A Note on Confidence Intervals and Model Specification

Marketing ZFP ◽  
2019 ◽  
Vol 41 (4) ◽  
pp. 33-42
Author(s):  
Thomas Otter
Keyword(s):  
Confidence Intervals ◽  
Generalized Linear Model ◽  
Statistical Information ◽  
Regression Coefficients ◽  
Model Specification ◽  
Model Parameters ◽  
Exploratory Research ◽  
Empirical Calibration ◽  
Credible Intervals ◽  
Model Structures

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.

Regression analysis of indicators of a numerical experiment to determine the cooling time of oil

2020 ◽  
pp. 89-97
Author(s):  
A. U. Yakupov ◽  
D. A. Cherentsov ◽  
K. S. Voronin ◽  
Yu. D. Zemenkov
Keyword(s):  
Regression Analysis ◽  
Computer Experiment ◽  
Calculation Model ◽  
Cooling Time ◽  
Regression Coefficients ◽  
Fisher Criterion ◽  
Empirical Relationships ◽  
Factors Affecting ◽  
Oil Pipeline ◽  
Significant Regression

The article performed the processing of the results of a computer experiment to determine the cooling time of oil in a stopped oil pipeline. We proposed a calculation model in previous works that allows you to simulate the process of cooling oil.There was a need to verify the previously obtained results when conducting a laboratory experiment on a stand with soil. To conduct the experiment, it was necessary to conduct the planning of the experiment. The factors affecting the cooling time of oil in the oil pipeline, which will vary in the proposed experiment, are determined, empirical relationships are established. A regression analysis was carried out, and the dispersion homogeneity was checked using the Cochren criterion. The estimates of reproducibility variances are calculated. The adequacy hypothesis was tested using the Fisher criterion. Significant regression coefficients are established.

Relationship between Coffee Prices in Spot and Futures Markets-An Empirical Analysis

2020 ◽  
pp. 180-188
Keyword(s):  
New York ◽  
Correlation Coefficients ◽  
Strong Relationship ◽  
Futures Market ◽  
Regression Coefficients ◽  
Futures Prices ◽  
Market Prices ◽  
Spot Prices ◽  
Correlation And Regression Analysis ◽  
Highly Correlated

The present study explored the relationship between spot and futures coffee prices. The Correlation and Regression analysis were carried out based on monthly observations of International Coffee Organization (ICO) indicator prices of the four groups (Colombian Milds, Other Milds, Brazilian Naturals, and Robustas) representing Spot markets and the averages of 2nd and 3rd positions of the Intercontinental Exchange (ICE) New York for Arabica and ICE Europe for Robusta representing the Futures market for the period 1990 to 2019. The study also used the monthly average prices paid to coffee growers in India from 1990 to 2019. The estimated correlation coefficients indicated both the Futures prices and Spot prices of coffee are highly correlated. Further, estimated regression coefficients revealed a very strong relationship between Futures prices and Spot prices for all four ICO group indicator prices. Hence, the ICE New York (Arabica) and ICE Europe (Robusta) coffee futures prices are very closely related to Spot prices. The estimated regression coefficients between Futures prices and the price paid to coffee growers in India confirmed the positive relationship, but the dispersion of more prices over the trend line indicates a lesser degree of correlation between the price paid to growers at India and Futures market prices during the study period.

scholarly journals 99 Breed authentication of five lines comparing Structure, Admixture, and an allele frequency method

2020 ◽  
Vol 98 (Supplement_3) ◽  
pp. 25-25
Author(s):  
Austin M Putz ◽  
Patrick Charagu ◽  
Abe Huisman
Keyword(s):  
Population Structure ◽  
Allele Frequency ◽  
Regression Coefficients ◽  
Frequency Method ◽  
Large White ◽  
Reference Allele ◽  
Software Packages ◽  
The Matrix ◽  
Snp Panel ◽  
Compare And Contrast

