Solved – Lagging/Leading Indicator Length Time

econometricselasticityrsurvivaltime series

I tried looking this question up on google and didn't find material that answered my question. But my questions are:

(1) Is there a method to determine how long it takes a leading indicator to affect a variable ? So if we are looking at the affects of oil production on sales, when oil drops how long does it take to affect sales.

Could I use survival analysis for this? This seems related but in a biological context

(2) Can we measure the degree to which oil production affects sales? If oil production drops by 10% it affects sales by 17%.

(3) What's the best way to determine the most important leading indicator? Univariate regression and compare models?

(4) Is there a package in R that could be used for this?

Best Answer

Go to Autobox.com and review the discussion about transfer functions.
The is a question about elasticities. Review any principles of economics text. A new version of Autobox calculates elasticities.
If your data is time series, it is inappropriate to use classical regression analysis. Applying classical regression analysis to summarize time series data will result in a violation of one or more of the underlying assumptions about the error terms. Use time series techniques to summarize time series data, and classical regression to summarize cross sectional data.
If you focus on R, then you will spend an inordinate amount to time learning how to program rather than on analysis. Investigate the advantages of Autobox.

Related Solutions

Handling Lagging in Grouped Time Series Data

There are several ways how you can get a lagged variable within a group. First of all you should sort the data, so that in each group the time is sorted accordingly.

First let us create a sample data.frame:

> set.seed(13)
> dt <- data.frame(location = rep(letters[1:2], each = 4), time = rep(1:4, 2), var = rnorm(8))
> dt
  location time        var
1        a    1  0.5543269
2        a    2 -0.2802719
3        a    3  1.7751634
4        a    4  0.1873201
5        b    1  1.1425261
6        b    2  0.4155261
7        b    3  1.2295066
8        b    4  0.2366797

Define our lag function:

 lg <- function(x)c(NA, x[1:(length(x)-1)])

Then the lag of variable within group can be calculated using tapply:

 > unlist(tapply(dt$var, dt$location, lg))
    a1         a2         a3         a4         b1         b2         b3         b4 
    NA  0.5543269 -0.2802719  1.7751634         NA  1.1425261  0.4155261  1.2295066

Using ddply from package plyr:

> ddply(dt, ~location, transform, lvar = lg(var))
  location time        var       lvar
1        a    1 -0.1307015         NA
2        a    2 -0.6365957 -0.1307015
3        a    3 -0.6417577 -0.6365957
4        a    4 -1.5191950 -0.6417577
5        b    1 -1.6281638         NA
6        b    2  0.8748671 -1.6281638
7        b    3 -1.3343222  0.8748671
8        b    4  1.5431753 -1.3343222

Speedier version using data.table from package data.table

 > ddt <- data.table(dt)
 > ddt[,lvar := lg(var), by = c("location")]
     location time        var       lvar
[1,]        a    1 -0.1307015         NA
[2,]        a    2 -0.6365957 -0.1307015
[3,]        a    3 -0.6417577 -0.6365957
[4,]        a    4 -1.5191950 -0.6417577
[5,]        b    1 -1.6281638         NA
[6,]        b    2  0.8748671 -1.6281638
[7,]        b    3 -1.3343222  0.8748671
[8,]        b    4  1.5431753 -1.3343222

Using lag function from package plm

 > pdt <- pdata.frame(dt)
 > lag(pdt$var)
   a-1        a-2        a-3        a-4        b-1        b-2        b-3        b-4 
    NA  0.5543269 -0.2802719  1.7751634         NA  1.1425261  0.4155261  1.2295066

Using lag function from package dplyr

> dt %>% group_by(location) %>% mutate(lvar = lag(var))        
Source: local data frame [8 x 4]
Groups: location        
  location time        var       lvar
1        a    1  0.5543269         NA
2        a    2 -0.2802719  0.5543269
3        a    3  1.7751634 -0.2802719
4        a    4  0.1873201  1.7751634
5        b    1  1.1425261         NA
6        b    2  0.4155261  1.1425261
7        b    3  1.2295066  0.4155261
8        b    4  0.2366797  1.2295066

Last two approaches require conversion from data.frame to another object, although then you do not need to worry about sorting. My personal preference is the last one, which was not available when writing the answer initially.

Update: Changed the data.table code to reflect the developments of the data.table package, pointed out by @Hibernating.

Update 2: Added dplyr example.

Solved – Propensity score weighting in Cox PH analysis and covariate selection

In theory, every variable you select as part of the propensity score weight need not be included as covariates in the model, because the weighting has already controlled for their potential confounding. With a proper weighting model you can, quite literally, just model the effect of the exposure.

That being said, there are reasons you may wish to include terms in the model:

"Doubly robust" estimates. There is no reason, save for a loss in precision, that you cannot use variables both in the weighting model and as covariates. In theory, you are protecting yourself against confounding two ways (hence this technique being referred to as "doubly robust"). Keep in mind this only protects you against either the PS model or the covariate model being misspecified by giving you a "second chance" to specify the correct model, it isn't a magic fix-all.
Multiple estimates of interest. Weighting makes the effect estimates from the covariates disappear - if you want a regression coefficient for the variable, you're going to want to include it as a covariate in the CoxPH step and not in the PS model.

Try searching for "Doubly robust" and similar terms in journals like Epidemiology or The American Journal of Epidemiology as well as the biostatistical literature and you should uncover some useful sources.

Best Answer

Related Solutions

Handling Lagging in Grouped Time Series Data

Solved – Propensity score weighting in Cox PH analysis and covariate selection

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