Statistical Reading Rainbow

For those of us who received statistical training outside of statistics departments, it often emphasized procedures over principles. This entailed that we learned about various statistical techniques and how to perform analysis in a particular statistical software, but glossed over the mechanisms and mathematical statistics underlying these practices. While that training methodology (hereby referred to as the ‘heuristic method’) has value, it has many drawbacks when the ultimate goal is to perform sound statistical analysis that is valid and thorough. Even in my current role as a data scientist at a technology company in the San Francisco Bay Area, I have had to go back and understand various procedures and metrics instead of just “doing data analysis”.

Given this realization, I have dedicated hours of time outside of work over the last couple years to “re-training” myself on many of the important concepts in both descriptive and inferential statistics. This post will give brief mention to the books that have been most useful is helping me develop a fuller understanding of the statistical sciences. These books have also helped me fill in the gaps and deficiencies from my statistical training in university and graduate school. Furthermore, these are the texts that I often revisit when I need a reference on some statistical topic of interest. This is at a minimum a a six year journey, so I have a long way to go until I am able to stand solidly in my understanding of statistics. While I am sacrificing a lot of my free time to this undertaking, it will certainly improve my knowledge and help prepare me for graduate school (PhD) in biostatistics, which I hope to attend in around five years.[1]

Please note that I am not taking issue with the ‘heuristic method’ of statistical training. It certainly has its place and provides students with the immediate knowledge required to satisfactorily prepare for work in private industry. In fact, I prefer the ‘heuristic method’ and still rely on straight forward rules in my day to day work as that ensures that best practices are followed and satisfactory analysis is performed. Furthermore, I certainly believe that it is superior to the hack-ey nature of data mining and data science education, but that is a different story.


Statistics in Plain English – Urdan
Clear, concise, and covers all the fundamental items that one would need to know. Everything from descriptive statistics to linear regression are covered, with many good examples. Even if you never use ANOVA or factor analysis, this is a good book to review and one that I strongly recommend to people who are interested in data science.

Principles of Statistics – Balmer
This is a classic text that offers a good treatment of probability theory, distributions, and statistical inference. The text contains a bit more math than ‘Statistics in Plain English’, so I think it should be read after completing the previous book.

Fundamentals of Modern Statistical Methods – Wilcox
This book reviews ‘traditional’ parametric statistics and provides a good overview of robust statistical methods. There is a fair amount on the historical evolution of various techniques, and I found that a bit unnecessary. But overall, this is still a solid introductory text to learn about statistical inference using robust techniques.

Regression Analysis:

Mostly Harmless Econometrics – Angrist
While I don’t regularly work with instrumental variables, generalized methods of moments, or regression discontinuity, this book is a great high level introduction to econometrics. The chapters on regression theory and quantile regression are phenomenal.

Regression Modeling Strategies – Harrell
This is my most referenced book and the one that really helped in my overall development as an applied statistician. All the important topics are covered, from imputation, regression splines, and so forth. This book includes R code for performing analysis using the RMS package. I end up citing this book quite a lot. For example, in a recent work email, I mentioned that Harrell “also says on page 61 that “narrowly distributed predictor variables will require higher sample sizes.”” Essential reading in my opinion.

Data Analysis Using Regression and Multilevel/Hierarchical Models – Gelman and Hill
The first half of this book cover statistical inference using single level models and the second half is dedicated to multilevel methods. Given that I am rarely work with panel data, I use the first half of this book a reference for things that I may need a quick refresher on. It is very accessible and has plenty of examples with R code.

Semiparametric Regression for the Social Sciences – Keele
This is one of my favorite statistical books. Well written and easy to comprehend, but still rigorous. Covers local regression, splines, and generalized additive models. There is also a solid chapter on the use of bootstrapping with semiparametric and nonparametric models.

Statistical Learning:

Statistical Learning from a Regression Perspective – Berk
As a skeptic who is wary of every hype machine, I really enjoyed Berks preface in which he discusses the “dizzying array of new statistical procedures” that have been introduced over the past several decades with “the hype of a big-budget movie.” I got this text for its treatment of topics such as boosting, bagging, random forest, and support vector machines. I will probably need to reread this book several more times before I fully comprehend everything.

Time Series:

Time Series: a Biostatistical Introduction – Diggle
The lack of quality time series books is really infuriating. Don’t get me wrong, there are some good texts on forecasting, such as the free online book from Hyndaman. However, I’ve yet to find a really good intermediate level treatment of time series analysis besides this one. Contains good coverage of repeated measurements, ARIMA modeling, and forecasting.

