Configural analysis of oscillating progression

Oscillating series of scores can be approximated with locally optimized smoothing functions. In this article, we describe how such series can be approximated with locally estimated (loess) smoothing, and how Configural Frequency Analysis (CFA) can be used to evaluate and interpret results. Loess functions are often hard to describe because they cannot be represented by just one function that has interpretable parameters. In this article, we suggest that specification of the CFA base model be based on the width of the window that is used for local curve optimization, the weight given to data points in the neighborhood of the approximated one, and by the function that is used to locally approximate observed data. CFA types indicate that more cases were found than expected from the local optimization model. CFA antitypes indicate that fewer cases were found. In a real-world data example, the development of Covid-19 diagnoses in France is analyzed for the beginning period of the pandemic.

Development of a mixture model allowing for smoothing functions of longitudinal trajectories

In the health and social sciences, two types of mixture models have been widely used by researchers to identify participants within a population with heterogeneous longitudinal trajectories: latent class growth analysis and the growth mixture model. Both methods parametrically model trajectories of individuals, and capture latent trajectory classes, using an expectation–maximization algorithm. However, parametric modeling of trajectories using polynomial functions or monotonic spline functions results in limited flexibility for modeling trajectories; as a result, group membership may not be classified accurately due to model misspecification. In this paper, we propose a smoothing mixture model allowing for smoothing functions of trajectories using a modified algorithm in the M step. Specifically, participants are reassigned to only one group for which the estimated trajectory is the most similar to the observed one; trajectories are fitted using generalized additive mixed models with smoothing functions of time within each of the resulting subsamples. The smoothing mixture model is straightforward to implement using the recently released “ gamm4” package (version 0.2–6) in R 3.5.0. It can incorporate time-varying covariates and be applied to longitudinal data with any exponential family distribution, e.g., normal, Bernoulli, and Poisson. Simulation results show favorable performance of the smoothing mixture model, when compared to latent class growth analysis and growth mixture model, in recovering highly flexible trajectories. The proposed method is illustrated by its application to body mass index data on individuals followed from adolescence to young adulthood and its relationship with incidence of cardiometabolic disease.

Improving Mouse Behaviour Assessment with Generalized Additive Modelling (GAM): The Case of the Home Cage Social Interaction Test

The Home Cage Social Interaction (HCSI) test is a standard tool for assessing locomotor activity and social behaviour in numerous mouse models of psychiatric disorders. Data obtained from this test are commonly analysed with linear modelling. However, linear modelling is unfit for HCSI data because the relation between HCSI response variables and time is cyclic rather than linear. Moreover, the response variables are commonly assumed to follow a Gaussian (normal) distribution, which is pretty much never the case with HCSI data. In brief, the statistical model currently applied to HCSI data is substantially incorrect.We thus propose to employ nonlinear modelling techniques such as General Additive Modelling (GAM) for HCSI data. GAM utilizes smoothing functions that allow for nonlinear relationships between the response variable and the covariates. Moreover, GAM enables the researcher to employ smoothing functions designed for analysing cyclic data. Finally, GAM also implements non-Gaussian exponential family distributions to meet the model’s statistical assumptions. We compare linear modelling and GAM on 27 HCSI statistically independent experiments involving wild-type and mutant mice over seven days. In all the cases, the GAM models outperform the linear models in both explained deviance and inference reliability. Most notably, the linear models tend towards Type I error with regard to the group effect and Type II error with respect to the time-by-group interaction. We thus recommend researchers to adopt the present statistical model to analyse HCSI data.

Modeling of multistage nonlinear Dual Mass Flywheel torsional damper based on smoothing function fitting

The smoothing function is used to solve the problem of low simulation efficiency of multi-stage stiffness Dual Mass Flywheel (DMF) model, and the influence of different smoothing functions and fitting factor β on the fitting effect is studied. Firstly, based on the analysis of the working principle of multi-stage stiffness DMF, a mathematical model of DMF considering multi-stage stiffness and damping nonlinearity is established, and the accuracy of the model is verified by bench test. Then, tanh function, arctangent function, and sigmoid function are used to smooth the segment points in the DMF model, which solves the problem of inefficiency and not easy to converge in simulation. Finally, a 3-DOF model of the transmission system with DMF is established to simulate and analyze the smooth effect of the smoothing function and the performance difference between different smoothing functions. The results show that the smoothing function can effectively improve the stability of the simulation model. By comparing the three smoothing functions, it can be seen that the sigmoid function has the most obvious effect, which can shorten the simulation time by 52%.

SOLVING MINERALOGY PROBLEMS WITH THE HELP OF THE “ORIGIN" PACKAGE

Algorithms for solving typical mineralogical problems associated with quantitative x-ray spectral analysis and quantitative x-ray phase analysis using the program “Origin” are developed. The calculation of the areas and midpoint of spectral lines using the tabular processor of the program “Origin” is considered. Various approaches to determining the parameters of spectral lines using the least squares method using the standard functions of the program “Origin” were tested. The creation of a user function for approximation of diffraction maxima by the Cauchy function taking into account the doublet character of Ka series of x-rays is also considered. Various built-in algorithms for smoothing functions (based on averaging, polynomial approximation and Fourier analysis – synthesis) were tested to find weak diffraction maxima against strong noise; optimal schemes for the application of these algorithms were found. The considered algorithms can be applied in universities when processing the results of laboratory works on the topics "Analysis of spectra of emission of atoms", "Quantitative x-ray spectral analysis" and "Quantitative x-ray phase analysis".

On the Smoothing of the Generalized Extreme Value Distribution Parameters Using Penalized Maximum Likelihood: A Case Study on UVB Radiation Maxima in the Mexico City Metropolitan Area

This paper concerns the use and implementation of penalized maximum likelihood procedures to fitting smoothing functions of the generalized extreme value distribution parameters to analyze spatial extreme values of ultraviolet B (UVB) radiation across the Mexico City metropolitan area in the period 2000–2018. The model was fitted using a flexible semi-parametric approach and the parameters were estimated by the penalized maximum likelihood (PML) method. In order to investigate the performance of the model as well as the estimation method in the analysis of complex nonlinear trends for UVB radiation maxima, a simulation study was conducted. The results of the simulation study showed that penalized maximum likelihood yields better regularization to the model than the maximum likelihood estimates. We estimated return levels of extreme UVB radiation events through a nonstationary extreme value model using measurements of ozone (O3), nitrogen oxides (NOx), particles of 10 μm or less in diameter (PM10), carbon monoxide (CO), relative humidity (RH) and sulfur dioxide (SO2). The deviance statistics indicated that the nonstationary generalized extreme value (GEV) model adjusted was statistically better compared to the stationary model. The estimated smoothing functions of the location parameter of the GEV distribution on the spatial plane for different periods of time reveal the existence of well-defined trends in the maxima. In the temporal plane, a presence of temporal cyclic components oscillating over a weak linear component with a negative slope is noticed, while in the spatial plane, a weak nonlinear local trend is present on a plane with a positive slope towards the west, covering the entire study area. An explicit spatial estimate of the 25-year return period revealed that the more extreme risk levels are located in the western region of the study area.