Predictive Time Series Analysis of Social Ties, 1985 to 2004

This analysis is an excellent example of how an analyst can develop a robust predictive model with a lot missing data. In this analysis I explore how age and gender predict strong social ties over time. Strong ties are important because during a life event (such as a death in the family or a divorce) a person’s ability to get through the crisis can depend on close family or friendship ties. Results from the General Social Survey showed that on average strong ties among Americans between 1985 and 2004 decreased by close to one-third. These findings imply that people are becoming more socially isolated. Based on these findings, I used regression modeling to explore the extent of this change.

At three time periods (1985, 1987 and 2004), the General Social Survey measured strong ties with this question:

From time to time, most people discuss important matters with other people. Looking back over the last six months, who are the people with whom you discussed matters important to you?

Respondents could include up to six people. For all three years the survey was administered, the mean number given is 2.5. Here is the frequency table showing the results:

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Interestingly, there is a linear decrease in the number of strong ties, from a mean of 2.9 in 1985 to 2.1 in 2004 :

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Regression Modeling

Since time series data exists for only 3 years, I initially ran the regression with the number given (the number of strong ties the respondent had) as the dependent variable and year as a factor variable:

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The regression model shows that in 1987 the average number of strong ties decreases by 0.45 compared to 1985, and decreased by 0.94 in 2004 compared to 1985.

I however wanted to develop a predictive model that spanned the years from 1985 through 2004. To accomplish this, I modeled year as a continuous variable. When I ran the regression I found that the model was heteroskedastic (it failed the Bruesch-Pagan test). I therefore ran a robust model to correct for heteroskedasticity. The results are shown below:

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The regression model shows that for every year, from 1985 through 2004, the average number of strong ties decreases by 0.04 every year.

If age and gender are added, the results are also highly statistically significant:

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For a yearly increase in age, strong ties decrease by 0.01. On average, women have 0.12 stronger ties than men.

The Widening Gender Gap

Exploring changes with gender over time can show if there is a widening gender gap. In this case, the above results are used to plot gender by year (see below). As year increases, men tend to have a faster decrease in stronger ties compared to women. In 1985, both men and women report having on average 3 strong ties. In 2004, this average drops to 1.95 for men and 2.15 for women:

gender_plot3_PSEdit

Modeling Cohort

To understand how strong ties change over time based on cohort, I modeled age as a categorical variable and interacted it with year. The young cohort was defined as a participant between the ages of 18 to 30, middle between 30 and 50 and older as 50 and above.

Results:

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The results show that as year increases,  all cohorts became more socially isolated but it varied according to age. The young cohort on average experienced a -0.06 reduction in strong ties per year. The middle cohort on average decreased by -0.11 per year and the older cohort by -0.55 per year.

Here is a plot of the results:

cohort_plot3_PSedit

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