Data Preparation in R: normalization, log - order I have a little problem with my data (GDP per capita, some control variables with negative minimums (e.g. FDI) and explanatory variables without negative values but also different ranges.
Originally, I derived growth rates for GDP per capita = (GDPpc_t=0 - GDPpc_t=1)/ GDPpc_t=1) *100. Then I normalized all variables/ the complete dataset and used log10(DF[,]+1) (+ 1 due to normalization, and log10() to make it easier to interpret).
But then a friend looked over it and said I should use log growth to calculate the growth rates. So, I started doing so and now I am completely confused.
The overall goal is to do a rolling fixed effects regression whereby I want to observe how coefficients/ elasticities change over time.
I am wondering:
Is the log now already applied to log growth? When I now normalize all data (also growth rate), and log() (not log10) the data, I get completely different estimates. So, this cannot be correct.
Leaving normalization completely away also brings different estimates.
Should I normalize before calculating the growth rates?
Can you please help me? In the following you can see a litte part of my data:
Log Growth rates:
Min. = -11.9384; Mean=1.6815; Max = 21.5104
One of the controls variables:
Min. = -57.5323; Median= 1.6087; Mean = 4.5322; Max = 86.4792
Two of the explanatory variables:
Min. = 0.01146; Mean=0.32895 ; Max=3.83870
Min. =10.47; Mean= 4506.50; Max. =15009.01
(Further, the data is not normally distributed)
Edit: I now tried the following:

*

*No adaption at all (best findings regarding R-squ. and significance)

*Normalization (similar sig. and R^2 to 1.)

*Log just the relevant variables for which I would     use elasticities --> here no problem of negativity (similar solutions to 1.)

*Create growth rates out of all variables (good R-squared but the variables of interest are insignificant)

*Cube root transformation (applied to all variables or GDP growth left out --> to all variables brings worse estimates)

*Square root transformation (similar to 5.)

Generally, I am copying a combination of 2 papers. The first paper (which has also the negative values) only normalizes and the second one logs all variables but has no negative values as control variables included. So, after looking at all alternatives I would only log the important variables. Its ok to do so, right ?
 A: GDP per capita is often better considered on a logarithmic scale, for at least two reasons:

*

*Over a range of countries, its distribution can be awkwardly skewed with outliers


*It tends to change multiplicatively, so changes in log GDP per capita might be more natural and/or more convenient than changes in GDP per capita.
That said, "growth" can be occasionally be negative and in principle could be zero, so log growth sounds at best a poor choice of measure and at worst quite wrong as you could not helpfully take logarithms of zero or negative values. (The mathematical fact that logarithms are defined for negative values does not help here.)
Discussing whether normalization is a good idea depends on knowing what you mean by it. Normalization in the sense of standardization (value $-$ mean) / SD can only be carried after logarithmic transformation. To see this, consider that if carried out before then some values will be negative and zero isn't impossible either, so the problem in the previous paragraph would bite hard.
log(something $+1$) sounds like a fudge here. Sometimes there is a good reason for it, but often it is a poor work-around to apply logarithms whenever that is not helpful.
