A Note on Confidence Intervals and Model Specification

Empirical research in marketing often is, at least in parts, exploratory. The goal of exploratory research, by definition, extends beyond the empirical calibration of parameters in well established models and includes the empirical assessment of different model specifications. In this context researchers often rely on the statistical information about parameters in a given model to learn about likely model structures. An example is the search for the 'true' set of covariates in a regression model based on confidence intervals of regression coefficients. The purpose of this paper is to illustrate and compare different measures of statistical information about model parameters in the context of a generalized linear model: classical confidence intervals, bootstrapped confidence intervals, and Bayesian posterior credible intervals from a model that adapts its dimensionality as a function of the information in the data. I find that inference from the adaptive Bayesian model dominates that based on classical and bootstrapped intervals in a given model.

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Statistical inferences with jointly type-II censored samples from two Pareto distributions

Open Physics ◽

10.1515/phys-2017-0064 ◽

2017 ◽

Vol 15 (1) ◽

pp. 557-565 ◽

Cited By ~ 1

Author(s):

Hanaa H. Abu-Zinadah

Keyword(s):

Confidence Intervals ◽

Life Time ◽

Model Parameters ◽

Type Ii ◽

Time Data ◽

Data Set ◽

Censored Samples ◽

Credible Intervals ◽

Life Tests ◽

Censoring Scheme

AbstractIn the several fields of industries the product comes from more than one production line, which is required to work the comparative life tests. This problem requires sampling of the different production lines, then the joint censoring scheme is appeared. In this article we consider the life time Pareto distribution with jointly type-II censoring scheme. The maximum likelihood estimators (MLE) and the corresponding approximate confidence intervals as well as the bootstrap confidence intervals of the model parameters are obtained. Also Bayesian point and credible intervals of the model parameters are presented. The life time data set is analyzed for illustrative purposes. Monte Carlo results from simulation studies are presented to assess the performance of our proposed method.

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Incremental model breakdown to assess the multi-hypotheses problem

Hydrology and Earth System Sciences ◽

10.5194/hess-22-4565-2018 ◽

2018 ◽

Vol 22 (8) ◽

pp. 4565-4581 ◽

Cited By ~ 3

Author(s):

Florian U. Jehn ◽

Lutz Breuer ◽

Tobias Houska ◽

Konrad Bestian ◽

Philipp Kraft

Keyword(s):

Hydrological Modeling ◽

Model Performance ◽

Complex Model ◽

Model Parameters ◽

Objective Functions ◽

Final Model ◽

Incremental Model ◽

Model Efficiency ◽

Improved Model ◽

Model Structures

Abstract. The ambiguous representation of hydrological processes has led to the formulation of the multiple hypotheses approach in hydrological modeling, which requires new ways of model construction. However, most recent studies focus only on the comparison of predefined model structures or building a model step by step. This study tackles the problem the other way around: we start with one complex model structure, which includes all processes deemed to be important for the catchment. Next, we create 13 additional simplified models, where some of the processes from the starting structure are disabled. The performance of those models is evaluated using three objective functions (logarithmic Nash–Sutcliffe; percentage bias, PBIAS; and the ratio between the root mean square error and the standard deviation of the measured data). Through this incremental breakdown, we identify the most important processes and detect the restraining ones. This procedure allows constructing a more streamlined, subsequent 15th model with improved model performance, less uncertainty and higher model efficiency. We benchmark the original Model 1 and the final Model 15 with HBV Light. The final model is not able to outperform HBV Light, but we find that the incremental model breakdown leads to a structure with good model performance, fewer but more relevant processes and fewer model parameters.

