Multiple regression model

by | Mar 11, 2025 | Essays

Fit a multiple regression model, testing whether a mediating variable partly or completely mediates the effect of an initial causal variable on an outcome variable. Think about whether or not the model will meet assumptions.
Fit the model, testing for mediation between two key variables.
Analyze the output, determining whether mediation was significant and how to interpret that result.
Reflect on possible implications of social change.

Sample solution

Dante Alighieri played a critical role in the literature world through his poem Divine Comedy that was written in the 14th century. The poem contains Inferno, Purgatorio, and Paradiso. The Inferno is a description of the nine circles of torment that are found on the earth. It depicts the realms of the people that have gone against the spiritual values and who, instead, have chosen bestial appetite, violence, or fraud and malice. The nine circles of hell are limbo, lust, gluttony, greed and wrath. Others are heresy, violence, fraud, and treachery. The purpose of this paper is to examine the Dante’s Inferno in the perspective of its portrayal of God’s image and the justification of hell. 

In this epic poem, God is portrayed as a super being guilty of multiple weaknesses including being egotistic, unjust, and hypocritical. Dante, in this poem, depicts God as being more human than divine by challenging God’s omnipotence. Additionally, the manner in which Dante describes Hell is in full contradiction to the morals of God as written in the Bible. When god arranges Hell to flatter Himself, He commits egotism, a sin that is common among human beings (Cheney, 2016). The weakness is depicted in Limbo and on the Gate of Hell where, for instance, God sends those who do not worship Him to Hell. This implies that failure to worship Him is a sin.


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God is also depicted as lacking justice in His actions thus removing the godly image. The injustice is portrayed by the manner in which the sodomites and opportunists are treated. The opportunists are subjected to banner chasing in their lives after death followed by being stung by insects and maggots. They are known to having done neither good nor bad during their lifetimes and, therefore, justice could have demanded that they be granted a neutral punishment having lived a neutral life. The sodomites are also punished unfairly by God when Brunetto Lattini is condemned to hell despite being a good leader (Babor, T. F., McGovern, T., & Robaina, K. (2017). While he commited sodomy, God chooses to ignore all the other good deeds that Brunetto did.

Finally, God is also portrayed as being hypocritical in His actions, a sin that further diminishes His godliness and makes Him more human. A case in point is when God condemns the sin of egotism and goes ahead to commit it repeatedly. Proverbs 29:23 states that “arrogance will bring your downfall, but if you are humble, you will be respected.” When Slattery condemns Dante’s human state as being weak, doubtful, and limited, he is proving God’s hypocrisy because He is also human (Verdicchio, 2015). The actions of God in Hell as portrayed by Dante are inconsistent with the Biblical literature. Both Dante and God are prone to making mistakes, something common among human beings thus making God more human.

To wrap it up, Dante portrays God is more human since He commits the same sins that humans commit: egotism, hypocrisy, and injustice. Hell is justified as being a destination for victims of the mistakes committed by God. The Hell is presented as being a totally different place as compared to what is written about it in the Bible. As a result, reading through the text gives an image of God who is prone to the very mistakes common to humans thus ripping Him off His lofty status of divine and, instead, making Him a mere human. Whether or not Dante did it intentionally is subject to debate but one thing is clear in the poem: the misconstrued notion of God is revealed to future generations.

 

References

Babor, T. F., McGovern, T., & Robaina, K. (2017). Dante’s inferno: Seven deadly sins in scientific publishing and how to avoid them. Addiction Science: A Guide for the Perplexed, 267.

Cheney, L. D. G. (2016). Illustrations for Dante’s Inferno: A Comparative Study of Sandro Botticelli, Giovanni Stradano, and Federico Zuccaro. Cultural and Religious Studies, 4(8), 487.

Verdicchio, M. (2015). Irony and Desire in Dante’s” Inferno” 27. Italica, 285-297.

Hypothetical Scenario:

We’ll examine the relationship between:

  • Causal Variable (X): Socioeconomic Status (SES)
  • Mediating Variable (M): Access to Healthcare
  • Outcome Variable (Y): Overall Health Outcomes

We hypothesize that SES (X) influences access to healthcare (M), which in turn influences overall health outcomes (Y). We want to test if access to healthcare mediates the relationship between SES and health outcomes.

1. Assumptions of Multiple Regression:

Before fitting the model, we must consider the assumptions of multiple regression:

  • Linearity: The relationships between variables are linear.
  • Independence of Errors: The errors (residuals) are independent.
  • Homoscedasticity: The variance of errors is constant across levels of the predictor variables.
  • Normality of Errors: The errors are normally distributed.
  • No Multicollinearity: Predictor variables are not highly correlated.

