." It is a statistical myth that variables should be log-transformed to make their distributions less skewed: what matters is correctly modeling the functional form (Rönkkö, Aalto, Tenhunen, & Aguirre-Urreta, 2022;Villadsen & Wulff, 2021b). When authors log-transform their dependent variable, they change its relationship to the covariates to comply with criteria that are largely irrelevant (non-normality of the error term is only a problem in small samples; see Wooldridge, 2002, Chapter 5). ...
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Background In acoustic telemetry studies, detection range is usually evaluated as the relationship between the probability of detecting an individual transmission and the distance between the transmitter and receiver. When investigating animal presence, however, few detections will suffice to establish an animal’s presence within a certain time frame. In this study, we assess detection range and its impacting factors with a novel approach aimed towards studies making use of binary presence/absence metrics. The probability of determining presence of an acoustic transmitter within a certain time frame is calculated as the probability of detecting a set minimum number of transmissions within that time frame. We illustrate this method for hourly and daily time bins with an extensive empirical dataset of sentinel transmissions and detections in a receiver array in a Belgian offshore wind farm. Results The accuracy and specificity of over 84% for both temporal resolutions showed the developed approach performs adequately. Using this approach, we found important differences in the predictive performance of distinct hypothetical range testing scenarios. Finally, our results demonstrated that the probability of determining presence over distance to a receiver did not solely depend on environmental and technical conditions, but would also relate to the temporal resolution of the analysis, the programmed transmitting interval and the movement behaviour of the tagged animal. The probability of determining presence differed distinctly from a single transmission’s detectability, with an increase of up to 266 m for the estimated distance at 50% detection probability ( D 50 ). Conclusion When few detections of multiple transmissions suffice to ascertain presence within a time bin, predicted range differs distinctly from the probability of detecting a single transmission within that time bin. We recommend the use of more rigorous range testing methodologies for acoustic telemetry applications where the assessment of detection range is an integral part of the study design, the data analysis and the interpretation of results.