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Mixed Generalized Linear Model for Estimating Household Trip Production

Transportation Research Record Journal of the Transportation Research Board ◽

10.3141/1718-08 ◽

2000 ◽

Vol 1718 (1) ◽

pp. 61-67 ◽

Cited By ~ 2

Author(s):

Chang-Jen Lan ◽

Patricia S. Hu

Keyword(s):

Linear Model ◽

Generalized Linear Model ◽

Negative Binomial ◽

Empirical Distribution ◽

Distribution Functions ◽

Model Specification ◽

Parameter Estimates ◽

Modeling Framework ◽

Personal Transportation ◽

Trip Production

An innovative modeling framework to estimate household trip rates using 1995 Nationwide Personal Transportation Survey data is presented. A generalized linear model with a mixture of negative binomial probability distribution functions was developed on the basis of characteristics observed from the empirical distribution of household daily trips. This model provides a more flexible framework and a better model specification for analyzing household-specific trip production behavior. Compared with traditional least squares-based regression models, the parameter estimates from the proposed model are more efficient. Although the mean accuracies from the two modeling approaches are comparable, the mixed generalized linear model is more robust in identifying outliers due to its unsymmetric prediction bounds derived from more correct model specification.

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The fallacy of placing confidence in confidence intervals - A commentary

10.31234/osf.io/kvxc4 ◽

2017 ◽

Author(s):

Jose D. Perezgonzalez

Keyword(s):

Confidence Intervals ◽

Common Ground ◽

Posterior Distributions ◽

Correct Interpretation ◽

Psychonomic Bulletin ◽

Credible Intervals ◽

Per Se

‘The fallacy of placing confidence in confidence intervals’ (Morey et al., 2016, Psychonomic Bulletin & Review, doi: 10.3758/s13423-015-0947-8) delved into a much needed technical and philosophical dissertation regarding the differences between typical (mis)interpretations of frequentist confidence intervals and the typical correct interpretation of Bayesian credible intervals. My contribution here partly strengthens the authors’ argument, partly closes some gaps they left open, and concludes with a note of attention to the possibility that there may be distinctions without real practical differences in the ultimate use of estimation by intervals, namely when assuming a common ground of uninformative priors and intervals as ranges of values instead of as posterior distributions per se.

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Parametric Bootstrap Methods for Estimating Model Parameters of Non-homogeneous Gamma Process

International Journal of Mathematical Engineering and Management Sciences ◽

10.33889/ijmems.2018.3.2-013 ◽

2018 ◽

Vol 3 (2) ◽

pp. 167-176 ◽

Cited By ~ 1

Author(s):

Yasuhiro Saito ◽

Tadashi Dohi

Keyword(s):

Confidence Intervals ◽

Bootstrap Method ◽

Parametric Bootstrap ◽

Gamma Process ◽

Estimation Accuracy ◽

Model Parameters ◽

Trend Function ◽

Bootstrap Methods ◽

Parametric Bootstrapping ◽

Simulation Based

Non-Homogeneous Gamma Process (NHGP) is characterized by an arbitrary trend function and a gamma renewal distribution. In this paper, we estimate the confidence intervals of model parameters of NHGP via two parametric bootstrap methods: simulation-based approach and re-sampling-based approach. For each bootstrap method, we apply three methods to construct the confidence intervals. Through simulation experiments, we investigate each parametric bootstrapping and each construction method of confidence intervals in terms of the estimation accuracy. Finally, we find the best combination to estimate the model parameters in trend function and gamma renewal distribution in NHGP.

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Posterior contraction in sparse generalized linear models

Biometrika ◽

10.1093/biomet/asaa074 ◽

2020 ◽

Author(s):

Seonghyun Jeong ◽

Subhashis Ghosal

Keyword(s):

Generalized Linear Models ◽

Bayesian Methods ◽

Generalized Linear Model ◽

Linear Models ◽

Continuous Distribution ◽

Fractional Power ◽

Regression Coefficients ◽

Link Function ◽

Convergence Properties ◽

Set Up

Summary We study posterior contraction rates in sparse high-dimensional generalized linear models using priors incorporating sparsity. A mixture of a point mass at zero and a continuous distribution is used as the prior distribution on regression coefficients. In addition to the usual posterior, the fractional posterior, which is obtained by applying Bayes theorem with a fractional power of the likelihood, is also considered. The latter allows uniformity in posterior contraction over a larger subset of the parameter space. In our set-up, the link function of the generalized linear model need not be canonical. We show that Bayesian methods achieve convergence properties analogous to lasso-type procedures. Our results can be used to derive posterior contraction rates in many generalized linear models including logistic, Poisson regression and others.

