Comparison Of Statistical Models Research Articles

The associations between exposure to mixed environmental endocrine disruptors and sex steroid hormones in men: a comparison of different statistical models

In recent years, worldwide fertility rates have continued to decrease. Humans are frequently exposed to a combination of environmental endocrine disruptors, which can cause male reproductive disorders. The study employed three distinct analytical models to examine the correlation between exposure to a combination of 25 chemicals and sex steroid hormone levels in adult males. This involved evaluating 12 chemicals and their metabolites from personal care and consumer products, as well as 13 metabolites linked to phthalates and plasticisers. The study analysed 25 chemicals and 3 measured sex steroid hormone outcomes, as well as two calculated hormonal outcomes (free androgen index, TT/E2 ratio) in 1262 adult men who participated in the National Health and Nutrition Examination Survey (NHANES) 2013–2016 in the United States. The study employed several statistical methods to estimate the relationships between single chemicals or chemical blends and sex hormones. These methods included linear regression, weighted quantile sum (WQS) regression, and Bayesian kernel machine (BKMR) regression. The results of the linear regression analysis indicate that chemical exposure has a negative correlation with E2, TT, and FAI, and a positive correlation with SHBG and TT/E2. The mixture effect analyses using the WQS and BKMR models further confirmed that BP3, MECPP, and MECOP were the most highly weighted chemical mixtures. The analyses also suggested that there were differences in the effects of different concentrations of EDCs on sex steroid hormones. Exposure to environmental endocrine-disrupting chemicals (EDCs) has been found to have a negative correlation with estradiol and total testosterone, as well as FAI. Conversely, this exposure has been found to have a positive correlation with sex hormone binding globulin and the TT/E2 ratio. The study also revealed differences in the effects of different concentrations of EDCs.

The Multicollinearity Effect on the Performance of Machine Learning Algorithms: Case Examples in Healthcare Modelling

Background: The data extracted from various fields inherently consists of extremely correlated measurements in parallel with the exponential increase in the size of the data that need to be interpreted owing to the technological advances. This problem, called the multicollinearity, influences the performance of both statistical and machine learning algorithms. Statistical models proposed as a potential remedy to this problem have not been sufficiently evaluated in the literature. Therefore, a comprehensive comparison of statistical and machine learning models is required for addressing the multicollinearity problem. Methods: Statistical models (including Ridge, Liu, Lasso and Elastic Net regression) and the eight most important machine learning algorithms (including Cart, Knn, Mlp, MARS, Cubist, Svm, Bagging and XGBoost) are comprehensively compared by using two different healthcare datasets (including Body Fat and Cancer) having multicollinearity problem. The performance of the models is assessed through cross validation methods via root mean square error, mean absolute error and r-squared criteria. Results: The results of the study revealed that statistical models outperformed machine learning models in terms of root mean square error, mean absolute error and r-squared criteria in both training and testing performance. Particularly the Liu regression often achieved better relative performance (up to 7.60% to 46.08% for Body Fat data set and up to 1.55% to 21.53% for Cancer data set on training performance and up to 1.56% to 38.08% for Body Fat data set and up to 3.50% to 23.29% for Cancer data set on testing performance) among regression methods as well as compared to machine algorithms. Conclusions: Liu regression is mostly disregarded in the machine learning literature, but since it outperforms the most powerful and widely used machine learning algorithms, it appears to be a promising tool in almost all fields, especially for regression-based studies including data with multicollinearity problem.

Statistical Comparison of Time Series Models for Forecasting Brazilian Monthly Energy Demand Using Economic, Industrial, and Climatic Exogenous Variables

Statistical Comparison of Time Series Models for Forecasting Brazilian Monthly Energy Demand Using Economic, Industrial, and Climatic Exogenous Variables

Personality Measurement of Students Using Item Response Theory Models: Stability Responses from Nigerian Institutions

Item Response Theory (IRT) is utilised to detect bias in assessment tools and address issues such as faked or manipulated responses, enhancing the reliability and stability of conclusions in personality assessment. This article examines the item parameter estimates of a scale and the effectiveness of one-, two-, and three-parameter logistic models in analysing response stability in personality measurement from repeated administration. Three hundred undergraduate students at three tertiary institutions in Nigeria were sampled using a multi-stage sampling procedure. Data was collected using an adapted version of the Big Five Inventory (BFI) with a reliability coefficient of 0.85. The results showed that the item parameter estimates (mean threshold) are within the recommended benchmarks. A comparison of the three IRT models based on the Likelihood ratio (InL), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC) values revealed that the two-parameter logistic model best fit the personality data among undergraduates from repeated administration. It is recommended that, rather than relying solely on a statistical decision-making process, IRT fit and model comparison should be applied to gain insight into the functioning of items and tests.

