Theoretical and Empirical Validation of Software Product Measures

SEMINAR IN RESEARCH METHODSRequired Readings for On-Site SeminarNOTE: Click on the title of the article/reading for a PDF copy.ity and Manipulation Checks96), ?a href="PDFs/Experiments,%20Internal%20Validity%20and%20Manipulation%20Checks/Jones_96.pdf">Ch in the Social and Behavioral Sciences, 2nd Edition, Sunderland, MS: Sinauer Associates.nthal, Essentials of Behavioral Research (New York: McGraw Hill); Ch. 4 (?aments,%20Internal%20Validity%20and%20Manipulation%20Checks/Rosenthal_Rosnow_Ch4.pdf">Structure and 1.1996), ?a href="PDFs/Experiments,%20Internal%20Validity%20and%20Manipulation%20Checks/Kardes_JCP_9 umer Psychology,?Journal of Consumer Psychology, 5 (3), 279-296.(1990), ?a href="PDFs/Experiments,%20Internal%20Validity%20and%20Manipulation%20Checks/Beggan_JPSP al Perception: The Mere Ownership Effect,? Journal of Personality and Social Psychology, 62 (2), 229-237.lidity1999), ?a href="PDFs/External,%20and%20Ecological%20Validity/Winer_JAMS_99.pdf">Experimentation in the rnal Validity,? Journal of the Academy of Marketing Science, 27, 349-358.999), ?a href="PDFs/External,%20and%20Ecological%20Validity/Lynch_JAMS_99.pdf">Theory and External Va ting Science, 27, 367-376.nd Alice M. Tybout (1999), ?a href="PDFs/External,%20and%20Ecological%20Validity/Calder_Tybout_JAMS_99 Future of Business Schools,? Journal of the Academy of Marketing Science, 27, 359-366.(1983), ?a href="PDFs/External,%20and%20Ecological%20Validity/Mook_AP_83.pdf">In Defense of External Inv 379-87.982), "On the External Validity of Experiments in Consumer Research," Journal of Consumer Research, Decembe Lynn W. Philips, and Alice M. Tybout (1982), "The Concept of External Validity," Journal of Consumer Research, DEuropean Journalswill include a detailed review of 2 current articles published in the marketing抯leading journals. During the ses makes manuscripts worthy of publishing in the field抯best journals. Please read the following very carefully: astava (2002), "Effect of face value on product valuation in foreign currencies," Journal of Consumer Research, 29t (2004), "Activating Sound and Meaning: The Role of Language Proficiency in Bilingual Consumer Environments 220-8.s - WSUopment, & Construct Validation. (1979), "A Paradigm for Developing Better Measures of Marketing Constructs," Journal of Marketing Research, 1), "Construct Validity: A Review of Basic Marketing Practices," Journal of Marketing Research, 18 (May), 133-45 (1997), "Dimensions of Brand Personality," Journal of Marketing Research, 34 (August), 347-356.T. and Donald W. Fiske (1959), "Convergent and Discriminant Validation by the Multitrait-Multimethod Matrix," Ps 05.P. and Youjae Yi (1993), "Multitrait-Multimethod Matrices in Consumer Research: Critique and New Developmen 143-70.A. (1994), ?a href="PDFs/Reliability%20and%20Validity/Peterson_JCR_94.pdf">A Meta-Analysis of Cronbach抯ch, 381-391.hat Is Coefficient Alpha? An Examination of Theory and Applications," Journal of Applied Psychology, 78, 98-10 nd M. Ronald Buckley (1988), "Measurement Error and Theory Testing in Consumer Research: An Empirical Illu nstruct Validation," Journal of Consumer Research, 14 (March), 579-82.ability: A Review of Psychometric Basics and Recent Marketing Practices," Journal of Marketing Research, 16, 6-arketing Journalwill include a detailed review of a recently published paper in a premiere marketing journal, including reviews, revpt (January 2006)om First Round Review, April 11, 2006)ents (From First Round Review, April 11, 2006)First Revision (April 19, 2007)tor (After First Round Review, April 19, 2007)iewers (After First Round Review, April 19, 2007)Reviewer Comments (From Second Round Review, June 07, 2007)Second Revision (October 03, 2007)tor (After Second Round Review, October 03, 2007)viewers(After Second Round Review; October 03, 2007)Letter (November 16, 2007)1986), "The Moderator-Mediator Variable Distinction in Social Psychological Research: Conceptual, Strategic, an lity and Social Psychology, 1173-1182., Charles M. Judd and Vincent Y. Yzerbyt (2005), ?aators%20&%20Mediators,%20Contrasts%20&%20Interactions/Muller_Judd_Yzerbyt_JPSP_05.pdf">When Mode ated,?Journal of Personality and Social Psychology, 89 (6), 852-863.s provide good overviews of these issues:/cm/mediate.htmp:///~davidpm/ripl/mediate.htm/cm/moderation.htmarch Ethics986), "College Sophomores in the Laboratory: Influences of a Narrow Data Base on Social Psychology's View of cial Psychology, 515-530.A. (2001), ?a href="PDFs/Student%20Samples%20and%20Research%20Ethics/Peterson_JCR_01.pdf">On the U search: Insights from a Second-Order Meta-Analysis,?Journal of Consumer Research, 28, 450-461.