Updated:

Multiple Logistic Regression in Action Coursework

Exclusively available on Available only on IvyPanda® Made by Human No AI

Introduction

The analysis of data shows that it meets the assumptions of multiple logistic regression. The findings show that cholesterol level is a significant predictor of hypertension while age category, sex, and obesity are insignificant predictors. Hosmer-Lemeshow test shows that the model is statistically significant while scatter plots reveal that the apparent outliers do not make the model inadequate.

Assumptions

  • The dependent variable ought to exist on a nominal scale (Field, 2012). The data have met this assumption because hypertension is a nominal scale with two categories.
  • The independent variables can exist on a continuous scale, nominal scale, or ordinal scale (Forthofer, Lee, & Hernandez, 2007). The data have met this assumption for age category, sex, obesity, and hypertension are on nominal scale while cholesterol level and age are on a continuous scale. Cholesterol category exists on an ordinal scale for the scale represents increasing levels of cholesterol.
  • Multicollinearity should not exist between two or more independent variables (Field, 2012). Age category and obese do not meet this assumption for they are collinear while other independent variables have met this assumption.
  • The data points should not have influential cases (Forthofer, Lee, & Hernandez, 2007). In the data, scatter plots confirm that there are no statistically significant outliers.

Variables

Table 1. Variables and Level of Measurement

VariablesLevels of Measurement
SexNominal scale
Age in yearsRatio scale
Serum cholesterolRatio scale
ObeseNominal scale
HypertensionNominal scale

Simple Binary Logistic Regression

The First Model

The binary logistic regression results indicate that the odds of having hypertension among individuals with cholesterol levels of 200-299 and 300 or greater are 2.647 times (p = 0.04) and 13.714 times (p = 0.001) respectively higher than among individuals with under 200 cholesterol level.

The Second Model

The outcomes of the binary logistic regression indicate that the odds of hypertension increases by 1.012 times (p = 0.002) in every increase in the level of cholesterol among individuals.

Influence of the Level of Measurement

For the independent variable, the level of measurement determines its influence as a predictor variable. From the binary logistic analysis, nominal scale of cholesterol level has odds of 2.647 (p = 0.040) and 13.714 (p = 0.001) for 200-299 and 300 or above categories. In contrast, the ratio scale of cholesterol level gives an odds ratio of 1.012 (p = 0.002), which is lower than that of the nominal scale.

Since the level of measurement of the independent variable (cholesterol level) gives different odds ratio, it has changed my interpretation of odds ratio for I perceive it as a change of dependent variable for each unit change in the independent variable.

Multivariate Logistic Regression

Logistic Model

Table 2

Variables in the Equation
BS.E.WalddfSig.Exp(B)95% C.I. for EXP(B)
LowerUpper
Step 1aScl_categorical10.1652.006
Scl_categorical(1).874.4883.2061.0732.397.9216.241
Scl_categorical(2)2.504.78610.1371.00112.2272.61857.100
Age_Cat(1).282.365.5951.4401.325.6482.711
sex(1)-.177.361.2411.623.837.4121.700
Constant-1.205.4726.5171.011.300
a. Variable(s) entered on step 1: Scl_categorical, Age_Cat, sex.

Odds Ratios and the Significance of Each

  • The odds ratio of hypertension among individuals with 200-299 cholesterol is 2.397 (p = 073) while that of individuals with 300 and above cholesterol level is 12.227 (p = 001).
  • The odds ratio of hypertension among individuals with age category of 40 and above is 1.325 (p = 0.440) and the odds ratio of hypertension among women is 0.837 (p = 0.623).
  • The addition of other variables has reduced the odds ratio of hypertension among individuals with 200-299 and 300 and above cholesterol levels from 2.647 and 13.714 to 2.397 and 12.325 respectively.

Hosmer-Lemeshow Test

The Chi-square statistic of Hosmer-Lemeshow test means that the logistic regression model fits the data, according to the assumption of goodness of fit, X(5) = 3.380, p = 0.642. A p-value that is less than the significance level (0.05) rejects the model for it does not fit the data while a p-value that is greater than the significance level (0.05) shows that the model fits the data (Hosmer & Lemeshow, 2004).

Logistic regression model

Scatter Plot of Deviance Residuals versus ID

The scatter plot (Figure 1) shows that there are outliers in the distribution of data points. In the evaluation of the logistic regression model, the presence of significant outliers implies that the model does not fit the data.