Forecasting and Comparison of Nonlinear Statistical Growth Models for Fish Seed Production in Eastern Coastal States of India

The study was carried out to compare the goodness of fit of three non–linear growth models viz., Monomolecular, Logistic and Gompertz growth models and analysing the instability index among the collected fish seed Production data from the eastern costal states of Indian for the period from 1994–1995 to 2019–2020. The parameters of each model were estimated using Levenberg–Marquardt (LM) iterative method. The ‘independence’ and ‘normality’ of error terms were examined by using ‘Run–test’ and ‘Shapiro–Wilk test’. Among the three models tested, monomolecular model was found as best model to describe variation in fish seed production in all Eastern Costal States of India. The values of CDI for fish seed production were 146.94 %, 79.30 % and 63.41% respectively which revealed that fish seed production had high instability in Odisha, Tamil Nadu and Andhra Pradesh while low instability (14.93 % and 13.13%) in West Bengal and India.

Analysis of the ψ(3770)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\psi (3770)}$$\\end{document} resonance in line with unitarity and analyticity constraints

We study the inclusive and exclusive cross sections of e+e-→hadrons\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e^+e^-\\rightarrow \ ext {hadrons}$$\\end{document} for center-of-mass energies between 3.70 and 3.83GeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$3.83\\,\\,\ extrm{GeV} $$\\end{document} to infer the mass, width, and couplings of the ψ(3770)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi (3770)$$\\end{document} resonance. By using a coupled-channel K-matrix approach, we setup our analysis to respect unitarity and the analyticity properties of the underlying scattering amplitudes. We fit several models to the full dataset and identify our nominal results through a statistical model comparison. We find that, accounting for the interplay between the ψ(2S)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi (2S)$$\\end{document} and the ψ(3770)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi (3770)$$\\end{document}, no further pole is required to describe the ψ(3770)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi (3770)$$\\end{document} line shape. In particular we derive from the pole location Mψ(3770)=3778.8±0.3MeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_{\\psi (3770)}~=~3778.8~\\pm ~0.3~\\,\ extrm{MeV} $$\\end{document} and Γψ(3770)=25.0±0.5MeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varGamma _{\\psi (3770)}~=~25.0~\\pm ~0.5~\\,\ extrm{MeV} $$\\end{document}. Moreover, we find the decay to D+D-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D^+D^-$$\\end{document} and D0D¯0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D^0\\bar{D}^0$$\\end{document} to be consistent with isospin symmetry and derive an upper bound on the branching ratio B(ψ(3770)→non-DD¯)<6%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {B}}(\\psi (3770) \\rightarrow \ ext {non-}D\\bar{D}) < 6\\%$$\\end{document} at 90%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$90\\%$$\\end{document} probability.

Comparison of statistical low-frequency earthquake activity models

Slow earthquakes are slow fault slip events. Quantifying and monitoring slow earthquake activity characteristics are important, because they may change before large earthquakes occur. Statistical seismicity models are useful for quantifying seismicity characteristics. However, no standard statistical model exists for slow earthquake activity. This study used a high-quality catalog of low-frequency earthquakes (LFEs), a type of slow earthquake, in the Nankai subduction zone from April 2004 to August 2015 and conducted the first comparison of existing statistical LFE activity models to determine which model better describes LFE activity. Based on this comparison, this study proposes a new hybrid model that incorporates existing model features. The new model considers the LFE activity history in a manner similar to the epidemic-type aftershock sequence (ETAS) model and represents the LFE aftershock rate (subsequent LFE occurrence rate) with a small number of model parameters, as in the Omori–Utsu aftershock law for regular earthquakes. The results show that the proposed model outperforms other existing models. However, the new model cannot reproduce a feature of LFE activity: the sudden cessation of intense LFE bursts. This is because the new model superimposes multiple aftershock activities and predicts extremely high seismicity rates during and after the LFE bursts. I suggest that reproducing and successfully predicting the sudden cessation of intense LFE bursts is critical for the further improvement of statistical LFE activity models. In addition, the empirical equations formulated in this study for the LFE aftershock rates may be useful for future statistical and physical modeling of LFE activity.Graphical