(1994), ?a href="PDFs/Student%20Samples%20and%20Research%20Ethics/Rosenthal_PS_94.pdf">Science a porting Psychological Research,? Psychological Science, 5 (3), 127-134. Plus read short resonses by Pomerantz d Mann (1994),ogical Association (2002), ?ant%20Samples%20and%20Research%20Ethics/Ethical%20Principles%20of%20Psychologists%20and%20Code sychologists and Code of Conduct,?Washington, DC (/ethics/). Familiarize yourself with the ionsM. R. DiMatteo (2001), ?a href="PDFs/Meta-Analysis%20and%20Replications/Rosenthal_DiMatteo_ARP_01.pdf Quantitative Methods for Literature Reviews,? Annual Review of Psychology, 52, 59-82.ardo Salas, and Norman Miller (1991), 揢sing Meta-Analysis to Test Theoretical Hypotheses in Social Psycholog n, 17 (3), 258-264.href="PDFs/Meta-Analysis%20and%20Replications/Hunter_JCR_01.pdf">The Desperate Need for Replications,? -158.f="PDFs/Meta-Analysis%20and%20Replications/Wilk_JCR_01.pdf">The Impossibility and Necessity of Re-Inquir urnal of Consumer Research, 28, 308-312.。

The Importance and Objectives of Research Papers Research papers play a crucial role in academic and scientific communities as they provide a systematic approach to investigate and explore various subjects. These papers are significant as they contribute to the accumulation of knowledge, advancement of scientific fields, and improvement of society as a whole. This article aims to discuss the significance and objectives of research papers.Significance of Research PapersResearch papers serve as a foundation that allows researchers to contribute to the existing body of knowledge. They provide an opportunity to thoroughly examine a topic, formulate hypotheses, gather and analyze data, and draw meaningful conclusions. By conducting research and publishing findings, scholars and experts can contribute to the development of their respective fields.Furthermore, research papers provide a platform for intellectual discourse and debate. They allow researchers to present their work to the scientific community, seek feedback, and engage in discussions that can lead to new ideas and collaborations. This exchange of knowledge and ideas drives innovation and fosters intellectual growth.Research papers also enable the replication and validation of scientific experiments. Through the detailed documentation of research methodologies, data collection techniques, and analysis procedures, other researchers can replicate studies to ensure the reproducibility of results. This validation process strengthens the credibility and reliability of scientific knowledge.Objectives of Research Papers1.Expand Knowledge: The primary objective of research papers is toadvance knowledge in a specific field or discipline. By conducting thoroughliterature reviews and carrying out original research, researchers contribute new insights, theories, or empirical evidence that expands the understanding ofa subject.2.Solve Problems: Research papers aim to address existing problemsor gaps in knowledge. They identify research questions, formulate hypotheses, and conduct investigations to provide potential solutions or recommendations.This objective is particularly important in applied research, where the focus is on solving practical problems and improving real-world situations.3.Test Theories: Another objective of research papers is to test existingtheories or propose new ones. Researchers develop hypotheses based onexisting knowledge and utilize empirical data to either validate or refute thesetheories. This objective strengthens