Bayesian Methods

Statistical Rethinking – McElreath
While I was introduced to robust techniques and nonparametric statistics in graduate school, there was nothing on Bayesian methods. Due to a fear of the topic, I avoided learning about it until this past year. This book by McElreath has been great as it is very accessible and provides code for understanding various principles. Over the next year, I am hoping to dive deeper into Bayesian techniques and this was a good first step.

[1] If you are an academic or doctoral students in a statistical field and are looking for a part-time research assistant, please contact me at I’m looking to gain as much research experience as possible before entering a doctoral program.

Introduction to the RMS Package

The rms package offers a variety of tools to build and evaluate regression models in R. Originally named ‘Design’, the package accompanies the book “Regression Modeling Strategies” by Frank Harrell, which is essential reading for anyone who works in the ‘data science’ space. Over the past year or so, I have transitioned my personal modeling scripts to rms as it makes things such as bootstrapping, model validation, and plotting predicted probabilities easier to do. While the package is fairly well documented, I wanted to put together a ‘simpler’ and more accessible introduction that would explain to R-beginners how they could start using the rms package. For those with limited statistics training, I strongly suggest reading “Clinical Prediction Models” and working your way up to “Regression Modeling Strategies”.

We start this introduction to the rms package with the datadist function, which computes statistical summaries of predictors to automate estimation and plotting of effects. The user will generally supply the final data frame to the datadist function and set the data distribution using the options function. Note that if you modify the data in your data frame, then you will need to reset the distribution summaries using datadist.

my.df = data.frame(one=c(rnorm(100)), two=c(rnorm(100)), y=rnorm(100))
dd = datadist(my.df)

my.df_new = subset(my.df, two >= 0.05)
ddd <- datadist(my.df_new)
options( datadist = "ddd" )

The main functions to estimate models in rms are ols for linear models and lrm for logistic regression or ordinal logistic regression. There are also a few other functions for performing survival analysis,but they will not be covered in this post.


ddd <- datadist(prostate)
options( datadist = "ddd" )

Using the prostate data, we built a linear model using ordinary least squares estimation. The argument x and y must be set to true if we plan on evaluate the model in later stages using the validate and calibrate functions. Because we haven’t altered the default contrasts or incorporated any smoothing splines, the coefficients and standard errors should be identical to the results of lm. Use the model variable name to see the estimates from the model and use the summary function to get an overview of the effects of each predictor on the response variable. One important thing to note that the effect point estimates in the summary.rms output relate to the estimated effect of an inter-quartile range increase in the predictor variable.

lmod = ols(wt ~ age + sbp + rx, data=prostate, x=TRUE, y=TRUE)
summary(lmod, age=c(50,70))

This may not seem like anything to write home about. But what makes the rms package special is that it makes the modeling process significantly easier. For the above linear regression model, let’s plot the predicted values and perform internal bootstrapped validation of the model. In the following code, the validate function is used to assess model fit and calibrate is used to assess if the observed responses agree with predicted responses.

plot(anova(lmod), what='proportion chisq') # relative importance
plot(Predict(lmod)) # predicted values
rms::validate(lmod, method="boot", B=500) # bootstrapped validation
my.calib <- rms::calibrate(lmod, method="boot", B=500) # model calibration
plot(my.calib, las=1)
vif(lmod) # test for multicolinearity

Let us now build a logistic regression model using the lrm function, plot the expected probabilities, and evaluate the model. We also use the pentrace function to perform logistic regression with penalized maximum likelihood estimation.

mod1 = lrm(as.factor(bm) ~ age + sbp + rx, data=prostate, x=TRUE, y=TRUE)

plot(anova(mod1), what='proportion chisq') # relative importance
plot(Predict(mod1, fun=plogis)) # predicted values
rms::validate(mod1, method="boot", B=500) # bootstrapped validation
my.calib <- rms::calibrate(mod1, method="boot", B=500) # model calibration
plot(my.calib, las=1)

penalty <- pentrace(mod1, penalty=c(0.5,1,2,3,4,6,8,12,16,24), maxit=25)
mod1_pen <- update(mod1, penalty=penalty$penalty)

There you have it, a very basic introduction to the rms package for beginners to the R programming language. Once again, I strongly suggest that readers who are not trained statisticians should read and fully comprehend “Clinical Prediction Models” and “Regression Modeling Strategies” by Frank Harrell. You can also access a number of handouts and lecture notes at here.