We would need to check these assumptions using diagnostic plots and statistical tests (e.g., scatterplots, residual plots, VIF) after fitting the model.

2. Fitting the Mediation Model:

We will use a series of regression models to test for mediation, typically following Baron and Kenny’s (1986) approach, or a more robust approach such as bootstrapping.

  • Model 1: Total Effect (X on Y):
    • Y = b0 + b1X + e1
    • We test if SES (X) significantly predicts health outcomes (Y).

Hypothetical Scenario:

We’ll examine the relationship between:

  • Causal Variable (X): Socioeconomic Status (SES)
  • Mediating Variable (M): Access to Healthcare
  • Outcome Variable (Y): Overall Health Outcomes

We hypothesize that SES (X) influences access to healthcare (M), which in turn influences overall health outcomes (Y). We want to test if access to healthcare mediates the relationship between SES and health outcomes.

1. Assumptions of Multiple Regression:

Before fitting the model, we must consider the assumptions of multiple regression:

  • Linearity: The relationships between variables are linear.
  • Independence of Errors: The errors (residuals) are independent.
  • Homoscedasticity: The variance of errors is constant across levels of the predictor variables.
  • Normality of Errors: The errors are normally distributed.
  • No Multicollinearity: Predictor variables are not highly correlated.

We would need to check these assumptions using diagnostic plots and statistical tests (e.g., scatterplots, residual plots, VIF) after fitting the model.

2. Fitting the Mediation Model:

We will use a series of regression models to test for mediation, typically following Baron and Kenny’s (1986) approach, or a more robust approach such as bootstrapping.

  • Model 1: Total Effect (X on Y):
    • Y = b0 + b1X + e1
    • We test if SES (X) significantly predicts health outcomes (Y).
  • Model 2: X on M:
    • M = b0 + b1X + e2
    • We test if SES (X) significantly predicts access to healthcare (M).
  • Model 3: M on Y (controlling for X):
    • Y = b0 + b1X + b2M + e3
    • We test if access to healthcare (M) significantly predicts health outcomes (Y) while controlling for SES (X).

3. Analyzing the Output and Interpreting Mediation:

  • Significant Total Effect (Model 1):
    • If b1 in Model 1 is significant, there is a total effect of SES on health outcomes.
  • Significant X on M (Model 2):
    • If b1 in Model 2 is significant, SES significantly predicts access to healthcare.
  • Significant M on Y (Model 3):
    • If b2 in Model 3 is significant, access to healthcare significantly predicts health outcomes, controlling for SES.
  • Reduction in X on Y Effect (Model 3):
    • If b1 in Model 3 is smaller than b1 in Model 1, there is evidence of mediation.
    • If b1 in Model 3 is no longer significant, there is evidence of complete mediation.
    • If b1 in Model 3 is still significant but smaller, there is evidence of partial mediation.
  • Bootstrapping:
    • A more robust method is to use bootstrapping to estimate the indirect effect (a*b) and its confidence interval.
    • If the confidence interval does not include zero, the indirect effect is considered significant, indicating mediation.

Interpretation:

  • Complete Mediation: If the effect of SES on health outcomes is no longer significant when access to healthcare is included in the model, it suggests that access to healthcare fully explains the relationship.
  • Partial Mediation: If the effect of SES on health outcomes is reduced but still significant when access to healthcare is included, it suggests that access to healthcare partially explains the relationship.

4. Possible Implications of Social Change:

  • Addressing Health Disparities: If mediation is significant, it highlights the importance of improving access to healthcare for individuals with lower SES to reduce health disparities.
  • Policy Implications: Findings can inform policies aimed at increasing access to healthcare, such as expanding insurance coverage, increasing the availability of community health centers, and addressing transportation barriers.
  • Social Justice: Mediation analysis can shed light on the mechanisms through which social inequalities translate into health disparities, supporting arguments for social justice interventions.
  • Community Interventions: If access to healthcare is a mediator, community-based programs that improve access to preventative care, health education, and social support services can be developed.
  • Economic Impacts: If a population has better access to healthcare, that could improve the populations ability to work, and thus improve the overall economic situation of that population.

Important Notes:

  • Correlation does not equal causation. Even with significant mediation, we cannot definitively prove causality.
  • This is a simplified example. Real-world mediation analyses often involve more complex models and control variables.
  • Always check the assumptions of multiple regression.
  • Consider using bootstrapping for more robust mediation testing.
  • Use up to date statistical software, that has built in mediation analysis tools.

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