theoretical frameworks and helps refine or develop new concepts.4.Contribute to Policy Development: Research papers can havesignificant implications for policy development and decision-making. Through rigorous research, policymakers can base their decisions on evidence-basedpractices and recommendations provided in these papers. This objectiveensures that policies and actions are informed, effective, and grounded in solid research.5.Promote Innovation: Research papers often aim to push theboundaries of knowledge and foster innovation. By providing new perspectives, original data, or alternative approaches, researchers inspire fellow scholars to explore new avenues of research. This objective contributes to thedevelopment of novel ideas and solutions to pressing issues.In conclusion, research papers serve a critical role in academic and scientific communities. They not only expand knowledge but also solve problems, test theories, contribute to policy development, and promote innovation. Through the dissemination of findings, researchers facilitate intellectual exchange and collaboration, leading to the growth and advancement of various fields.。

机制检验的英语Mechanism validationMechanism validation is the process of testing and verifying the underlying principles and assumptions that govern a particular system or process. It involves a rigorous evaluation of the mechanisms that drive a system or process to ensure that they are accurate, effective, and consistent with established theories and models.Mechanism validation is an important step in scientific research and engineering design, as it helps to ensure that the system or process being studied is reliable and can be trusted to produce consistent and predictable results. This is particularly important in fields such as medicine, where the effectiveness of treatments and drugs depends on the accurate understanding and validation of the underlying mechanisms. The process of mechanism validation typically involves a combination of empirical testing, mathematical modeling, and theoretical analysis. Empirical testing involves conducting experiments and collecting data to test the predictions of the underlying mechanisms, while mathematical modeling and theoretical analysis involve developing mathematical and conceptual models to explain the observed phenomena.In order to ensure that the mechanisms being studied are valid, it is important to carefully consider and test the assumptions that underlie them. These assumptions may include things like the behavior of the materials or fluids involved, the accuracy of the measurements being used, and the influence of external factors such as temperature, pressure, or humidity. Overall, mechanism validation is a critical aspect of scientific research and engineering design, as it helps to ensure that the systems and processes being studied are accurate, reliable, and consistent with established theories and models. By rigorously testing and verifying the underlying mechanisms, researchers and engineers can build systems and processes that are effective, efficient, and capable of producing predictable and consistent results.。

Package‘GGMridge’November24,2023Type PackageTitle Gaussian Graphical Models Using Ridge Penalty Followed byThresholding and ReestimationVersion1.4Date2023-11-24Author Min Jin Ha[aut,cre],Shannon T.Holloway[ctb]Maintainer Shannon T.Holloway<****************************>Depends mvtnorm,MASS,stats,graphicsDescription Estimation of partial correlation matrix using ridge penaltyfollowed by thresholding and reestimation.Under multivariate Gaussianassumption,the matrix constitutes an Gaussian graphical model(GGM).License GPL-2LazyLoad yesNeedsCompilation noEncoding UTF-8RoxygenNote7.2.1Collate'EM.mixture.R''scaledMat.R''svdFunc.R''splitSets.R''mbda.cv.R''R.separate.ridge.R''StructuredEstimate.R''ksStat.R''getEfronp.R''lambda.TargetD.R''lambda.cv.R''transFisher.R''lambda.pcut.cv1.R''lambda.pcut.cv.R''simulateData.R'Repository CRANDate/Publication2023-11-2422:20:04UTCR topics documented:EM.mixture (2)getEfronp (3)ksStat (4)lambda.cv (5)lambda.pcut.cv (6)12EM.mixture