Abstract Two commonly used population structure software packages are freely available for breed authentication, Structure and Admixture. Structure uses a Bayesian approach to model population structure, while Admixture uses a frequentist approach. More recently, an allele frequency method has been updated to use quadratic programming to constrain the multiple linear regression coefficients of the regression of genotype count (divided by two) on the matrix of allele frequencies for each known breed or line. This constraint forced coefficients to sum to one and be greater than or equal to 0 and less than or equal to 1. The goal of this research was to compare and contrast these three methods to determine the breed/line authenticity for each of the five genetic lines. These five lines included Large White, Landrace, a lean Duroc, a meat quality Duroc, and a Pietrain line. Only animals with a 50K SNP panel were used in this analysis. Analyses were run five times for Structure and Admixture to check repeatability. The allele frequency method did not need to be repeated because it remains the same as long as the reference allele frequency matrix stays constant. For Structure, results of breed composition were inconsistent across replicates. Structure separated at least one of the maternal lines in three out of the five replicates with only 500 animals and kept the Duroc lines together as one population. Only 500 animals could be utilized in each run of Structure due to computational restraints. Admixture was very consistent across runs for each animal, but also failed to separate the two Duroc lines, instead splitting one of the two maternal lines. Finally, the allele frequency method split all five lines correctly and was 100% reproducible as long as the reference allele frequency matrix stays the same across runs.

scholarly journals Secular trends of population attributable risk of overweight and obesity for hypertension among Chinese adults from 1991 to 2011

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Jian Gou ◽  
Huiying Wu
Keyword(s):  
Population Attributable Risk ◽  
Attributable Risk ◽  
Secular Trends ◽  
Overweight And Obesity ◽  
Regression Coefficients ◽  
Chinese Adults ◽  
Intervention Effect ◽  
Obesity Epidemic ◽  
The Past ◽  
Increasing Trend

AbstractWe determined if the increasing trend in hypertension can be partly attributed to increasing prevalence of overweight/obesity in China over the past two decades. Data were collected from 1991 to 2011 and the population attributable risk (PAR), which is used to estimate the intervention effect on hypertension if overweight/obese, were eliminated. Linear regression was used to evaluate the secular trends. The age-standardized prevalence of overweight and obesity increased by 26.32% with an overall slope of 1.27% (95% CI: 1.12–1.43%) per year. Hypertension also increased by 12.37% with an overall slope of 0.65% (95% CI: 0.51–0.79%) per year. The adjusted ORs of overweight/obesity for hypertension across the survey years remained unchanged; however, the trend in PAR increased steadily from 27.1 to 44.6% with an overall slope of 0.81% (95% CI: 0.34–1.28%) per year (P = 0.006). There was no significant gender difference in the slopes of increasing PAR, as measured by regression coefficients (β = 0.95% vs. β = 0.63% per year, P = 0.36). Over the past two decades, the increase in the prevalence of hypertension in China was partly attributed to the overweight/obesity epidemic, which highlights the importance of controlling weight and further reducing the burden of hypertension.

scholarly journals Public Compliance With Social Distancing Measures and SARS-CoV-2 Spread

2021 ◽  
pp. 003335492110112
Author(s):  
Hongjie Liu ◽  
Chang Chen ◽  
Raul Cruz-Cano ◽  
Jennifer L. Guida ◽  
Minha Lee
Keyword(s):  
Growth Rate ◽  
Reproduction Number ◽  
Early Stage ◽  
Human Mobility ◽  
The United States ◽  
Density Change ◽  
Regression Coefficients ◽  
Daily Growth Rate ◽  
Daily Growth ◽  
Social Distancing

Objective We quantified the association between public compliance with social distancing measures and the spread of SARS-CoV-2 during the first wave of the epidemic (March–May 2020) in 5 states that accounted for half of the total number of COVID-19 cases in the United States. Methods We used data on mobility and number of COVID-19 cases to longitudinally estimate associations between public compliance, as measured by human mobility, and the daily reproduction number and daily growth rate during the first wave of the COVID-19 epidemic in California, Illinois, Massachusetts, New Jersey, and New York. Results The 5 states mandated social distancing directives during March 19-24, 2020, and public compliance with mandates started to decrease in mid-April 2020. As of May 31, 2020, the daily reproduction number decreased from 2.41-5.21 to 0.72-1.19, and the daily growth rate decreased from 0.22-0.77 to –0.04 to 0.05 in the 5 states. The level of public compliance, as measured by the social distancing index (SDI) and daily encounter-density change, was high at the early stage of implementation but decreased in the 5 states. The SDI was negatively associated with the daily reproduction number (regression coefficients range, –0.04 to –0.01) and the daily growth rate (from –0.009 to –0.01). The daily encounter-density change was positively associated with the daily reproduction number (regression coefficients range, 0.24 to 1.02) and the daily growth rate (from 0.05 to 0.26). Conclusions Social distancing is an effective strategy to reduce the incidence of COVID-19 and illustrates the role of public compliance with social distancing measures to achieve public health benefits.