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Seeking edge-on galaxies with substantial extraplanar dust using a radiative transfer model: determination of the model parameter uncertainties for EON_10.477_41.954 (FGC 79)

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz2442 ◽

2019 ◽

Vol 489 (4) ◽

pp. 4690-4704 ◽

Cited By ~ 1

Author(s):

Jong-Ho Shinn

Keyword(s):

Radiative Transfer ◽

Confidence Intervals ◽

Three Dimensional ◽

Radiative Transfer Model ◽

Model Parameters ◽

Transfer Model ◽

Target Classification ◽

Parameter Uncertainties ◽

Model Parameter ◽

Galaxy Model

ABSTRACT We have revisited the target EON_10.477_41.954 in order to determine more accurately the uncertainties in the model parameters that are important for target classification (i.e. galaxies with or without substantial extraplanar dust). We performed a Markov chain Monte Carlo (MCMC) analysis for the 15 parameters of the three-dimensional radiative-transfer galaxy model we used previously for target classification. To investigate the convergence of the MCMC sampling – which is usually neglected in the literature but should not be – we monitored the integrated autocorrelation time (τint), and we achieved effective sample sizes >5650 for all the model parameters. The confidence intervals are unstable at the beginning of the iterations where the values of τint are increasing, but they become stable in later iterations where those values are almost constant. The final confidence intervals are ∼5–100 times larger than the nominal uncertainties used in our previous study (the standard deviation of three best-fitting results). Thus, those nominal uncertainties are not good proxies for the model-parameter uncertainties. Although the position of EON_10.477_41.954 in the target-classification plot (the scale height to diameter ratio of dust versus that of light source) decreases by about 20–30 per cent when compared to our previous study, its membership in the ‘high-group’ – i.e. among galaxies with substantial extraplanar dust – nevertheless remains unchanged.

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Mapping QTLs for binary traits in backcross and F2 populations

Genetics Research ◽

10.1017/s0016672300033887 ◽

1996 ◽

Vol 68 (1) ◽

pp. 55-63 ◽

Cited By ~ 69

Author(s):

P. M. Visscher ◽

C. S. Haley ◽

S. A. Knott

Keyword(s):

Quantitative Trait Loci ◽

Linear Regression ◽

Quantitative Trait ◽

Generalized Linear Model ◽

Model Parameters ◽

Qtl Detection ◽

Binary Traits ◽

Standard Linear ◽

Marker Spacing ◽

Qtl Effects

SummaryMapping quantitative trait loci (QTLs) for binary traits in backcross and F2 populations was investigated using stochastic stimulation. Data were analysed using either linear regression or a generalized linear model. Parameters which were varied in the simulations were the population size (200 and 500), heritability in the backcross or F2 population (0·01, 0·05, 0·10), marker spacing (10 and 20 cM) and the incidence of the trait (0·50, 0·25, 0·10). The methods gave very similar results in terms of estimates of the QTL location and QTL effects and power of QTL detection, and it was concluded that in practice treating the zero-one data as continuous and using standard linear regression was efficient.

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Explorations in statistics: confidence intervals

AJP Advances in Physiology Education ◽

10.1152/advan.00006.2009 ◽

2009 ◽

Vol 33 (2) ◽

pp. 87-90 ◽

Cited By ~ 43

Author(s):

Douglas Curran-Everett

Keyword(s):

Confidence Interval ◽

Confidence Intervals ◽

Hypothesis Test ◽

Statistical Information ◽

Experimental Result ◽

P Value ◽

Population Parameter ◽

True Value ◽

Level Of Confidence ◽

The Mean

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This third installment of Explorations in Statistics investigates confidence intervals. A confidence interval is a range that we expect, with some level of confidence, to include the true value of a population parameter such as the mean. A confidence interval provides the same statistical information as the P value from a hypothesis test, but it circumvents the drawbacks of that hypothesis test. Even more important, a confidence interval focuses our attention on the scientific importance of some experimental result.

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