lambda.pcut.cv1 (8)lambda.TargetD (9)mbda.cv (10)R.separate.ridge (12)scaledMat (13)simulateData (14)structuredEstimate (15)transFisher (16)Index18 EM.mixture Estimation of the mixture distribution using EM algorithmDescriptionEstimation of the parameters,null proportion,and degrees of freedom of the exact null density in the mixture distribution.UsageEM.mixture(p,eta0,df,tol)Argumentsp A numeric vector representing partial correlation coefficients.eta0An initial value for the null proportion;1-eta0is the non-null proportion.df An initial value for the degrees of freedom of the exact null density.tol The tolerance level for convergence.ValueA list object containingdf Estimated degrees of freedom of the null density.eta0Estimated null proportion.iter The number of iterations required to reach convergence.Author(s)Min Jin HaReferencesSchafer,J.and Strimmer,K.(2005).An empirical Bayes approach to inferring large-scale gene association networks.Bioinformatics,21,754–764.getEfronp3 getEfronp Estimation of empirical null distribution.DescriptionEstimation of empirical null distribution using Efron’s central matching.UsagegetEfronp(z,bins=120L,maxQ=9,pct=0,pct0=0.25,cc=1.2,plotIt=FALSE)Argumentsz A numeric vector of z values following the theoretical normal null distribution.bins The number of intervals for density estimation of the marginal density of z.maxQ The maximum degree of the polynomial to be considered for density estimation of the marginal density of z.pct Low and top(pct*100)f(z).pct0Low and top(pct0*100)estimate f0(z).cc The central parts(µ−σcc,µ+σcc)of the empirical distribution z are used for an estimate of the null proportion(eta).plotIt TRUE if density plot is to be produced.ValueA list containingcorrectz The corrected z values to follow empirically standard normal distribution.correctp The corrected p values using the correct z values.q The chosen degree of polynomial for the estimated marginal density.mu0hat The location parameter for the normal null distribution.sigma0hat The scale parameter for the normal null distribution.eta The estimated null proportion.4ksStatAuthor(s)Min Jin HaReferencesEfron,B.(2004).Large-scale simultaneous hypothesis testing.Journal of the American Statistical Association,99,96–104.Ha,M.J.and Sun,W.(2014).Partial correlation matrix estimation using ridge penalty followed by thresholding and re-estimation.Biometrics,70,762–770.Examplesp<-100#number of variablesn<-50#sample size################################Simulate data###############################simulation<-simulateData(G=p,etaA=0.02,n=n,r=1)data<-simulation$data[[1]]stddata<-scale(x=data,center=TRUE,scale=TRUE)################################estimate ridge parameter###############################lambda.array<-seq(from=0.1,to=20,by=0.1)*(n-1.0)fit<-lambda.cv(x=stddata,lambda=lambda.array,fold=10L)lambda<-fit$lambda[which.min(fit$spe)]/(n-1.0)################################calculate partial correlation#using ridge inverse###############################w.upper<-which(upper.tri(diag(p)))partial<-solve(lambda*diag(p)+cor(data))partial<-(-scaledMat(x=partial))[w.upper]################################get p-values from empirical#null distribution###############################efron.fit<-getEfronp(z=transFisher(x=partial))ksStat The Kolmogorov-Smirnov Statistic for p-ValuesDescriptionCalculates the Kolmogorov-Smirnov statistic for p-valueslambda.cv5UsageksStat(p)Argumentsp A numeric vector with p-values.ValueKolmogorov-Smirnov statisticAuthor(s)Min Jin HaExamplesp<-stats::runif(100)ksStat(p=p)ks.test(p,y="punif")#compare with ks.testlambda.cv Choose the Tuning Parameter of the Ridge InverseDescriptionChoose the tuning parameter of the ridge inverse by minimizing cross validation estimates of the total prediction errors of the p separate ridge regressions.Usagelambda.cv(x,lambda,fold)Argumentsx An n by p data matrix.lambda A numeric vector of candidate tuning parameters.fold fold-cross validation is performed.ValueA list containinglambda The selected tuning parameter,which minimizes the total prediction errors.spe The total prediction error for all the candidate lambda values.Author(s)Min Jin HaReferencesHa,M.J.and Sun,W.