Predicting airborne ascospores of Sclerotinia sclerotiorum through machine learning and statistical methods

AbstractA main biological constraint of dry bean (Phaseolus vulgaris) production in Canada is white mould, caused by the fungal pathogen Sclerotinia sclerotiorum. The primary infectious propagules of S. sclerotiorum are airborne ascospores and monitoring the air for inoculum levels could help predict the severity of white mould in bean fields. Daily air samples were collected in commercial dry bean fields in Alberta, Manitoba and Ontario and ascospores were quantified using quantitative PCR. Daily weather data was obtained from in‐field weather stations. The number of ascospores on a given day was modelled using 63 different environmental variables and several modelling methods, both regression and classification approaches, were implemented with machine learning (ML) (random forests, logistic regression and support vector machines) and statistical (generalized linear models) approaches. Across all years and provinces, ascospores were most highly correlated with ascospore release from the previous day (r ranged from 0.15 to 0.6). This variable was also the only variable included in all models and had the greatest weight in all models. Models without this variable had much poorer performance than those with it. Correlations of ascospores with other environmental variables varied by province and sometimes by year. A comparison of ML and statistical models revealed that they both performed similarly, but that the statistical models were easier to interpret. However, the precise relationship between airborne ascospore levels and in‐field disease severity remains unclear, and spore sampling methods will require further development before they can be deployed as a disease management tool.

Strong Prediction: Language Model Surprisal Explains Multiple N400 Effects.

Theoretical accounts of the N400 are divided as to whether the amplitude of the N400 response to a stimulus reflects the extent to which the stimulus was predicted, the extent to which the stimulus is semantically similar to its preceding context, or both. We use state-of-the-art machine learning tools to investigate which of these three accounts is best supported by the evidence. GPT-3, a neural language model trained to compute the conditional probability of any word based on the words that precede it, was used to operationalize contextual predictability. In particular, we used an information-theoretic construct known as surprisal (the negative logarithm of the conditional probability). Contextual semantic similarity was operationalized by using two high-quality co-occurrence-derived vector-based meaning representations for words: GloVe and fastText. The cosine between the vector representation of the sentence frame and final word was used to derive contextual cosine similarity estimates. A series of regression models were constructed, where these variables, along with cloze probability and plausibility ratings, were used to predict single trial N400 amplitudes recorded from healthy adults as they read sentences whose final word varied in its predictability, plausibility, and semantic relationship to the likeliest sentence completion. Statistical model comparison indicated GPT-3 surprisal provided the best account of N400 amplitude and suggested that apparently disparate N400 effects of expectancy, plausibility, and contextual semantic similarity can be reduced to variation in the predictability of words. The results are argued to support predictive coding in the human language network.

Comparison of statistical models for individual’s ability index and ranking

ABSTRACT Economic efficiency demands accurate assessment of individual ability for selection purposes. This study investigates Classical Test Theory (CTT) and Item Response Theory (IRT) for estimating true ability and ranking individuals. Two Monte Carlo simulations and real data analyses were conducted. Results suggest a slight advantage for IRT, but ability estimates from both methods were highly correlated (r=0.95), indicating similar outcomes. The Logistic two-parameter IRT model emerged as the most reliable and rigorous approach.

Statistical analysis and comparison of deep convolutional neural network models for the identification and classification of maize leaf diseases

Statistical analysis and comparison of deep convolutional neural network models for the identification and classification of maize leaf diseases

Predicting Incident Dementia in Cerebral Small Vessel Disease: Comparison of Machine Learning and Traditional Statistical Models

Predicting Incident Dementia in Cerebral Small Vessel Disease: Comparison of Machine Learning and Traditional Statistical Models

Bayesian hybrid index and genomic cline estimation with the R package gghybrid.