Extract Google Trends Data with Python

Anyone who has regularly worked with Google Trends data has had to deal with the slightly tedious task of grabbing keyword level data and reformatting the spreadsheet provided by Google. After looking for a seamless way to pull the data, I came upon the PyTrends library on GitHub, and sought to put together some quick user defined functions to manage the task of pulling daily and weekly trends data.

# set working directory (location where code is)
import os

import re
import csv
import time
import pandas as pd
from random import randint
from GT_Automation_Code import pyGTrends

# set gmail credentials and path to extract data
google_username = "*****"
google_password = "*****"

Daily_Data = [ ]
# define daily pull code
def GT_Daily_Run(keys):
    path = 'path'

    # connect to Google
    connector = pyGTrends(google_username, google_password)
    # make request
    connector.request_report(keys, date="today 90-d", geo="US")
    # wait a random amount of time between requests to avoid bot detection
    time.sleep(randint(5, 10))
    # download file
    connector.save_csv(path, '_' + "GT_Daily" + '_' + keys.replace(' ', '_'))

    name = path + '_' + "GT_Daily" + '_' + keys.replace(' ', '_')
    with open(name + '.csv', 'rt') as csvfile:    
        csvReader = csv.reader(csvfile)
        data = []

        for row in csvReader:
            if any('2015' in s for s in row): 

        day_df = pd.DataFrame(data)
        cols = ["Day", keys]    
        day_df.columns = [cols]  

keywords = ['soccer', 'football', 'baseball']    

map(lambda x: GT_Daily_Run(x), keywords)  

rge = [Daily_Data[0], Daily_Data[1], Daily_Data[2]]    

df_final_daily = reduce(lambda left,right: pd.merge(left,right, on='Day'), rge)
df_final_daily = df_final_daily.loc[:, (df_final_daily != "0").any(axis=0)]
df_final_daily.to_csv("Daily_Trends_Data.csv", index=False)

Weekly_Data = [ ]     
# define weekly pull code
def GT_Weekly_Run(keys):

    path = 'path'
    # connect to Google
    connector = pyGTrends(google_username, google_password)
    # make request
    connector.request_report(keys, geo="US")
    # wait a random amount of time between requests to avoid bot detection
    time.sleep(randint(5, 10))
    # download file
    connector.save_csv(path, '_' + "GT_Weekly" + '_' + keys.replace(' ', '_'))

    name = path + '_' + "GT_Weekly" + '_' + keys.replace(' ', '_') 

    with open(name + '.csv', 'rt') as csvfile:    
        csvReader = csv.reader(csvfile)
        data = []
        datex = re.compile('(19|20)dd-(0[1-9]|1[012])-(0[1-9]|[12][0-9]|3[01])')

        for row in csvReader:
        week_df = pd.DataFrame(data)
        cols = ["Week", keys]    
        week_df.columns = [cols]
map(lambda x: GT_Weekly_Run(x), keywords)  

rge = [Weekly_Data[0], Weekly_Data[1], Weekly_Data[2]]    

df_final_weekly = reduce(lambda left,right: pd.merge(left,right, on='Week'), rge)
df_final_weekly = df_final_weekly.loc[:, (df_final_weekly != "0").any(axis=0)] 
df_final_weekly.to_csv("Weekly_Trends_Data.csv", index=False)

Batch Forecasting in R

Given a data frame with multiple columns which contain time series data, let’s say that we are interested in executing an automatic forecasting algorithm on a number of columns. Furthermore, we want to train the model on a particular number of observations and assess how well they forecast future values. Based upon those testing procedures, we will estimate the full model. This is a fairly simple undertaking, but let’s walk through this task. My preference for such procedures is to loop through each column and append the results into a nested list.

First, let’s create some data.

ddat <- data.frame(date = c(seq(as.Date("2010/01/01"), as.Date("2010/03/02"), by=1)),
                      value1 = abs(round(rnorm(61), 2)),
                      value2 = abs(round(rnorm(61), 2)),
                      value3 = abs(round(rnorm(61), 2)))

We want to forecast future values of the three columns. Because we want to save the results of these models into a list, lets begin by creating a list that contains the same number of elements as our data frame.

lst.names <- c(colnames(data))
lst <- vector("list", length(lst.names))
names(lst) <- lst.names

I’ve gone ahead and written a user defined function that handles the batch forecasting process. It takes two arguments, a data frame and default argument which specifies the number of observations that will be used in the training set. The model estimates, forecasts, and diagnostic measures will be saved as a nested list and categorized under the appropriate variable name.

