# Binomial Logistic Regression Quantitative Research Essay

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Updated: Aug 6th, 2019

## Introduction

The appropriate regression analysis for task 6 is the binomial logistic regression. According to Norris, Qureshi, Howitt, and Cramer (2014), binomial logistic regression applies when the dependent variable is dichotomous. In this case, the dependent variable, condom use, has only two outcomes, namely, condom used and condom not used.

The present analysis requires hierarchical logistic regression to separate predictors into two blocks. The first block comprises gender, perceived risk, and safety while the second block comprises sexual experience, self-control, and previous usage of condom.

## Logistic Regression Analysis

Table 1 indicates that the regression model with gender, perceived risk, and safety as predictors of condom use is significant, (χ2(3) = 30.892, p = 0.000). Furthermore, Table 2 indicates that gender, perceived risk, and safety explain 35.7% (Nagelkerke R Square) of the variation in condom use.

Table 1

 Omnibus Tests of Model Coefficients Chi-square df Sig. Step 1 Step 30.892 3 .000 Block 30.892 3 .000 Model 30.892 3 .000

Table 2

 Model Summary Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square 1 105.770a .266 .357

Table 3

 Variables in the Equation B S.E. Wald df Sig. Exp(B) 95% C.I. for EXP(B) Lower Upper Step 1a gender(1) .317 .496 .407 1 .523 1.373 .519 3.631 safety -.464 .218 4.541 1 .033 .629 .410 .963 perceive .940 .223 17.780 1 .000 2.560 1.654 3.964 Constant -2.476 .752 10.851 1 .001 .084

Table 3 shows that safety Wald χ2(1) = 4.541, p = 0.033) and perceived risk (Wald χ2(1) = 17.780, p = 0.000) are significant predictors of condom use, while gender (Wald χ2(1) = 0.407, p = 0.523) is not a significant predictor of condom use. In this view, the analysis refutes previous findings because it shows that gender is not a statistically significant predictor of condom use.

The odds ratios for gender, safety, and perceived risk are 1.373 (0.519 to 3.631), 0.629 (0.410 to 0.963), and 2.56 (1.654 to 3.964) respectively. The odds ratio for gender means that females are 1.373 times likely not to use condom than males.

Field (2013) states that odds ratios greater than one increases odds of a certain outcome, while odds ratios less than one reduces the odds of a certain outcome. The odds ratio for safety means that a unit increase in safety results in a reduction of condom use by 37.1%, while the odds ratio for perceived risk means that a unit increase in perceived risk results in an increase in the odds of condom use by 156%.

Table 4 indicates that the logistic regression model with all the six predictors, namely, gender, perceived risk, safety, sexual experience, self-control, and previous usage of condom is statistically significant, χ2(7) = 48.692, p = 0.000).

Table 4

 Omnibus Tests of Model Coefficients Chi-square df Sig. Step 1 Step 17.799 4 .001 Block 17.799 4 .001 Model 48.692 7 .000

Model summary table (Table 5) shows that gender, perceived risk, safety, sexual experience, self-control, and previous usage of condom explain 51.7% (Nagelkerke R Square) of the variation in condom use. This model explains more of the variation in condom use than the previous model.

Table 5

 Model Summary Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square 1 87.971a .385 .517

In the analysis of the contribution of each predictor, Table 6 suggests that safety (Wald χ2(1) = 4.178, p = 0.041), perceived risk (Wald χ2(1) = 16.040, p = 0.000), previous use with a partner (Wald χ2(1) = 3.88, p = 0.049), and self-control (Wald χ2(1) = 7.511, p = 0.006) are statistically significant predictors of condom use.

However, gender (Wald χ2(1) = 0.000, p = 0.996) no previous use of condom (Wald χ2(1) = 4.033, p = 0.133) and first time with a partner (Wald χ2(1) = 0.000, p = 0.991), and sex experience (Wald χ2(1) = 2.614, p = 0.106) are not statistically significant predictors of condom use.

Table 6

 Variables in the Equation B S.E. Wald df Sig. Exp(B) 95% C.I. for EXP(B) Lower Upper Step 1a gender(1) .003 .573 .000 1 .996 1.003 .326 3.081 safety -.482 .236 4.178 1 .041 .617 .389 .980 perceive .949 .237 16.040 1 .000 2.583 1.624 4.111 previous 4.033 2 .133 previous(1) 1.087 .552 3.880 1 .049 2.966 1.005 8.750 previous(2) -.017 1.400 .000 1 .991 .984 .063 15.289 selfcon .348 .127 7.511 1 .006 1.416 1.104 1.815 sexexp .180 .112 2.614 1 .106 1.198 .962 1.491 Constant -4.960 1.147 18.714 1 .000 .007

The odds ratio for gender is 1.003 (0.326 to 3.081), which means that change of gender has no significant change in the odds of condom use. Odds ratios for safety and previous use with the first partner are 0.617 (0.389 to 0.980) and (0.063 to 15.289) are less than 1, which means that they reduce the odds of condom use.

These odds ratios mean that a unit increase in safety reduces the odds of condom use by 38.3% and a unit increase in previous use with the first person reduces the odds of condom use by 1.6%. Perceived risk, previous use of condom, and self-control are three predictors that are significant and have their odds ratios greater than one.

Odds ratios for perceived risk, previous use of condom, and self-control are 2.583 (1.624 to 4.111), 2.966 (1.005 to 8.750), and 1.416 (1.104 to 1.815) respectively. These ratios mean that: a unit increase in perceived risk increases the odds of condom use by 158.3%, a unit increase in previous use of condom increases the odds of condom use by 196.6%, and a unit increase in self-control increases the odds of condom use by 41.6%.

## References

Field, A. (2013). Discovering Statistics using IBM SPSS Statistics (4th ed.). London: SAGE Publisher.

Norris, G., Qureshi, F., Howitt, D., & Cramer, D. (2014). Introduction to Statistics with SPSS for Social Science. New York: Routledge.

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