Revisiting Horizontal Stratification in Higher Education: College Prestige Hierarchy and Educational Assortative Mating in China

Existing research on assortative mating has examined marriage between people with different levels of education, yet heterogeneity in educational assortative mating outcomes of college graduates has been mostly ignored. Using data from the 2010 Chinese Family Panel Study and log-multiplicative models, this study examines the changing structure and association of husbands' and wives' educational attainment between 1980 and 2010, a period in which Chinese higher education experienced rapid expansion and stratification. Results show that the graduates of first-tier institutions are less likely than graduates of lower-ranked colleges to marry someone without a college degree. Moreover, from 1980 to 2010, female first-tier-college graduates were increasingly more likely to marry people who graduated from similarly prestigious colleges, although there is insufficient evidence to draw the same conclusion about their male counterparts. This study thus demonstrates the extent of heterogeneity in educational assortative mating patterns among college graduates and the tendency for elite college graduates to marry within the educational elite.

Statistical approach and multiplicative models for electric vehicles charging behaviour patterns

Since the charging processes of electric vehicles are stochastic and time-dependent, the paper views an approach based on a statistical analysis of real data on electricity consumption at charging station connection points. Other types of data (geographical, public sites, distance between individual charging stations, etc.) are also taken into account when making the analysis. Multiplicative models are the most suitable for studying and forecasting time series with pronounced cyclicity and seasonality. Their application allows us to consider the correlation of the load in the consuming nodes with regional features, climatic factors and seasonality. The method and approach discussed in this paper make possible the processing of a large amount of data and the detection of load cyclicity in the load schedule of electricity facilities. The results of the model will identify the requested charging power in a developing charging infrastructure.

What Is the Numerical Nature of Pain Relief?

Pain relief, or a decrease in self-reported pain intensity, is frequently the primary outcome of pain clinical trials. Investigators commonly report pain relief in one of two ways: using raw units (additive) or using percentage units (multiplicative). However, additive and multiplicative scales have different assumptions and are incompatible with one another. In this work, we describe the assumptions and corollaries of additive and multiplicative models of pain relief to illuminate the issue from statistical and clinical perspectives. First, we explain the math underlying each model and illustrate these points using simulations, for which readers are assumed to have an understanding of linear regression. Next, we connect this math to clinical interpretations, stressing the importance of statistical models that accurately represent the underlying data; for example, how using percent pain relief can mislead clinicians if the data are actually additive. These theoretical discussions are supported by empirical data from four longitudinal studies of patients with subacute and chronic pain. Finally, we discuss self-reported pain intensity as a measurement construct, including its philosophical limitations and how clinical pain differs from acute pain measured during psychophysics experiments. This work has broad implications for clinical pain research, ranging from statistical modeling of trial data to the use of minimal clinically important differences and patient-clinician communication.

Additive and multiplicative probabilistic models of infant looking times

Additive and multiplicative regression models of habituation were compared regarding the fit to looking times from a habituation experiment with infants aged between 3 and 11 months. In contrast to earlier studies, the current study considered multiple probability distributions, namely Weibull, gamma, lognormal and normal distribution. In the habituation experiment the type of contrast between the habituation and the test trial was varied (luminance, color or orientation contrast), crossed with the number of habituation trials (1, 3, 5, or 7 habituation trials) and crossed with three age cohorts (4, 7, 10 months). The initial mean LT to dark stimuli (around 3.7 s) was considerably shorter than the mean LT to green and gray stimuli (around 5 s). Infants showed the strongest dishabituation to changes from dark to bright (luminance contrast) and weak-to-no dishabituation to a 90-degrees rotation of the gray stimuli (orientation contrast). The dishabituation was stronger after five and seven habituation trials, but the result was not statistically robust. The gamma distribution showed the best fit in terms of log-likelihood and mean absolute error and the best predictive performance. Furthermore, the gamma distribution showed small correlations between parameters relative to other models. The normal additive model showed an inferior fit and medium correlations between the parameters. In particular, the positive correlation between the initial looking time (LT) and the habituation rate was likely responsible for a different interpretation relative to the multiplicative models of the main effect of age on the habituation rate. Otherwise, the additive and multiplicative models provided similar statistical conclusions. The performance of the model versions without pooling and with partial pooling across participants (also called random-effects, multi-level or hierarchical models) were compared. The latter type of models showed worse data fit but more precise predictions and reduced correlations between the parameters. The performance of model variants with auto-regressive time structures were explored but showed considerably worse fit. The performance of quadratic models that allowed non-monotonic changes in LTs were investigated as well. However, when fitted with LT data, these models did not produce non-monotonic change in LTs. The study underscores the utility of partial-pooling models in terms of providing more accurate predictions. Further, it agrees with previous research in that a multiplicative LT model is preferable. Nevertheless, the current results suggest that the impact of the choice of an additive model on the statistical inference is less dramatic then previously assumed.