Admixture, the interbreeding of individuals from differentiated source populations, is now known to be a widespread phenomenon. Genomic studies of natural hybridisation can help to answer many questions on the impacts of admixture on adaptive evolution, reproductive isolation, and speciation. When a large variety of admixture proportions between two source populations exist, both geographic and genomic cline analysis are suitable methods for inferring biased, restricted or excessive gene flow at individual loci into the foreign genomic background, providing evidence for reproductive isolation, selection across an environmental transition, balancing selection, and adaptive introgression. Genomic cline analysis replaces geographic location with genome-wide hybrid index and is therefore useable in circumstances that violate geographic cline assumptions. Here, I introduce gghybrid, an R package for simple and flexible Bayesian estimation of Buerkle's hybrid index and Fitzpatrick's logit-logistic genomic clines using bi-allelic data, suitable for both small and large datasets. gghybrid allows any ploidy and uses Structure input file format. It has separate functions for hybrid index and cline estimation, treating each individual and locus respectively as an independent analysis, making it highly parallelisable. Admixture proportions from other software can alternatively be used in cline analysis, alongside parental allele frequencies. Parameters can be fixed and samples pooled for statistical model comparison with AIC or waic. Here, I describe the functions, pipeline, and statistical properties of gghybrid. Simulations reveal that model comparison with waic is preferred, and use of Bayesian posterior distributions and p values to select candidate non-null loci is problematic and should be avoided.

The mechanism of MinD stability modulation by MinE in Min protein dynamics.

The patterns formed both in vivo and in vitro by the Min protein system have attracted much interest because of the complexity of their dynamic interactions given the apparent simplicity of the component parts. Despite both the experimental and theoretical attention paid to this system, the details of the biochemical interactions of MinD and MinE, the proteins responsible for the patterning, are still unclear. For example, no model consistent with the known biochemistry has yet accounted for the observed dual role of MinE in the membrane stability of MinD. Until now, a statistical comparison of models to the time course of Min protein concentrations on the membrane has not been carried out. Such an approach is a powerful way to test existing and novel models that are difficult to test using a purely experimental approach. Here, we extract time series from previously published fluorescence microscopy time lapse images of in vitro experiments and fit two previously described and one novel mathematical model to the data. We find that the novel model, which we call the Asymmetric Activation with Bridged Stability Model, fits the time-course data best. It is also consistent with known biochemistry and explains the dual MinE role via MinE-dependent membrane stability that transitions under the influence of rising MinE to membrane instability with positive feedback. Our results reveal a more complex network of interactions between MinD and MinE underlying Min-system dynamics than previously considered.

Feature statistical analysis and comparison of machine learning models for university admission prediction

In recent years, the pursue for academic degrees has intensified, leading to a surge in the number of undergraduate students applying for graduate programs at renowned universities worldwide. Consequently, universities have adopted a multifaceted approach to evaluate applicants, moving beyond traditional metrics like GPA to assess their overall potential. This study aims to comprehend the criteria employed by universities to select graduate applicants and assist undergraduate students in planning their academic trajectory. To achieve this, a diverse set of machine learning models are compared, including multiple linear regression and K-nearest neighbors, decision trees, support vector machines, and Bayesian classifiers. These models were trained with online admission probability data to predict the likelihood of admission and uncover the primary factors guiding university selection processes. The findings reveal that while research experience can enhance competitiveness in graduate admissions, academic indicators such as GPA, GRE scores, and language proficiency remain critical determinants of acceptance. Moreover, higher-ranked institutions exhibit a higher proportion of applicants with research experience. For candidates with strong GPAs, it is essential to demonstrate competitive language proficiency, augment research experience through well-crafted recommendation letters and personal statements. Conversely, applicants with lower GPAs should strive for outstanding GRE scores to compensate for academic performance.

Comparison of statistical and optimization models for projecting future PV installations at a sub-national scale

Spatially-disaggregated projections of new solar photovoltaic (PV) installations are essential for planning electricity grids and managing the electricity system at large scale. Such projections at sub-national level can be obtained by statistical models or by electricity system optimization models, but there is barely any study that compares the performances of these approaches. This study aims to compare methods for projecting PV installations at a level of 143 districts in Switzerland, using a simple extrapolation method (as a benchmark of the common practice today), a multiple linear regression model, two spatial regression models, and a spatially-explicit optimization model (EXPANSE) with various features to account for policy. The performance of different approaches is evaluated retrospectively for 2012–2020, using multiple accuracy indicators. The evaluation results show that statistical regression models, which account for socio-demographic and techno-economic characteristics as predictors of future PV growth, overall perform better than simple extrapolation or optimization. Although commonly used, extrapolation has the highest variability in accuracy, indicating the least robust performance. The optimization model tends to underestimate PV installations in its least-cost scenarios, if the role of policy is not considered. Incorporating solar PV policies and renewable electricity generation targets increases the overall accuracy of the optimization model at a national level, but not necessarily at a spatially-explicit level. We thus conclude that statistical models are preferred over extrapolation or optimization models for projecting future PV installations at a sub-national scale.