On the error of estimates from successive forest inventories with SPR

1987 ◽  
Vol 17 (5) ◽  
pp. 442-447
Author(s):  
Tiberius Cunia
Keyword(s):  
Forest Inventory ◽  
Random Sampling ◽  
Regression Coefficients ◽  
Partial Replacement ◽  
Forest Inventories ◽  
Continuous Forest ◽  
Regression Functions ◽  
The Given ◽  
Linear Regressions ◽  
Continuous Forest Inventory

The approach used by Cunia to combine the error from sample plots with the error from volume or biomass tables when Continuous Forest Inventory (CFI) estimates of current values and growth are calculated is extended to the CFI systems using Sampling with Partial Replacement (SPR). The formulae are derived for the case of SPR on two measurement occasions when (i) volume or biomass tables are constructed from linear regressions for which an estimate of the covariance matrix of the regression coefficients is known, and (ii) the sample plots or points are selected by random sampling independently of the given volume or biomass regression functions.

scholarly journals Type 2 diabetes is more predictable in women than men by multiple anthropometric and biochemical measures

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Tangying Li ◽  
Huibiao Quan ◽  
Huachuan Zhang ◽  
Leweihua Lin ◽  
Lu Lin ◽  
...  
Keyword(s):  
Blood Pressure ◽  
Type 2 Diabetes ◽  
Diastolic Blood Pressure ◽  
Roc Analysis ◽  
Operating Characteristic ◽  
Regression Coefficient ◽  
Regression Coefficients ◽  
Sexually Dimorphic ◽  
Fasting Insulin

AbstractMen and women are sexually dimorphic but whether common anthropometric and biochemical parameters predict type 2 diabetes (T2D) in different ways has not been well studied. Here we recruit 1579 participants in Hainan Province, China, and group them by sex. We compared the prediction power of common parameters of T2D in two sexes by association, regression, and Receiver Operating Characteristic (ROC) analysis. HbA1c is associated with FPG stronger in women than in men and the regression coefficient is higher, consistent with higher prediction power for T2D. Age, waist circumference, BMI, systolic and diastolic blood pressure, triglyceride levels, total cholesterol, LDL, HDL, fasting insulin, and proinsulin levels all predict T2D better in women. Except for diastolic blood pressure, all parameters associate or tend to associate with FPG stronger in women than in men. Except for diastolic blood pressure and fasting proinsulin, all parameters associate or tend to associate with HbA1c stronger in women than in men. Except for fasting proinsulin and HDL, the regression coefficients of all parameters with FPG and HbA1c were higher in women than in men. Together, by the above anthropometric and biochemical measures, T2D is more readily predicted in women than men, suggesting the importance of sex-based subgroup analysis in T2D research.

scholarly journals Detecting Instruction Effects—Deciding Between Covariance Analytical and Change-Score Approach

2021 ◽  
Author(s):  
Carmen Köhler ◽  
Johannes Hartig ◽  
Alexander Naumann
Keyword(s):  
Latent Variable ◽  
Outcome Measurement ◽  
Predictor Variable ◽  
Change Score ◽  
Regression Coefficients ◽  
Outcome Variable ◽  
Analysis Model ◽  
Hypothetical Data ◽  
Instructional Research ◽  
Time Point

AbstractThe article focuses on estimating effects in nonrandomized studies with two outcome measurement occasions and one predictor variable. Given such a design, the analysis approach can be to include the measurement at the previous time point as a predictor in the regression model (ANCOVA), or to predict the change-score of the outcome variable (CHANGE). Researchers demonstrated that both approaches can result in different conclusions regarding the reported effect. Current recommendations on when to apply which approach are, in part, contradictory. In addition, they lack direct reference to the educational and instructional research contexts, since they do not consider latent variable models in which variables are measured without measurement error. This contribution assists researchers in making decisions regarding their analysis model. Using an underlying hypothetical data-generating model, we identify for which kind of data-generating scenario (i.e., under which assumptions) the defined true effect equals the estimated regression coefficients of the ANCOVA and the CHANGE approach. We give empirical examples from instructional research and discuss which approach is more appropriate, respectively.

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