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# Assessment of interaction

Introduction

Often the relationship between two variables is modified by another control variable. This means that the strength and/or direction of an association varies according to the value of one or more additional variable(s).

 Definition: Interaction exists when the true association between two variables changes as the value of a third variable changes.[1]

The interaction effect is multiplicative as demonstrated in the figure below. The independent variables, X and Z, have an effect on outcome, Y. In addition, the combined variable, XZ, also has an effect on Y. This means that removing Z will change the effect of X on Y and vice versa.

You should test for interaction if you have two independent variables that predict an outcome (dependent variable) and you suspect that combining these variables will have an additional effect on the outcome. In other words, the relationship between X and Y will be stronger, weaker or in the opposite direction at different values of Z.

Example

To demonstrate, we will use data from a sample of 1,277 women of reproductive age in Thai Nguyen province. Stata software is used for statistical analysis. We want to examine the relationship between women’s use of modern contraceptive methods and the number of living children a woman already has.

Research question: What is the effect of having one additional child on the use of modern contraceptives among women of reproductive age in Thai Nguyen province?

We predict that the more children a woman has, the more likely she will be to use modern contraception to prevent further pregnancies. However, we suspect that this relationship varies according to women’s age. This is because both number of children and age have been shown to predict contraceptive practices. In addition, younger women and older women may have different attitudes and practices related to both family size and contraceptive use. To explore this relationship, we follow the steps below.

[1] Agresti A. & Finlay B. (1997). Statistical Methods for the Social Sciences. 3rd ed. Upper Saddle River, NJ: Prentice Hall, Inc.

Univariate analyses

Descriptive statistics of the variables are provided below.

Dependent (Outcome) variable: Modern contraceptive use [use_modern]

• No=0= Uses no contraception or uses traditional contraceptive method
• Yes=1= Uses modern contraceptive method (IUD, condom, or pill)

Independent variables:

• Variable of interest: Number of living children (continuous) [total_child_alive]
• Suspected interaction or moderator variable: Age in years (continuous) [age]

Bivariate analysis

Using bivariate analysis, we can test the association between the independent variables and modern contraceptive use. Because both of the independent variables are continuous, we employ a t-test.

Both number of living children and age are significantly associated with modern contraceptive use (P<0.01).

To see if there is evidence of interaction, we examine the strength of the relationship between the outcome and the independent variable of interest at different levels of the third variable. In this example, we do so by using the logit command to calculate the odds ratio (OR) for using modern contraception (yes vs. no) with each additional child at different ages – 25 years, 35 years and 45 years.

A) 25 years

B) 35 years

C) 45 years

Results suggest that there is an interaction since the relationship between modern contraceptive use and number of living children is different among women aged 25 years (OR=7.48), 35 years (OR=1.00) and 45 years (OR=2.08).

Multivariate analysis

Now we want to analyze how the relationship between modern contraceptive use and number of living children is influenced by age. First, we fit a model with the main effects of number of living children and age. Multiple logistic regression is used because there is more than one independent variable with a binary outcome (Note: the binary outcome should be coded as 0 and 1).

Findings show that the variable number of living children is still significantly associated with modern contraceptive use, controlling for age (P<0.001). You can also say that age is associated with modern contraceptive use, controlling for number of living children (P<0.001). Having one additional child is associated with 1.76 times higher odds of using modern contraception with a 95% confidence interval of 1.48-2.10.

Create an interaction variable

The most common approach for modeling interaction is to introduce a “cross-product” interaction variable into the model. This variable is created by multiplying the two independent variables. In this case, we create the interaction variable by multiplying number of living children and age.

Fit the model with the interaction variable

After creating the interaction variable, we add it to the model.

Wald test

Use the Wald test to confirm that the interaction term is significant in the model.

The interaction term is statistically significant (P<0.001), which means that the relationship between modern contraceptive use and number of living children depends on women’s age.

Obtain the odds ratios

We now know that there is an association between modern contraceptive use and number of living children and that this association varies by age. To measure the magnitude of this association, we estimate the ORs for women of different ages. The lincom command is used to generate the OR and 95% confidence interval (CI).

A) Comparing two women aged 25 years – one woman has 1 more child than the other

Note: Because age is the same for both women, it is held constant. This means that you do not need to include the variable “age” in the equation for the lincom command. Only the variables that differ between the respondents you are comparing should be included.

B) Comparing two women aged 35 years – one woman has 1 more child than the other

C) Comparing two women aged 45 years – one woman has 1 more child than the other

Conclusion

The association between number of living children and modern contraceptive use depends on age. As age increases, the relationship between modern contraceptive use and number of children diminishes. Among women aged 25 years, having one additional child is associated with 3.40 times increased odds of using modern contraception. By comparison, women aged 45 years with one additional child have only 1.28 greater odds of using modern contraceptives compared to their counterparts with fewer children. This is also seen in the graph below. The slope is steeper for 25 year olds than 45 year olds, indicating that the relationship between number of children and modern contraception use is stronger in this age group.

Sarah Keithly - Thongke.info