(2014).Partial correlation matrix estimation using ridge penalty followed by thresholding and re-estimation.Biometrics,70,762–770.Examplesp<-100#number of variablesn<-50#sample size################################Simulate data###############################simulation<-simulateData(G=p,etaA=0.02,n=n,r=1)data<-simulation$data[[1L]]stddata<-scale(x=data,center=TRUE,scale=TRUE)################################estimate ridge parameter###############################lambda.array<-seq(from=0.1,to=20,by=0.1)*(n-1.0)fit<-lambda.cv(x=stddata,lambda=lambda.array,fold=10L)lambda<-fit$lambda[which.min(fit$spe)]/(n-1.0)################################calculate partial correlation#using ridge inverse###############################partial<-solve(lambda*diag(p)+cor(data))partial<--scaledMat(x=partial)lambda.pcut.cv Choose the Tuning Parameter of the Ridge Inverse and ThresholdingLevel of the Empirical p-ValuesDescriptionChoose the tuning parameter of the ridge inverse and p-value cutoff by minimizing cross validation estimates of the total prediction errors of the p separate ridge regressions.Usagelambda.pcut.cv(x,lambda,pcut,fold=10L)Argumentsx n by p data matrix.lambda A vector of candidate tuning parameters.pcut A vector of candidate cutoffs of pvalues.fold fold-cross validation is performed.ValueThe total prediction errors for all lambda(row-wise)and pcut(column-wise)Author(s)Min Jin HaReferencesHa,M.J.and Sun,W.(2014).Partial correlation matrix estimation using ridge penalty followed by thresholding and re-estimation.Biometrics,70,762–770.Examplesp<-100#number of variablesn<-50#sample size################################Simulate data###############################simulation<-simulateData(G=p,etaA=0.02,n=n,r=1)data<-simulation$data[[1L]]stddata<-scale(x=data,center=TRUE,scale=TRUE)################################Selection of a lambda and a#p-value cutoff###############################lambda.array<-seq(from=0.1,to=5,length=10)*(n-1.0)pcut.array<-seq(from=0.01,to=0.05,by=0.01)tpe<-lambda.pcut.cv(x=stddata,lambda=lambda.array,pcut=pcut.array,fold=3L)w.mintpe<-which(tpe==min(tpe),arr.ind=TRUE)lambda<-lambda.array[w.mintpe[1L]]alpha<-pcut.array[w.mintpe[2L]]lambda.pcut.cv1Choose the Tuning Parameter of the Ridge Inverse and ThresholdingLevel of the Empirical p-Values.Calculate total prediction error fortest data afterfitting partial correlations from train data for all valuesof lambda and pcut.DescriptionChoose the Tuning Parameter of the Ridge Inverse and Thresholding Level of the Empirical p-Values.Calculate total prediction error for test data afterfitting partial correlations from train data for all values of lambda and pcut.Usagelambda.pcut.cv1(train,test,lambda,pcut)Argumentstrain An n x p data matrix from which the model isfitted.test An m x p data matrix from which the model is evaluated.lambda A vector of candidate tuning parameters.pcut A vector of candidate cutoffs of pvalues.ValueTotal prediction error for all the candidate lambda and pvalue cutoff values.Author(s)Min Jin HaReferencesHa,M.J.and Sun,W.(2014).Partial correlation matrix estimation using ridge penalty followed by thresholding and re-estimation.Biometrics,70,762–770.Examplesp<-100#number of variablesn<-50#sample size################################Simulate data###############################simulation<-simulateData(G=p,etaA=0.02,n=n,r=1)data<-simulation$data[[1L]]lambda.TargetD9################################Split into train/test sets###############################testindex<-sample(1L:n,10L)train<-data[-testindex,,drop=FALSE]stdTrain<-scale(x=train,center=TRUE,scale=TRUE)test<-data[testindex,,drop=FALSE]stdTest<-scale(x=test,center=TRUE,scale=TRUE)################################Calculate total prediction#errors for all candidate#lambda and p-value cutoffs###############################lambda.array<-seq(from=0.1,to=5,length=10)*(n-1.0)pcut.array<-seq(from=0.01,to=0.05,by=0.01)tpe<-lambda.pcut.cv1(train=stdTrain,test=stdTest,lambda=lambda.array,pcut=pcut.array)lambda.TargetD Shrinkage Estimation of a Covariance Matrix Toward an Identity Ma-trixDescriptionEstimation of a weighted average of a sample covariance(correlation)matrix and an identity matrix. Usagelambda.TargetD(x)Argumentsx Centered data for covariance shrinkage and standardized data for correlation shrinkage.DetailsAn analytical approach to the estimate ridge parameter.ValueThe estimates of shrinkage intensity.mbda.cv Author(s)Min Jin HaReferencesSchafer,J.and Strimmer,K.