Essay Sample on Multiple Regression: Assumptions and Usage

Introduction

The author's use of multiple regression is explained by many factors, especially those related to the fact that the variables used in the study meet the assumptions of multiple regression. First, I believe that the authors' use of multiple regression is because there were more than two independent variables which were used to predict the dependent variable. That is, one of the conditions that should be met before using multiple regression analysis is the presence of more than two predictor or independent variables (Brue, 2015; Ciaburro, 2018; Hong, Li, & Fan, 2019; Martin & Kaplan, 2016). In Tharek et al.'s (2018) study, three independent variables were being studied; hence the authors' use of multiple regression was justified. They included the Diabetes Management Self-Efficacy Scale (DMSES) score, duration of Type 2 Diabetes Mellitus (T2DM), and waist circumference. The authors sought to examine whether DMSES score, duration of T2DM, and waist circumference statistically significantly predicted glycemic control (the dependent variable).

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Another reason why the authors used multiple regression analysis is that there was only one dependent variable that was being examined, glycemic control (Tharek et al., 2018). Noteworthy, one of the assumptions that should be met before using multiple regression analysis is the presence of one dependent variable that is measured at the continuous level of measurement (Hoyle, 2014; Niezrecki, 2015; Stommel & Dontje, 2014). In Tharek et al.'s (2018) study, glycemic control (the dependent variable) was measured using HbA1c levels. This is the gold standard measurement for measuring glycemic control (Sato, 2014; Sherwani, Khan, Ekhzaimy, Masood, & Sakharkar, 2016). The HbA1c levels obtained using the Bio-Rad D-10 HPLC instrument were numerical (measured at the continuous level of measurement, hence suitable for multiple regression analysis. For instance, it was reported that "the mean HbA1c was 7.99" showing that glycemic control was measured at the continuous level of measurement (Tharek et al., 2018).

Moreover, Tharek et al.'s (2018) use of multiple regression analysis is because all the dependent variables were measured at the continuous level of measurement. For instance, the first independent variable, DMSES score, was assessed using DMSES-Malay scale comprising of four subscales (foot care medications and follow-up, physical activity, eating plan, and blood glucose monitoring). All the items on these subscales were measured on a 10-point Likert scale thus yielding numerical scores for each of the items, the subscales, and total mean DMSES score (Tharek et al., 2018). Also, the second independent variable, duration of T2DM was measured in years thus yielding numerical data (Tharek et al., 2018). Lastly, waist circumference was assessed using a tape measure thus yielding numerical scores (in centimeters).

Determining if Multiple Regression Analysis was the Most Appropriate Choice

I think that the authors' use of multiple regression analysis to determine if DMSES score, duration of T2DM, and waist circumference statistically significantly predicted glycemic control was the most appropriate choice because of many reasons. One of the key reasons is that the independent variables (DMSES score, duration of T2DM, and waist circumference) and the dependent variable (glycemic control) were measured at the continuous level of measurement (either an interval or ratio variables). The second reason why I believe that multiple regression analysis was appropriate is that the model assumptions were met. One of the assumptions that were met was that of the absence of interaction and multicollinearity problem (Tharek et al., 2018). According to Warne (2017), the data being analyzed must not show multicollinearity. This implies that the independent variables of the study should not show high correlations with one another. Another assumption that was met in this study is that the model reasonably fits well.

Evaluating if the Authors Display the Data Well

It is essential to explain that the authors appropriately displayed the data. That is, the results of the multiple regression analysis were well displayed in tables which were appropriately labelled. All the independent variables and the extent to which they contributed to the model were shown in table 5.

Evaluating if the Results of the Study Stand Alone

Yes. The results of this study, as shown in the tables, can stand alone. This is because the authors did an excellent job in reporting the data useful in understanding how each of the independent variables predicted the outcome. The most important data that is useful in making the results of the study stand alone include beta coefficients and R2. For instance, the better coefficient for DMSES score is -0.398 means that an increase in participants' self-efficacy scores by one would reduce the glycemic control (HbA1c) by 0.398% (Tharek et al., 2018). For the second independent variable, duration of T2DM, with a beta coefficient of 0.177, increasing the duration of T2DM by one year leads to an increase in glycemic control by 0.177% (Tharek et al., 2018). Lastly, for the third independent variable (waist circumference), with a beta coefficient of 0.135, an increase in waist circumference by 1 cm leads to an increase in glycemic control by 0.135% (Tharek et al., 2018).

References

Brue, G. (2015). Six sigma for managers, second edition (Briefcase books series). New York, NY: McGraw Hill Professional.

Ciaburro, G. (2018). Keras 2.x Projects: 9 projects demonstrating faster experimentation of neural network and deep learning applications using Keras. Birmingham, UK: Packt Publishing Ltd.

Hong, W.-C., Li, M.-W., & Fan, G.-F. (2019). Short-term load forecasting by artificial intelligent technologies. Basel, Switzerland: MDPI.

Hoyle, R. H. (2014). Handbook of structural equation modeling. New York, NY: Guilford Publications.

Martin, N. D., & Kaplan, L. J. (2016). Principles of adult surgical critical care. New York, NY: Springer.

Niezrecki, C. (2015). Structural health monitoring and damage detection, volume 7: proceedings of the 33rd IMAC, a conference and exposition on structural dynamics, 2015. New York, NY: Springer.

Sato, A. (2014). [Indicators of glycemic control --hemoglobin A1c (Hba1c), glycated albumin (Ga), and 1,5-anhydroglucitol (1,5-AG)]. The Japanese Journal of Clinical Pathology, 62(1), 45-52.

Sherwani, S. I., Khan, H. A., Ekhzaimy, A., Masood, A., & Sakharkar, M. K. (2016). Significance of hba1c test in diagnosis and prognosis of diabetic patients. Biomarker Insights, 11, 95-104. https://doi.org/10.4137/BMI.S38440

Stommel, M., & Dontje, K. J. (2014). Statistics for advanced practice nurses and health professionals. New York, NY: Springer Publishing Company.

Tharek, Z., Ramli, A. S., Whitford, D. L., Ismail, Z., Mohd Zulkifli, M., Ahmad Sharoni, S. K., ... Jayaraman, T. (2018). Relationship between self-efficacy, self-care behavior and glycemic control among patients with type 2 diabetes mellitus in the Malaysian primary care setting. BMC Family Practice, 19(1), 39. https://doi.org/10.1186/s12875-018-0725-6