Development and application of a United States-wide correction for PM_2.5 data collected with the PurpleAir sensor

PurpleAir sensors, which measure particulate matter (PM), are widely used by individuals, community groups, and other organizations including state and local air monitoring agencies. PurpleAir sensors comprise a massive global network of more than 10 000 sensors. Previous performance evaluations have typically studied a limited number of PurpleAir sensors in small geographic areas or laboratory environments. While useful for determining sensor behavior and data normalization for these geographic areas, little work has been done to understand the broad applicability of these results outside these regions and conditions. Here, PurpleAir sensors operated by air quality monitoring agencies are evaluated in comparison to collocated ambient air quality regulatory instruments. In total, almost 12 000 24 h averaged PM2.5 measurements from collocated PurpleAir sensors and Federal Reference Method (FRM) or Federal Equivalent Method (FEM) PM2.5 measurements were collected across diverse regions of the United States (US), including 16 states. Consistent with previous evaluations, under typical ambient and smoke-impacted conditions, the raw data from PurpleAir sensors overestimate PM2.5 concentrations by about 40 % in most parts of the US. A simple linear regression reduces much of this bias across most US regions, but adding a relative humidity term further reduces the bias and improves consistency in the biases between different regions. More complex multiplicative models did not substantially improve results when tested on an independent dataset. The final PurpleAir correction reduces the root mean square error (RMSE) of the raw data from 8 to 3 µg m−3, with an average FRM or FEM concentration of 9 µg m−3. This correction equation, along with proposed data cleaning criteria, has been applied to PurpleAir PM2.5 measurements across the US on the AirNow Fire and Smoke Map (https://fire.airnow.gov/, last access: 14 May 2021) and has the potential to be successfully used in other air quality and public health applications.

Understanding interactions between risk factors, and assessing the utility of the additive and multiplicative models through simulations

Understanding the genetic background of complex diseases requires the expansion of studies beyond univariate associations. Therefore, it is important to use interaction assessments of risk factors in order to discover whether, and how genetic risk variants act together on disease development. The principle of interaction analysis is to explore the magnitude of the combined effect of risk factors on disease causation. In this study, we use simulations to investigate different scenarios of causation to show how the magnitude of the effect of two risk factors interact. We mainly focus on the two most commonly used interaction models, the additive and multiplicative risk scales, since there is often confusion regarding their use and interpretation. Our results show that the combined effect is multiplicative when two risk factors are involved in the same chain of events, an interaction called synergism. Synergism is often described as a deviation from additivity, which is a broader term. Our results also confirm that it is often relevant to estimate additive effect relationships, because they correspond to independent risk factors at low disease prevalence. Importantly, we evaluate the threshold of more than two required risk factors for disease causation, called the multifactorial threshold model. We found a simple mathematical relationship (square root) between the threshold and an additive-to-multiplicative linear effect scale (AMLES), where 0 corresponds to an additive effect and 1 to a multiplicative. We propose AMLES as a metric that could be used to test different effects relationships at the same time, given that it can simultaneously reveal additive, multiplicative and intermediate risk effects relationships. Finally, the utility of our simulation study was demonstrated using real data by analyzing and interpreting gene-gene interaction odds ratios from a rheumatoid arthritis case-control cohort.

Development and Application of a United States wide correction for PM_2.5 data collected with the PurpleAir sensor

