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I have a distributed lag model of the form: 

lm(wellbeing ~ temperature + temperature_lag1 + temperature_lag2 + time + individual, df)

where I'm interested in finding out the long-run multiplier for the effect of daily temperatures on an individual's wellbeing.

I understand that the coefficient for the multiplier would simply be the sum of the beta coefficients for temperature, temperature_lag1 and temperature_lag2.

However, I'm not entirely sure how to go about calculating the standard error for the multiplier.

I've seen suggestions for doing so by regressing:

dif1 <- temperature_lag1 - temperature
dif2 <- temperature_lag2 - temperature
lm(wellbeing ~ temperature + dif1 + dif2 + time + individual, df)

With the beta for temperature acting as the SE for the long-run multiplier. However, I'm not sure how valid this approach is?

Any guidance would be much appreciated.

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  • $\begingroup$ I'd look into the dlnm package that explicitly fits distributed lag models. $\endgroup$
    – COOLSerdash
    Sep 18, 2019 at 11:30
  • $\begingroup$ Thanks. I'll certainly take a look at dlnm. Though at this stage, I'd be especially keen to understand the theory/practice behind how the SEs are calculated. $\endgroup$
    – Shida
    Sep 18, 2019 at 12:05

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