Standardizing data with categorical and quantitative data

Question

I'm analyzing a data set as a final project. This is a categorical data analysis course so I will be focusing on a logistic regression analysis. I scrapped together the data set from flight data and weather data. Data is for flights coming into ORD. I want to model flight delay (whether a flight is delayed or not). Here is the a summary of the variables involved:

> summary(flight_data)
  DAY_OF_MONTH    DAY_OF_WEEK      AIRLINE_ID    CRS_DEP_TIME      DEP_DELAY          TAXI_OUT         TAXI_IN       
 Min.   : 1.00   Min.   :1.000   19977  :7838   Min.   : 333.0   Min.   :-21.000   Min.   :  1.00   Min.   :  1.000  
 1st Qu.: 6.00   1st Qu.:2.000   19805  :6082   1st Qu.: 510.0   1st Qu.: -4.000   1st Qu.: 10.00   1st Qu.:  5.000  
 Median :17.00   Median :4.000   20398  :3974   Median : 761.0   Median : -1.000   Median : 12.00   Median :  7.000  
 Mean   :15.17   Mean   :4.058   19386  : 576   Mean   : 760.2   Mean   :  9.072   Mean   : 15.23   Mean   :  8.009  
 3rd Qu.:24.00   3rd Qu.:6.000   19790  : 553   3rd Qu.: 985.0   3rd Qu.:  7.000   3rd Qu.: 17.00   3rd Qu.:  9.000  
 Max.   :30.00   Max.   :7.000   20355  : 453   Max.   :1439.0   Max.   :931.000   Max.   :301.00   Max.   :179.000  
                                 (Other): 866                                                                        
  CRS_ARR_TIME       AIR_TIME        DISTANCE            Weather.Type     Wind.Speed        Wind.Dir           region    
 Min.   :   1.0   Min.   : 11.0   Min.   :  67.0   DRIZZLE     :  219   Min.   : 0.000   Min.   : 1.00   midwest  :5856  
 1st Qu.: 625.0   1st Qu.: 55.0   1st Qu.: 334.0   FOG         :   35   1st Qu.: 6.000   1st Qu.: 8.00   northeast:4487  
 Median : 865.0   Median : 99.0   Median : 647.0   MIST        :  569   Median : 8.000   Median :20.00   south    :5833  
 Mean   : 849.9   Mean   :105.8   Mean   : 762.1   None        :17823   Mean   : 8.462   Mean   :19.16   west     :4166  
 3rd Qu.:1075.0   3rd Qu.:130.0   3rd Qu.: 925.0   RAIN        : 1420   3rd Qu.:11.000   3rd Qu.:29.75                   
 Max.   :1438.0   Max.   :486.0   Max.   :4244.0   THUNDERSTORM:  276   Max.   :25.000   Max.   :37.00 

I have a few questions:

1. I have categorical variables, as well as quantitative variables. Clearly many of the variables are on different scales (time, degrees, etc). Should I standardize my variables? Does it matter? Do I do this to just the quantitative ones?

2. We learned a bit about GAMs in our class. I would like to check whether some of my variables appear to be linear in the log-odds of arrival-delay (if not that would justify use of a GAM). Is this the following code an appropriate approach to this question?

Windspeed:

logodds <- NULL x<-NULL for( i in unique(flight_data[,13])){ idx <- which(flight_data[,13] == i) x <- c(x,i) logodds <- c(logodds,log( sum(flight_data[idx,9])/(nrow(flight_data) - sum(flight_data[idx,9])))) } plot(logodds~x)

Answer 1

1) In general, standardizing the quantitative variables is not necessary, though there are situations where it may be useful. When conducting multiple regression, when should you center your predictor variables & when should you standardize them? estimates.

2) In regards to checking the linearity of your predictors, it doesn't make sense to me to check the linearity of each predictor prior to including them with other predictors in the full model. The reason is that it is possible for an apparent non-linear relationship in a univariate logistic regression to disappear after including other variables in the model, especially when the predictors are correlated. After including all desired terms in the model, you could use partial residual plots to check the functional form of each predictor. For other options or recommendations, you might want to check out Diagnostics for logistic regression?.

In regards to whether or not to use a GAM, the decision should not be predicated on whether or not the relationships appear to be linear, but what you hope to get out of the model. A multivariate logistic regression would provide interpretable parameter estimates allowing you to provide an interesting summary regarding how the variables are related to flight delays. A GAM may be able to provide a better fit to the data (overfit?), but the potential gain in predictive accuracy is at the cost of interpretability of the model. The following post is related and may help you realize the divide between parameter estimation and predicive accuracy The Two Cultures: statistics vs. machine learning?