A state-space approach for longitudinal outcomes: An application to neuropsychological outcomes

Longitudinal assessments are crucial in evaluating the disease state and trajectory in patients with neurodegenerative diseases. Neuropsychological outcomes measured over time often have a non-linear trajectory with autocorrelated residuals and a skewed distribution. We propose the adjusted local linear trend model, an extended state-space model in lieu of the commonly used linear mixed-effects model in modeling longitudinal neuropsychological outcomes. Our contributed model has the capability to utilize information from the stochasticity of the data while accounting for subject-specific trajectories with the inclusion of covariates and unequally spaced time intervals. The first step of model fitting involves a likelihood maximization step to estimate the unknown variances in the model before parsing these values into the Kalman filter and Kalman smoother recursive algorithms. Results from simulation studies showed that the adjusted local linear trend model is able to attain lower bias, lower standard errors, and high power, particularly in short longitudinal studies with equally spaced time intervals, as compared to the linear mixed-effects model. The adjusted local linear trend model also outperforms the linear mixed-effects model when data is missing completely at random, missing at random, and, in certain cases, even in data with missing not at random.

Single-cell generalized trend model (scGTM): a flexible and interpretable model of gene expression trend along cell pseudotime

Modeling single-cell gene expression trends along cell pseudotime is a crucial analysis for exploring biological processes. Most existing methods rely on nonparametric regression models for their flexibility; however, nonparametric models often provide trends too complex to interpret. Other existing methods use interpretable but restrictive models. Since model interpretability and flexibility are both indispensable for understanding biological processes, the single-cell field needs a model that improves the interpretability and largely maintains the flexibility of nonparametric regression models. Here we propose the single-cell generalized trend model (scGTM) for capturing a gene's expression trend, which may be monotone, hill-shaped, or valley-shaped, along cell pseudotime. The scGTM has three advantages: (1) it can capture non-monotonic trends that are still easy to interpret, (2) its parameters are biologically interpretable and trend informative, and (3) it can flexibly accommodate common distributions for modeling gene expression counts. To tackle the complex optimization problems, we use the particle swarm optimization algorithm to find the constrained maximum likelihood estimates for the scGTM parameters. As an application, we analyze several single-cell gene expression data sets using the scGTM and show that it can capture interpretable gene expression trends along cell pseudotime and reveal molecular insights underlying the biological processes. We also provide an open-access Python package for fitting the scGTM at https://github. com/ElvisCuiHan/scGTM.

Customer Profilling for Precision Marketing using RFM Method, K-MEANS algorithm and Decision Tree

Precision marketing is the companys ability to offer products specifically made to customers. This decision can give the company the ability to attract customers to always buy continuously. This study presents a trend model for accurately predicting monthly supply quantities / The method used in the first stage is the RFM (Recency, Frequency, Monetary) method for selecting attributes to group customers into different groups. The output of the first stage is clustered using the K-Means Algorithm. The output of clustering is then classified using the Decision Tree and compared with the K Nearest Neighbor method. The dataset that is processed is sales data from Syifamart As-Syifa Boarding School in Subang with 351,158 rows of data. The clustering process produces 4 optimal clusters. The four clusters are then classified using the Decision Tree algorithm to determine the potential and non-potential characteristics of each customer.

DYNAMICS OF THE LEASING MARKET IN THE RUSSIAN FEDERATION AND FORECAST OF ITS DEVELOPMENT

На основании проведенного исследования сложившегося уровня рынка лизинговых услуг в России установлены основные тенденции его развития. При проведении сравнительного анализа за период с 2014 по 2020 гг. рассчитаны темпы роста по показателям совокупного портфеля лизинговых услуг, определены топ-10 компаний по величине стоимости капитала, а также установлены основные направления отраслевой специфики имущества лизингодателей. Научная новизна заключается в определении причин и факторов, вызвавших подобную динамику развития рынка лизинга в России. Практическая значимость состоит в составлении прогноза развития рынка лизинговых услуг на период 2021-2022 гг. при помощи трендовой модели полиномиального вида 6 порядка, выбор которой был обусловлен возможностями применяемой программной системы MS Excel. В результате проведенного исследования сформулированы рекомендации по развитию рынка лизинговых услуг в РФ. Based on the study of the current level of the leasing services market in Russia, the main trends of its development are established. When conducting a comparative analysis for the period from 2014 to 2020, the growth rates for the indicators of the total portfolio of leasing services were calculated, the top 10 companies were determined by the value of capital, and the main directions of the industry specifics of the property of lessors were established. According to the results of the study, the reasons and factors that caused such dynamics of the development of the leasing market in Russia were identified. The practical significance consists in making a forecast of the development of the leasing services market for the period 2021-2022 using a trend model of the 6-order polynomial type. the choice of which was determined by the capabilities of the MS Excel software system used. As a result of the study, recommendations for the development of the leasing services market in the Russian Federation are formulated.