Figure 1
Figure 1

Scatter Plot of Cook’s Distance versus ID

Cook’s distance as shown in the scatter plot (Figure 2) depicts that there are influential cases in the data points. Specifically, there are ten influential cases, which have Cook’s distance of more than 0.1. The existence of the influential cases means that the model does not accurately fit the data, and thus, these cases require consideration to enhance the fit of the model.

Figure 2
Figure 2

Scatter Plot of Deviance versus the Predicted Probabilities

In the scatter plot (Figure 3), the distribution of data points does not cause concern in the model for the apparent outliers in Figure 1 and Figure 2 do not have a significant impact on the model. Therefore, the scatter plot shows that the model is adequate in predicting the relationship between the dependent variable and predictors.

Figure 3
Figure 3

References

Hosmer, J., & Lemeshow, S. (2004). Applied logistic regression. Hoboken, NJ: John Wiley & Sons.

Field, A. (2012). Discovering statistics using IBM SPSS statistics. New York, NY: SAGE Publisher.

Forthofer, N., Lee, S., & Hernandez, M. (2007). Biostatistics: A guide to design, analysis, and discovery. Amsterdam, Netherlands: Elsevier Academic Press.

More related papers Related Essay Examples
Cite This paper
You're welcome to use this sample in your assignment. Be sure to cite it correctly

Reference

IvyPanda. (2022, September 27). Multiple Logistic Regression in Action. https://ivypanda.com/essays/multiple-logistic-regression-in-action/

Work Cited

"Multiple Logistic Regression in Action." IvyPanda, 27 Sept. 2022, ivypanda.com/essays/multiple-logistic-regression-in-action/.

References

IvyPanda. (2022) 'Multiple Logistic Regression in Action'. 27 September.

References

IvyPanda. 2022. "Multiple Logistic Regression in Action." September 27, 2022. https://ivypanda.com/essays/multiple-logistic-regression-in-action/.

1. IvyPanda. "Multiple Logistic Regression in Action." September 27, 2022. https://ivypanda.com/essays/multiple-logistic-regression-in-action/.


Bibliography


IvyPanda. "Multiple Logistic Regression in Action." September 27, 2022. https://ivypanda.com/essays/multiple-logistic-regression-in-action/.

If, for any reason, you believe that this content should not be published on our website, please request its removal.
Updated:
This academic paper example has been carefully picked, checked and refined by our editorial team.
No AI was involved: only quilified experts contributed.
You are free to use it for the following purposes:
  • To find inspiration for your paper and overcome writer’s block
  • As a source of information (ensure proper referencing)
  • As a template for you assignment
Privacy Settings

IvyPanda uses cookies and similar technologies to enhance your experience, enabling functionalities such as:

  • Basic site functions
  • Ensuring secure, safe transactions
  • Secure account login
  • Remembering account, browser, and regional preferences
  • Remembering privacy and security settings
  • Analyzing site traffic and usage
  • Personalized search, content, and recommendations
  • Displaying relevant, targeted ads on and off IvyPanda

Please refer to IvyPanda's Cookies Policy and Privacy Policy for detailed information.

Required Cookies & Technologies
Always active

Certain technologies we use are essential for critical functions such as security and site integrity, account authentication, security and privacy preferences, internal site usage and maintenance data, and ensuring the site operates correctly for browsing and transactions.

Site Customization

Cookies and similar technologies are used to enhance your experience by:

  • Remembering general and regional preferences
  • Personalizing content, search, recommendations, and offers

Some functions, such as personalized recommendations, account preferences, or localization, may not work correctly without these technologies. For more details, please refer to IvyPanda's Cookies Policy.

Personalized Advertising

To enable personalized advertising (such as interest-based ads), we may share your data with our marketing and advertising partners using cookies and other technologies. These partners may have their own information collected about you. Turning off the personalized advertising setting won't stop you from seeing IvyPanda ads, but it may make the ads you see less relevant or more repetitive.

Personalized advertising may be considered a "sale" or "sharing" of the information under California and other state privacy laws, and you may have the right to opt out. Turning off personalized advertising allows you to exercise your right to opt out. Learn more in IvyPanda's Cookies Policy and Privacy Policy.

1 / 1