(2005).A shrinkage approach to large-scale covariance matrix estima-tion and implications for functional genomics.Statistical Applications in Genetics and Molecular Biology,4,32.Ha,M.J.and Sun,W.(2014).Partial correlation matrix estimation using ridge penalty followed by thresholding and re-estimation.Biometrics,70,762–770.Examples################################Simulate data###############################simulation<-simulateData(G=100,etaA=0.02,n=50,r=10)dat<-simulation$data[[1L]]stddat<-scale(x=dat,center=TRUE,scale=TRUE)mbda<-lambda.TargetD(x=stddat)################################the ridge parameter###############################mbda<mbda/(mbda)################################partial correlation matrix###############################partial<-solve(cor(dat)+mbda*diag(ncol(dat)))partial<--scaledMat(x=partial)mbda.cv Choose the Tuning Parameter of a Ridge Regression Using Cross-ValidationDescriptionChoose the tuning parameter of a ridge regression using cross-validation.Usagembda.cv(y,x,lambda,fold)mbda.cv11 Argumentsy Length n response vector.x n x p matrix for covariates with p variables and n sample size.lambda A numeric vector for candidate tuning parameters for a ridge regression.fold fold-cross validation used to choose the tuning parameter.ValueA list containinglambda The selected tuning parameter,which minimizes the prediction error.spe The prediction error for all of the candidate lambda values.Author(s)Min Jin HaReferencesHa,M.J.and Sun,W.(2014).Partial correlation matrix estimation using ridge penalty followed by thresholding and re-estimation.Biometrics,70,762–770.Examplesp<-100#number of variablesn<-50#sample size################################Simulate data###############################simulation<-simulateData(G=p,etaA=0.02,n=n,r=1)data<-simulation$data[[1L]]stddat<-scale(x=data,center=TRUE,scale=TRUE)X<-stddat[,-1L,drop=FALSE]y<-stddat[,1L]mbda<mbda.cv(y=y,x=X,lambda=seq(from=0.01,to=1,by=0.1),fold=10L)lambda<mbda$lambda[which.min(mbda$spe)]12R.separate.ridgeR.separate.ridge Estimation of Partial Correlation Matrix Using p Separate Ridge Re-gressions.DescriptionThe partial correlation matrix is estimated by p separate ridge regressions with the parameters se-lected by cross validation.UsageR.separate.ridge(x,fold,lambda,verbose=FALSE)Argumentsx n x p data matrix;n is the#of samples and p is the#of variables.fold Ridge parameters are selected by fold-cross validations separately for each re-gression.lambda The candidate ridge parameters for all p ridge regressions.verbose TRUE/FALSE;if TRUE,print the procedure.ValueA list containingR The partial correlation matrix.lambda.sel The selected tuning parameters for p ridge regressions.Author(s)Min Jin HaReferencesHa,M.J.and Sun,W.(2014).Partial correlation matrix estimation using ridge penalty followed by thresholding and re-estimation.Biometrics,70,762–770.Examplesp<-100#number of variablesn<-50#sample size################################Simulate data###############################simulation<-simulateData(G=p,etaA=0.02,n=n,r=1)data<-simulation$data[[1L]]stddata<-scale(x=data,center=TRUE,scale=FALSE)scaledMat13################################estimate ridge parameter###############################w.upper<-which(upper.tri(diag(p)))lambda.array<-seq(from=0.1,to=20,by=0.1)*(n-1.0)partial.sep<-R.separate.ridge(x=stddata,lambda=lambda.array,fold=5L,verbose=TRUE)$R[w.upper]scaledMat Scale a square matrixDescriptionScale a square matrix to have unit diagonal elements.UsagescaledMat(x)Argumentsx A square matrix with positive diagonal elementsValueScaled matrix of x.Author(s)Min Jin HaExamples################################Simulate data###############################simulation<-simulateData(G=100,etaA=0.02,n=50,r=10)dat<-simulation$data[[1L]]correlation<-scaledMat(x=stats::cov(dat))14simulateData