Sales Forecasting by Using Exponential Smoothing Method and Trend Method to Optimize Product Sales in PT. Zamrud Bumi Indonesia During the Covid-19 Pandemic

Forecasting is important for a company in achieving goals effectively and efficiently. Forecasting aims to determine the next steps to be taken based on historical data. PT. Zamrud Bumi Indonesia is one of the manufacturing companies in the management of agricultural liquid fertilizers with the trademark “Power Bumi”. The purpose of this study is to analyze the sales pattern of Power Bumi products during the covid-19 pandemic and compare the forecasting method that is able to produce the smallest error value in forecasting sales of Power Bumi products PT. Zamrud Bumi Indonesia. This study uses 2 methods, namely exponential smoothing and least square trend model. To calculate the error rate using MAD, MSE and MAPE. The results show that the exponential smoothing alpha 0.9 method has the smallest error value compared to other forecasting methods. In forecasting product sales, the MAD value is 130.329, MSE is 28251.23 and MAPE is 22.00% with a forecast of 627.628 boxes. Although the exponential smoothing a 0.9 method produces a forecast value that is relatively low than other methods. However, the comparison of products sold and forecasting results has a relatively small average difference (MSE). It can be interpreted that the exponential smoothing a 0.9 method is able to suppress the forecasting error value for the 2nd period. After getting the forecasting results, it can be concluded that the number of products sold for the 2nd covid-19 pandemic period will not differ much from the number of sales in the 1st covid-19 pandemic period. If the company applies this scientific forecasting method, then sales will be optimal so that excess or shortage of stock can be avoided and the predetermined sales target can be achieved. In addition, the costs incurred during the production process to sales will be more efficient.

Inclusive education in Kazakhstan: analysis of the organizing process and the possibility of its further development

The purpose of the study is to analyze the process of organization and the possibility of using inclusive education in Kazakhstan on the basis of the identified forecast values.The methodological basis of the study is a system of various techniques that make up a set of methods, mechanisms, principles, and measures to improve the effectiveness of the use of tools for improving inclusive education, which are a necessary condition for the further development of the education system.Research methods. The following methods were used in the study:- theoretical, which include: theoretical analysis of the research of domestic and foreign scientists in the field of inclusive education; analysis of legislative and regulatory documents on the implementation of inclusive education and education in general;- methods of high-quality data processing;- methods of mathematical and statistical processing.Methods of mathematical modeling and forecasting were used in the processing and systematization of data. A trend model was constructed using the least squares method, which allowed us to prove the hypothesis that the indicator "Total number of children with special educational needs covered by inclusive education" contains a linear trend and to make a forecast for 2021-2023.The conclusions and results of the study were presented using a graphical method of presenting the results obtained.The methods used for the study of economic phenomena and the processing of primary information in their entirety allow us to ensure the reliability of the analysis and the validity of the conclusions.The originality / value of the research. The study is based on the hypothesis that the indicator "Total number of children with special educational needs covered by inclusive education" contains a linear development trend, and if this is proved by the author in the course of the study, it will be possible to make a forecast for 2021-2023.Findings. The author determined the forecast values of the indicator "The total number of children with special educational needs covered by inclusive education" for 2021-2023, as a result of which:1) according to the Irwin criterion, it was found that the original time series does not contain anomalous observations;2) using the criterion of "ascending" and "descending" series, it was determined that the time series under consideration contains a trend component;3) as a result of data approximation, a trend model was obtained;4) the quality of the resulting model was evaluated in two ways: checking the adequacy and evaluating the accuracy of the model.5) predicted values of the share of educational organizations (the share of state preschool organizations, the share of state general education schools, the share of state technical and vocational education (TVE) organizations) that have created conditions for inclusive education for 2021-2023 have been determined.As a result of the study, the author analyzed the trends in the development of inclusive education in Kazakhstan, which showed that the promotion and development of access to inclusive education, social integration and non – discriminatory treatment of persons with special educational needs is relevant. In this regard, there is an urgent need to review the concept of inclusive education at the national level and conduct empirical research on the integration of children from vulnerable groups into the general education system of Kazakhstan in order to fully cover children with special educational needs with inclusive education.

Modeling Macroeconomic Indicators in Unstable Economies

A method for analysis of the dynamics of macroeconomic indicators based on the model of a piecewise trend for economies of unstable growth is proposed. The relevance of the article is supported by the absence of adequate mathematical models and the inadequacy of traditional continuous models to describe the features of economic dynamics of this type. Its application is demonstrated on the examples of Ukraine, Greece and Italy in comparison with stable developing countries of Eastern Europe - the Czech Republic, Slovakia and Poland. In the process of approbation new indices of instability based on this model have been developed. A higher degree of conformity of the proposed model is proved in comparison with traditional continuous models not only for countries with signs of unstable economic dynamics, but also for some countries with stable economies. During approbation, a new index of instability of growth was developed based on this piecewise linear trend model. The indices of instability of growth were calculated for 43 European countries for the period from 1989 to 2019 and their rating was built.JEL Classification: E27, D61, G17