Time Trends for Panel Data

[Buki Peters]

Hello,

I am writing a descriptive paper on substance use estimates across 4 years (2013-2017) using a longitudinal data.

I initially calculated the point estimates (prevalence) for each year and compared the confidence interval overlap from 2013 and 2017 to suggest significance. Now, I'm getting push back from colleagues suggesting I should do a real test for trend rather than comparing CIs. While this makes sense, I'm not sure what test to carry out since I assume lincom works best for cross-sectional data. Also, since I did not conduct a regression, I am unable to carry out the other xt..tests that are normally used to test time differences in panel data. Also, since I have so much data, I considered using lincom only for estimates that were 'significant' when I used the confidence overlap test, but I was informed that seemed like cherry-picking.

Can I use lincom to test for differences between 2013 and 2017 estimates using longitudinal data or is there any other test you suggest that I can use?

Thank you

[Tom Scott]

Buki Peters I don't think you provided enough information. What is/are your research question(s) exactly. If you are just looking at a trend of marijuana use let's say, I don't think there is any "test for a trend" that you can do. What is the comparison? You could test whether the trend differs across groups (e.g., male vs female) or whether the change in the last 2 years is distinct from the change in the first 2 years, but that doesn't sound like what you want to do. I would just calculate change scores across the first and last year and across each year to look at the total change and the average yearly change. If you can find a benchmark for what you think the trend should have been (e.g., change in alcohol use over the same time), you can test whether the substance use trend is statistically distinct.

[Buki Peters]

Tom Scott Thank you for your response. I apologize for not providing enough information; hope this helps.

So, my research goal (more of a goal than a question) is presenting 'Prevalence of cigarette use from 2013 to 2017', so I'm more or less just providing prevalence estimates of cigarette use for 2013, 2014, 2015, 2016, and 2017.

But the dataset is a longitudinal and I want to see if the change in estimates from 2013 to 2017 is significant e.g Overall cigarette prevalence estimate from 2013 (9.1%) to 2017 (6.0%) suggests a decrease of 3.1 percentage points or 34.1% decrease. I was wondering if there was a way to test if this is a 'real' decrease by using some sort of significant testing.

I could have use lincom in Stata to test if this change over time is significant but lincom is used mostly with cross-sectional estimates or would require some sort of panel data restructuring that is quite intensive. Also, since this is not a regression paper, I really can't do the regular time trend tests used in regression analyses.

So, I was just wondering if there is any other test anyone knows about that I can use to test for significance. Hope this explains a bit better.

[Tom Scott]

Buki Peters It sounds like what you are looking for is a within-person t-test (http://web.pdx.edu/~newsomj/pa551/lecture8.htm) but I do not think it makes sense to do that. It might make more sense to look at the typical (average) variation year to year and see if the 34% decrease is typical or represents a shift. You would probably do a t-test of the "average" 4 year change compared to the 2013-2017 change. I'm not sure if you have pre-2013 data, though.

[Buki Peters]

Tom Scott this makes sense. Thank you for your help.

[Jeff Wooldridge]

Here is an easy thing to do, if I understand correctly. I'll assume you have dummies for the different years, y2014 to y2017.

reg smoke y2014 y2015 y2016 y2017, vce(cluster id)

The coefficient on y2017 gives you the estimated difference between 2017 and 2013, and you have a robust (clustered) standard error. Or, if you prefer to see the mean for each year,

reg smoke y2013 y2014 y2015 y2016 y2017, nocons vce(cluster id)
lincom y2017 - y2013

[Buki Peters]

Jeff Wooldridge super late, but thank you so much