batch <- function(data, n_train=55){
  lst.names <- c(colnames(data))
  lst <- vector("list", length(lst.names))
  names(lst) <- lst.names    
  for( i in 2:ncol(data) ){  
    lst[[1]][["train_dates"]] <- data[1:(n_train),1]
    lst[[1]][["test_dates"]] <- data[(n_train+1):nrow(data),1]
    est <- auto.arima(data[1:n_train,i])
    fcas <- forecast(est, h=6)$mean
    acc <- accuracy(fcas, data[(n_train+1):nrow(data),i])
    fcas_upd <- data.frame(date=data[(n_train+1):nrow(data),1], forecast=fcas,                           actual=data[(n_train+1):nrow(data),i])
    lst[[i]][["estimates"]] <- est
    lst[[i]][["forecast"]] <- fcas
    lst[[i]][["forecast_f"]] <- fcas_upd
    lst[[i]][["accuracy"]] <- acc
    cond1 = diff(range(fcas[1], fcas[length(fcas)])) == 0
    cond2 = acc[,3] >= 0.025
      mfcas = forecast(ma(data[,i], order=3), h=5)        
      lst[[i]][["moving_average"]] <- mfcas
    } else {
      est2 <- auto.arima(data[,i])
      fcas2 <- forecast(est, h=5)$mean
      lst[[i]][["estimates_full"]] <- est2
      lst[[i]][["forecast_full"]] <- fcas2

This isn’t the prettiest code, but it gets the job done. Note that lst was populated within a function and won’t be available in the global environment. Instead, I chose to simply print out the contents of the list after the function is evaluated.

R Programming Notes

I’ve been on a note taking binge recently. This post covers a variety of topics related to programming in R. The contents were gathered from many sources and structured in such a way that it provided the author with a useful reference guide for understanding a number of useful R functions.


The function executes a function call on a list of arguments."R_Function", "List_of_Arguments")

This is equivilant to telling R which arguments the function should operate on.

R_Function( "List_of_Arguments" ){

Consider the following list with four elements. We can use this function to find the total sum across all list elements or bind the rows into a data frame.

x1 <- c(1,2,5)
x2 <- c(1,3,6)
x3 <- c(1,4,7)
x4 <- c(1,5,8), list(x1,x2,x3,x4))  # sum all list elements, list(x1,x2,x3,x4))  # rbind the list elements

Let’s consider a scenario where we have a small data frame and want to run a general linear model on different combintions of attributes. One solution to this problem is to create the formula object as a list within a function, and then utilize to run a linear model on the desired attribute.

dat <- data.frame(x1 = rnorm(100, m=50), x2 = rnorm(100, m=50), x3 = rnorm(100, m=50), y = rnorm(100))
new_mod <- function(form){
  lstt = list(formula=as.formula(paste("y ~ ", form, sep="")),"dat"))
  summary("lm", lstt))


The eval function evaluates an expression, an object that represents an action that can be performed in R. An expression is different from an operation, which refers to the execution of an operation. In the following example, we assigned a value to a variable and performed an operation using that variable.

x <- 4
y <- x * 10

The expression and quote functions are used to takes an expression as an argument and returns an expression without evaluation.

ee = expression(y~x1)
z <- quote(y <- x * 10)

In the above example, z is referred to as a call object. They are usually created with the call function. For example, the following code pieces together commands into a call object and evaluates them.

mycall <- call("lm", quote(y ~ x1), data=quote(dat))
mod <- eval(mycall)


Another common procedure is to replace certain variables within a user defined function. This can be achieved with the substitute function. The below code replaces x1 and x2 in the expression with the values from the list.

replace <- list(x1 ="alphabet"), x2 ="zoology"))
substitute(expression(x1 + x2 + log(x1) + x3), replace)


There are a number of commands for working within column and row names in R. It’s generally suggested that the setNames function be used when modifying data structure names within a function.

names_new <- c("one","two","three","four")
new_dat <- expression(data.frame(x1 = rnorm(100, m=50), x2 = rnorm(100, m=50), x3 = rnorm(100, m=50), y = rnorm(100)))
head(setNames(eval(new_dat), names_new))
my_lst <- list(lname ="xls"))
setNames(my_lst, "x1")

When working with data within a function, it will often be useful to write code that creates the names and data structure, and then evaluates the pieces together.