Comparison of different statistical models for the analysis of fracture events: findings from the Prevention of Falls Injury Trial (PreFIT)

BackgroundFractures are rare events and can occur because of a fall. Fracture counts are distinct from other count data in that these data are positively skewed, inflated by excess zero counts, and events can recur over time. Analytical methods used to assess fracture data and account for these characteristics are limited in the literature.MethodsCommonly used models for count data include Poisson regression, negative binomial regression, hurdle regression, and zero-inflated regression models. In this paper, we compare four alternative statistical models to fit fracture counts using data from a large UK based clinical trial evaluating the clinical and cost-effectiveness of alternative falls prevention interventions in older people (Prevention of Falls Injury Trial; PreFIT).ResultsThe values of Akaike information criterion and Bayesian information criterion, the goodness-of-fit statistics, were the lowest for negative binomial model. The likelihood ratio test of no dispersion in the data showed strong evidence of dispersion (chi-square = 225.68, p-value < 0.001). This indicates that the negative binomial model fits the data better compared to the Poisson regression model. We also compared the standard negative binomial regression and mixed effects negative binomial models. The LR test showed no gain in fitting the data using mixed effects negative binomial model (chi-square = 1.67, p-value = 0.098) compared to standard negative binomial model.ConclusionsThe negative binomial regression model was the most appropriate and optimal fit model for fracture count analyses.Trial registrationThe PreFIT trial was registered as ISRCTN71002650.

A novel deep-learning technique for forecasting oil price volatility using historical prices of five precious metals in context of green financing – A comparison of deep learning, machine learning, and statistical models

This study proposes a novel deep-learning convolution neural network (CNN) to forecast crude oil prices based on historical prices of five precious metals (Gold, Silver, Platinum, Palladium, and Rhodium) in context of green financing. The proposed deep learning CNN has three components: a convolution block called a group block, a novel convolutional neural network architecture called GroupNet, and a regression layer. The proposed model is tested against seven machine learning models and three traditional statistical models for predicting oil price volatility using the same independent variables (5 precious metals). A comparison of the deep learning model (our proposed model) with machine learning/deep learning models and statistical methods indicates that the proposed deep learning model has the highest prediction accuracy. A feature selection technique is also applied using the WEKA ML tool to improve the accuracy of the proposed model and existing machine learning and traditional statistical models. The findings indicate a non-linear correlation between oil price volatility and prices of precious metals. Moreover, statistical analysis indicates that deep learning can be used to predict oil price volatility with greater accuracy than machine learning and statistical methods while using precious metals as predictors. The results also indicate that machine learning models (Decision Tables and M5rules) can be used to predict oil price volatility with considerable accuracy. Moreover, the study proves that traditional statistical models can perform better than a few machine learning models (Lazy LWL and GPR).

Statistical model comparison based on variation parameters for monitoring thermal deformation of workpiece in end-milling

Statistical model comparison based on variation parameters for monitoring thermal deformation of workpiece in end-milling

Statistical comparison of predictive models for quantitative analysis and classification in the framework of LIBS spectroscopy: A tutorial

Laser-Induced Breakdown Spectroscopy (LIBS) is a widely accepted technique used for both classification and quantification purposes considering complex and heterogeous samples. Based on a set of training spectra acquired from diverse and representative samples within a specific application domain, it becomes possible to apply various data processing techniques and modeling methods to construct the predictive model in question. Naturally the complexity of both the laser-matter and the laser-plasma interactions and the heterogeneity of natural samples often requires the development of various predictive models, which are then compared based on figures of merit such as the RMSEP (Root Mean Square Error of Prediction) value for quantification or the classification rate for qualitative analysis. Our ultimate goal is, of course, to select the model that appears to be the most accurate, which ultimately boils down to searching for the lowest RMSEP value or the highest classification rate. This is precisely where the whole problem lies because even if we observe a different level of error for two models, for example, this difference is not necessarily statistically significant. In such a case, we are therefore not allowed to say that the lower error indicates the best predictive model to consider. The purpose of this article is to provide a tutorial on introducing a statistical model comparison procedure, whether they are quantitative or qualitative. Two LIBS data sets have been used to illustrate the principles of the proposed method.