مدل‌بندی رگرسیونی چندکی آمیخته تاوانیده دوگانه از طریق رویکرد درستنمایی

مدل اثرهای آمیخته از جمله ابزارهای قوی آماری است که برای مدل‌بندی ارتباط بین متغیر پاسخ و متغیرهای تبیینی در تحلیل داده‌هایی با ساختار سلسله مراتبی به‌کار می‌رود. زمانی‌که توزیع خطاها غیر نرمال باشد، برآوردگرهای به‌دست آمده در این  مدل‌ها با  استفاده از هر یک از روش‌های کمترین توان دوم خطاها و ماکسیمم درستنمایی  از  کارایی لازم برخوردار نیستند.  در این‌گونه مواقع می‌توان از مدل رگرسیون چندکی آمیخته به‌عنوان جایگزین استفاده کرد. به‌علاوه،  زمانی‌که تعداد متغیرهای مورد بررسی در این نوع مدل‌بندی افزایش می‌یابد، رگرسیون چندکی آمیخته تاوانیده یکی از بهترین روش‌ها برای افزایش دقت پیشگویی و تفسیرپذیری مدل است. در این مقاله  با در نظر گرفتن توزیع لاپلاس نامتقارن برای اثرهای تصادفی، یک مدل تاوانیده دوگانه به عنوان تابعی همزمان از اثرهای تصادفی و  پارامترهای مدل پیشنهاد می‌شود. سپس، عملکرد روش پیشنهادی با استفاده از مطالعه  شبیه‌سازی آماری مورد ارزیابی قرار گرفته و بحث راجع به  نتایج حاصل به همراه مقایسه با برخی مدل‌های رقیب ارائه می‌شود. به‌علاوه، کاربستی از آن در تحلیل یک مثال واقعی نمایش داده خواهد شد.

double penalized mixed effects quantile regression modeling using the maximum likelihood approach

mixed effects is one of the powerful statistical approaches used to model the relationship between the response variable and some predictors in analyzing data with a hierarchical structure. estimating parameters in these models is often done via either the least squares error or maximum likelihood approaches. the estimated parameters obtained through either of these approachescould be more efficient if the error distributions are non-normal.in such cases, using the mixed effects quantile regression is preferred alternatively.moreover, when the number of variables studied increases, thepenalized mixed effects quantile regression is one of the best methods to gainprediction accuracy and the model’s interpretability. we propose a new toolto model the hierarchical structural data by introducing the penalty, a functionof random effects and fixed effects. this new idea can simultaneouslyestimate the parameters and predict random effects. we can then make furtherstatistical inferences on the parameters using the likelihood functionbuilt based on modeling such as a new penalized mixed effects quantile regressionmodel.material and methodsin this paper, under the assumption of an asymmetric laplace distributionfor random effects, we proposed a double penalized model in which boththe random and fixed effects are independently penalized. then, invoking astandard algorithm to estimate the parameters using the likelihood approachconstructs our subsequent step in modeling the data. since the likelihoodfunction had no tractable form, we considered the em algorithm to approx imate the integrals. to do so, we also extended the previously proposedalgorithm to derive the maximum likelihood estimate of the parameters.results and discussionthe performance of the new method proposed in this paper is evaluated in thesimulation studies, and a discussion of the results is presented along with acomparison with some competing models. our simulation experiments showthat in addition to the robustness of the presented method, it performs bettercompared to the types of penalty in the model based on different penaltyparameters. applying the proposed model in real data analysis also showedthat the new idea works well compared with some standard tools. the excitingfeature of the double-penalized model is on confining the computationprocedure to estimate only one tune parameter because the other one is optimized,using the samples and updated components while implementing thealgorithm. our results showed that considering a lower value for the tuningparameter of penalizing the fixed effects is preferred. we cannot recommendchoosing a specific distribution for the random effects while using our proposedmodel. however, we can assure that our model does the same task asother competing models do in this regard.conclusionthe model presented in this paper is a double penalized model, which is afunction of random effects and model parameters. in this paper, we achievedthe optimal shrinkage for the effects using the simulated and real data. similarto some standard methods, the degree of shrinkage for the random effectsin our model depends on the tuning parameter selection. we aim to studythe efficiency of our proposed model while one prefers to follow a bayesianapproach. also, correctly choosing the penalty parameters from a theoreticalviewpoint is another proposal for future research.