PurpleAir sensors which measure particulate matter (PM) are widely used by individuals, community groups, and other organizations including state and local air monitoring agencies. PurpleAir sensors comprise a massive global network of more than 10,000 sensors. Previous performance evaluations have typically studied a limited number of PurpleAir sensors in small geographic areas or laboratory environments. While useful for determining sensor behavior and data normalization for these geographic areas, little work has been done to understand the broad applicability of these results outside these regions and conditions. Here, PurpleAir sensors operated by air quality monitoring agencies are evaluated in comparison to collocated ambient air quality regulatory instruments. In total, almost 12,000 24-hour averaged PM2.5 measurements from collocated PurpleAir sensors and Federal Reference Method (FRM) or Federal Equivalent Method (FEM) PM2.5 measurements were collected across diverse regions of the United States (U.S.), including 16 states. Consistent with previous evaluations, under typical ambient and smoke impacted conditions, the raw data from PurpleAir sensors overestimate PM2.5 concentrations by about 40 % in most parts of the U.S. A simple linear regression reduces much of this bias across most U.S. regions, but adding a relative humidity term further reduces the bias and improves consistency in the biases between different regions. More complex multiplicative models did not substantially improve results when tested on an independent dataset. The final PurpleAir correction reduces the root mean square error (RMSE) of the raw data from 8 µg m−3 to 3 µg m−3 with an average FRM or FEM concentration of 9 µg m−3. This correction equation, along with proposed data cleaning criteria, has been applied to PurpleAir PM2.5 measurements across the U.S. in the AirNow Fire and Smoke Map (fire.airnow.gov) and has the potential to be successfully used in other air quality and public health applications.

METHODOLOGY OF THE ANALYTICAL MODELING AND FACTOR ANALYSIS OF THE PRODUCTION EQUIPMENT PRODUCTIVITY

The article deals with the methodology of modeling and factor analysis of a production equipment unit productivity. It is emphasized that the productivity is an important generalizing indicator, that reflects the efficiency of the production equipment use. The final results of any enterprise’s activity directly depend on its absolute value and growth rates. The change of this indicator is influenced by various factors, that characterize the availability, structure and use of the production equipment in terms of time and capacity. In this regard, the factor analysis of the given indicator, i.e. the study of the influence of any individual factors on its change, has a relevant importance. The article emphasizes that the mathematical modeling of this indicator is an important way of solving any economic and statistical tasks, in particular, of studying the influence of the most important factors on the change in the productivity of a production equipment unit. The calculation of the quantitative influence of the mentioned factors on the change in the productivity of a production equipment unit is proposed to be carried out on the basis of the chain substitutions method. In the process of modeling of the factor systems of this indicator it is proposed to implement a phased factor analysis of a production equipment unit productivity, i.e. to consistently decompose the value of this index into a number of its initial indicators, which depending on the goals and objectives of the enterprise, gives the possibility to calculate the influence of those factors, that are the most significant and relevant at the moment. The methodology of the analytical modeling and factor analysis of production equipment productivity, given in the article, allows to present this indicator in the form of some deterministic multiplicative models, to determine the influence of the most important factors on its change, to investigate the regularities of such an influence, to justify the appropriate management decisions regarding the further development of the enterprise. Keywords: methodology, modeling, productivity, method, factor.

Explaining Declining Trends in Educational Homogamy: The Role of Institutional Changes in Higher Education in Japan

Research on educational assortative mating has devoted much attention to educational expansion but has been less focused on a concurrent trend of importance – growing differentiation among higher education institutions. This study proposes that the bifurcation between high- and low-tier institutions in the context of high participation in tertiary education may help us understand the mixed evidence on educational homogamy trends across countries. I focus on Japan, which is characterized by a clear and widely acknowledged hierarchy of institutional selectivity, as an interesting case study. By applying log-linear and log-multiplicative models to data from the Japanese Panel Survey of Consumers and the Keio Household Panel Study, I find the following results. First, the odds of homogamy are higher among graduates of selective (national/public) universities than among graduates of nonselective (private) universities. Second, homogamy trends among graduates of selective and nonselective universities have diverged in recent years. I discuss these diverging trends, which have been obscured in earlier studies, provide new insights into the role of educational assortative mating in the creation of stratification and inequality.

Comparison of Mixed and Multiplicative Models when Trend Cycle Component is Linear

The purpose of this study is to present the linear trend cycle component with the emphasis on the choice between mixed and multiplication models in time series analysis. Most of the existing studies have adequately dwelt more on choice of model between additive and multiplicative, with little or no regards to the mixed model. The main aim of this study is to compare the row, column and overall means and variances for mixed and multiplicative models using Buys-Ballot table for seasonal time series. Specific objectives are 1) to obtain and compare the expected values of means for mixed and multiplicative models 2) to estimate and compare trend parameters and seasonal indices (when there is no trend, that is (b = 0)). The study indicate that column variances ( ) of the Buys-Ballot table depends on the season j only through the square of the seasonal effect for mixed model and it is for multiplicative model, a quadratic function of the column j and square of the seasonal effect .