simulateData Generate Simulation Data from a Random Network.DescriptionGenerate a random network where both the network structure and the partial correlation coeffi-cients are random.The data matrices are generated from multivariate normal distribution with the covariance matrix corresponding to the network.UsagesimulateData(G,etaA,n,r,dist="mvnorm")ArgumentsG The number of variables(vertices).etaA The proportion of non-null edges among all the G(G-1)/2edges.n The sample size.r The number of replicated G by N data matrices.dist A function which indicates the distribution of sample."mvnorm"is multivari-ate normal distribution and"mvt"is multivariate t distribution with df=2.Thedefault is set by"mvnorm".ValueA list containingdata a list,each element containing an n X G matrix of simulated data.true.partialcorThe partial correlation matrix which the datasets are generated from.truecor.scaledThe covariance matrix calculted from the partial correlation matrix.sig.node The indices of nonzero upper triangle elements of partial correlation matrix. Author(s)Min Jin HaReferencesSchafer,J.and Strimmer,K.(2005).An empirical Bayes approach to inferring large-scale gene association networks.Bioinformatics,21,754–764.Examplessimulation<-simulateData(G=100,etaA=0.02,n=50,r=10)structuredEstimate15 structuredEstimate Estimation of Partial Correlation Matrix Given Zero Structure.DescriptionEstimation of nonzero entries of the partial correlation matrix given zero structure.UsagestructuredEstimate(x,E)Argumentsx n by p data matrix with the number of variables p and sample size n.E The row and column indices of zero entries of the partial correlation matrix. ValueA list containingR The partial correlation matrix.K The inverse covariance matrix.RSS The residual sum of squares.Author(s)Min Jin HaReferencesHa,M.J.and Sun,W.(2014).Partial correlation matrix estimation using ridge penalty followed by thresholding and re-estimation.Biometrics,70,762–770.Examplesp<-100#number of variablesn<-50#sample size################################Simulate data###############################simulation<-simulateData(G=p,etaA=0.02,n=n,r=1)data<-simulation$data[[1L]]stddata<-scale(x=data,center=TRUE,scale=TRUE)################################estimate ridge parameter###############################lambda.array<-seq(from=0.1,to=20,by=0.1)*(n-1.0)fit<-lambda.cv(x=stddata,lambda=lambda.array,fold=10L) lambda<-fit$lambda[which.min(fit$spe)]/(n-1)################################calculate partial correlation#using ridge inverse###############################w.upper<-which(upper.tri(diag(p)))partial<-solve(lambda*diag(p)+cor(data))partial<-(-scaledMat(x=partial))[w.upper]################################get p-values from empirical#null distribution###############################efron.fit<-getEfronp(z=transFisher(x=partial),bins=50L,maxQ=13)################################estimate the edge set of#partial correlation graph with#FDR control at level0.01###############################w.array<-which(upper.tri(diag(p)),arr.ind=TRUE)th<-0.01wsig<-which(p.adjust(efron.fit$correctp,method="BH")<th)E<-w.array[wsig,]dim(E)################################structured estimation###############################fit<-structuredEstimate(x=stddata,E=E)th.partial<-fit$RtransFisher Fisher’s Z-TransformationDescriptionFisher’s Z-transformation of(partial)correlation.UsagetransFisher(x)Argumentsx A vector having entries between-1and1.ValueFisher’s Z-transformed values.Author(s)Min Jin HaExamples################################Simulate data###############################simulation<-simulateData(G=100,etaA=0.02,n=50,r=1) dat<-simulation$data[[1L]]stddat<-scale(x=dat,center=TRUE,scale=TRUE)mbda<-lambda.TargetD(x=stddat)################################the ridge parameter###############################mbda<mbda/(mbda)################################partial correlation matrix###############################partial<-solve(cor(dat)+mbda*diag(ncol(dat)))partial<--scaledMat(x=partial)################################Fisher s Z transformation of#upper diagonal of the partial#correlation matrix###############################w.upper<-which(upper.tri(diag(nrow(dat))))psi<-transFisher(x=partial[w.upper])IndexEM.mixture,2getEfronp,3ksStat,4lambda.cv,5lambda.pcut.cv,6lambda.pcut.cv1,8lambda.TargetD,9mbda.cv,10R.separate.ridge,12scaledMat,13simulateData,14structuredEstimate,15transFisher,1618。

