China
Africa
Explore chapters and articles related to this topic
The Many Variables & The Spurious Waffles
Published in Richard McElreath, Statistical Rethinking, 2020
The resulting plot appears in Figure 5.5. It’s easy to see from this arrangement of the simulations that the model under-predicts for States with very high divorce rates while it over-predicts for States with very low divorce rates. That’s normal. This is what regression does—it is skeptical of extreme values, so it expects regression towards the mean. But beyond this general regression to the mean, some States are very frustrating to the model, lying very far from the diagonal. I’ve labeled some points like this, including Idaho (ID) and Utah (UT), both of which have much lower divorce rates than the model expects them to have. The easiest way to label a few select points is to use identify:
Instrument evaluation
Published in C M Langton, C F Njeh, The Physical Measurement of Bone, 2016
Christopher F Njeh, Didier Hans
In interpreting data due to treatment effect, clinicians should be aware of the statistical phenomenon known as regression to the mean. Regression towards the mean occurs whenever we select an extreme group based on one variable and then measure another variable for that group. The second group mean will be closer to the mean for all subjects than the first, and the weaker the correlation between the two variables the bigger the effect will be [10]. This phenomenon is due in part to measurement error and biological variation [11]. The clinical consequence is that a subject that has demonstrated a particularly high BMD gain in the first year after treatment is likely to show a reduced increase or perhaps even a decrease in BMD in the second year. Similarly, a subject who has lost an unexpectedly large amount of bone after the first year of treatment is likely to show less of a loss, even a gain, in the second year. Over a longer period of time, the extremes will be less deviant from the mean because some of the errors of repeated measurements will smooth the results [12]. Cummings et al [13] demonstrated this effect using data from two randomized, double-blinded, placebo-control trials of alendronate and raloxifene treatment. They concluded that effective treatment for osteoporosis should not be changed because of loss of BMD during the first year of use.
Safety evaluation of variable speed limit system in British Columbia
Published in Journal of Transportation Safety & Security, 2022
Mohamed El Esawey, Joy Sengupta, John E. Babineau, Emmanuel Takyi
Typically, several factors occur simultaneously and may influence road safety performance, and therefore, the effect of these factors should be separated from the treatment effect. These factors are commonly referred to as the confounding factors and they include history, maturation, and the regression to the mean (Sayed, deLeur, & Sawalha, 2004). History refers to the possibility that factors other than the countermeasure being investigated caused all or part of the observed change in collisions. Maturation refers to the effect of collision trends over time. The regression to the mean refers to the tendency of extreme events to be followed by less extreme values, even if no change has occurred in the underlying mechanism that generates the process. The method adopted in this study corrects for the regression to the mean effects, which is an important consideration in road safety analysis by using an Empirical Bayes (EB) technique. The method uses before-and-after collision and traffic volume data to correct for the changes in traffic and collision trends over time. The method is described in detail in the Highway Safety Manual (AASHTO, 2010; Hauer, 1997; Persaud et al., 2001). The method employs Safety Performance Functions (SPFs), which are mathematical models that relate the collision frequency experienced by a road entity to various traffic and geometric characteristics of this entity. The models are developed via a generalized linear modeling approach (GLM) which assumes a non-normal distribution error structure (usually Poisson or negative binomial). In general, SPFs can be developed to predict the number of collisions per year/season or per an entire period (e.g. three years of before treatment). The utilization of annual/seasonal SPFs (i.e. opposed to period models) requires the availability of annual/seasonal data of the covariates, especially traffic volumes. One advantage of developing annual/seasonal SPFs is that it enables the use of annual/seasonal multipliers, also known as correction factors, which account for history and maturation confounding factors.