Commonality Analysis: A Method for Decomposing Explained Variance in Multiple Regression Analyses

Abstract

Commonality analysis is a procedure for decomposing R2 in multiple regression analyses into the percent of variance in the dependent variable associated with each independent variable uniquely, and the proportion of explained variance associated with the common effects of predictors. Commonality analysis thus sheds additional light on the magnitude of an obtained multivariate relationship by identifying the relative importance of all independent variables, findings which can be of theoretical and practical significance. In this paper we offer a brief explication of commonality analysis; a step-by-step discussion of how communication researchers may perform commonality analyses using output from computer-assisted statistical analysis programs like SPSS; and we provide an extended example illustrating a commonality analysis.

Calibration and assessment of electrochemical air quality sensors by co-location with regulatory-grade instruments

“…The 1 Hz measurements are then averaged over a user-defined interval (1 min in the present study) and transmitted to a remote server where data are stored in a MySQL database and visualized in real time. Flags were set to mark the first 4 h after a node was turned on to indicate a sensor warmup period (Roberts et al, 2012;Smith et al, 2017). In addition, flags are set whenever the ADC or RHT sensor reported a failure.…”

“…There are multiple advantages to this approach: the reference instruments are regularly calibrated, the reference measurement data are generally made publicly available (e.g., EPA AirNow, US EPA, 2017;OpenAQ, Hasenkopf, 2017), and the calibrations are carried out under ambient conditions that are (at least partially) representative of the sensor measurements to be made. Indeed, the effectiveness of co-location has been demonstrated in several recent studies, with sensor outputs (voltages) and other environmental parameters (e.g., temperature) related to the true concentration values (from the reference instruments) via some form of regression from either parametric models (Jiao et al, 2016;Lewis et al, 2015;Masson et al, 2015;Mueller et al, 2017;Popoola et al, 2016;Sadighi et al, 2017;Smith et al, 2017) or machine-learning/nonparametric methods (Cross et al, 2017;Spinelle et al, 2015;Zimmerman et al, 2017).…”

“…However, accurate calibration of such sensors poses a major challenge. Even setting aside the logistical difficulties associated with calibrating a large number of sensors distributed throughout a network, there are specific technical challenges that can limit the accuracy of any calibration; these include the sensitivity of sensors to environmental conditions (temperature and relative humidity, RH) (Cross et al, 2017;Masson et al, 2015;Mead et al, 2013;Popoola et al, 2016), cross sensitivities to other (sometimes unknown or unmeasured) atmospheric species (Lewis et al, 2015;Mueller et al, 2017;Spinelle et al, 2015;Zimmerman et al, 2017), and long-term sensitivity decay (drift) associated with the evaporation of electrolyte solution (Mead et al, 2013;Smith et al, 2017).…”

Intelligence and temporal accuracy of behaviour: unique and shared associations with reaction time and motor timing

“…Ver 2. Drift), as well as unique contributions of each variable were calculated using linear combinations of the multiple regression coefficients between intelligence and different subsets of independent variables, according to Seibold & McPhee (Seibold and McPhee 1979). The results of this analysis was represented graphically (see Fig.…”

“…Secondly, a commonality analysis was performed to determine the proportion of the total variance in intelligence associated with common and unique effects of the different timing variables (Seibold and McPhee 1979). Only the timing variables that showed significant zeroorder correlations with intelligence were included as independent variables in this analysis, i.e.…”