英语作文有关实验的题目Title: The Role of Experiments in Scientific Inquiry。

In the realm of scientific exploration, experiments serve as indispensable tools for probing hypotheses,testing theories, and unraveling the mysteries of the natural world. Through meticulously designed procedures and systematic observations, experiments offer a pathway to uncovering new knowledge and refining existing understanding. This essay delves into the significance of experiments in scientific inquiry, exploring theiressential role in advancing human understanding and driving innovation.To begin with, experiments provide a controlled environment where variables can be manipulated and outcomes measured with precision. This controlled setting allows scientists to isolate specific factors and observe their effects, thus enabling the establishment of cause-and-effect relationships. By carefully controlling variablesand conditions, researchers can minimize external influences and draw reliable conclusions about the phenomena under investigation.Moreover, experiments offer a means of testing hypotheses formulated through deductive reasoning or inspired by empirical observations. Hypotheses serve as educated guesses or tentative explanations for observed phenomena. Through experimentation, scientists subject these hypotheses to empirical scrutiny, either confirming or refuting their validity based on the evidence gathered. This iterative process of hypothesis testing lies at the heart of scientific inquiry, driving the advancement of knowledge and the refinement of theories.Furthermore, experiments foster a spirit of curiosity and exploration, encouraging scientists to push the boundaries of existing knowledge and explore new frontiers. By posing questions and designing experiments to address them, researchers embark on a journey of discovery, driven by a desire to unravel the mysteries of the universe. Whether exploring the depths of outer space or theintricacies of subatomic particles, experiments serve as vehicles for human ingenuity and exploration, fueling the quest for understanding.Additionally, experiments play a crucial role in validating scientific theories and models, providing empirical support for theoretical frameworks. Theories serve as overarching explanations for natural phenomena, offering insights into the underlying principles governing the universe. Through experimentation, scientists gather empirical evidence to either support or challenge these theories, refining and revising them in light of new data. This symbiotic relationship between theory and experiment forms the cornerstone of scientific progress, fostering a dynamic interplay between observation and theory-building.Moreover, experiments drive technological innovation and practical applications, translating theoreticalinsights into real-world solutions. From the development of new materials and medicines to the optimization of industrial processes, experiments underpin technological advancements that shape the course of human civilization.By applying scientific principles to practical problems, researchers harness the power of experimentation to drive innovation and improve the quality of life for people around the globe.In conclusion, experiments occupy a central position in the landscape of scientific inquiry, serving as catalysts for discovery, innovation, and understanding. By providing a systematic framework for hypothesis testing, empirical validation, and theory building, experiments empower scientists to unravel the mysteries of the natural world and push the boundaries of human knowledge. As we continue to harness the power of experimentation to explore new frontiers and tackle complex challenges, we embark on a journey of discovery that promises to enrich our understanding of the universe and transform the world we inhabit.。