Use the missing function to check whether an argument was supplied by the user.

func <- function(x){
        x = 5
    y = x*x; y


The stop function is used to halt a function, and is usually used when a particular condition is met.

guess <- function(n){
  if( n >= 6 ){


Use the warning function to throw a comment when a condition is met. It does not halt the function.

guess <- function(n){
  if( n >= 6 ){
      warning("BE CAREFUL!")


When functions are evaluated, R scans each function argument it can understand. When ellipsis are added as a function argument, it allows for other arguments to be passed into the function. This technique is frequently used when plotting and should be used when the function is designed to take any number of named or unnamed arguments.

plotter <- function(x, y, ...){
  plot(x, y, ...)

To make use of ellipsis, it’s suggested that the user scan through the … and turn them into a list. This is because some of the arguments in dots may be intended for several different functions.


SQL Cheat Sheet

I’ve been putting together a basic SQL cheat sheet that could be used as a reference guide. Here are a series of common procedures that should be of use for anyone who uses SQL to extract data. No explanations are provided as they should largely be known to the end user.


COUNT(DISTINCT year) AS years_count
COUNT(DISTINCT month) AS months_count


SELECT name, email, COUNT(*)
FROM users
GROUP BY name, email
HAVING COUNT(*) &gt; 1

SELECT name, email
    FROM users
    WHERE email in
    SELECT email
    FROM users
    GROUP BY email
    HAVING COUNT(*)&gt;1

SELECT firstname, lastname, list.address FROM list
GROUP BY address HAVING count(id) &gt; 1) dup ON list.address = dup.address

FROM training_details AS td
INNER JOIN users as u on u.user_id = td.user_id
GROUP BY 1, 2, 3
HAVING COUNT(*) &gt;= 2
ORDER BY td.order_date DESC;


 FROM report_runs rr
 LEFT JOIN report_schedule_runs rs ON rs.report_run_id =
 LEFT JOIN list_run_report_runs lrrr ON lrrr.report_run_id =
 LEFT JOIN list_schedule_runs lsr ON lsr.list_run_id = lrrr.list_run_id
 GROUP BY 1,2,3,4,5,6,7


SELECT count(1) FROM table;



SELECT * FROM student WHERE name LIKE ‘d%n’;
(returns dan or den)




SELECT SUM (Sales) FROM Store_Information
WHERE Store_Name IN
(SELECT Store_Name FROM Geography
WHERE Region_Name = 'West');


SELECT SUM (a1.Sales) FROM Store_Information a1
WHERE a1.Store_Name IN
(SELECT Store_Name FROM Geography a2
WHERE a2.Store_Name = a1.Store_Name);


SELECT sub.*
  FROM (
        SELECT *
          FROM table
         WHERE day_of_week = 'Friday'
       ) sub
 WHERE sub.resolution = 'NONE'


  FROM table
                 FROM table
                ORDER BY date
                LIMIT 5


SELECT incidents.*,
       sub.incidents AS incidents_that_day
  FROM tutorial.sf_crime_incidents_2014_01 incidents
  JOIN ( SELECT date,
          COUNT(incidnt_num) AS incidents
           FROM tutorial.sf_crime_incidents_2014_01
          GROUP BY 1
       ) sub
    ON =
 ORDER BY sub.incidents DESC, time


SELECT * FROM users WHERE TO_DAYS(last_login) = ( TO_DAYS(NOW()) - 1 )



SELECT FROM banned_users


SELECT CONCAT(emp.firstname, '-', emp.lastname) AS emp_full_name FROM emp;


SELECT LEFT(date, 10) AS cleaned_date,
       RIGHT(date, 17) AS cleaned_time
FROM table

SELECT SUBSTR(date, 4, 2) AS day
FROM table


Select database: use [database];

Show all tables: show tables;

Show table structure: describe [table];

Counting and selecting grouped records:
SELECT *, (SELECT COUNT([column]) FROM [table]) AS count
FROM [table]
GROUP BY [column];

Select records containing [value]:
SELECT * FROM [table]
WHERE [column] LIKE '%[value]%';

Select records starting with [value]:
SELECT * FROM [table]
WHERE [column] LIKE '[value]%';

Select records starting with val and ending with ue:
SELECT * FROM [table]
WHERE [column] LIKE '[val_ue]';

Select a range:
SELECT * FROM [table]
WHERE [column] BETWEEN [value1] and [value2];

Select with custom order and only limit:
SELECT * FROM [table]
WHERE [column]
ORDER BY [column] ASC
LIMIT [value]; 


INNER JOIN: returns rows when there is a match in both tables.

LEFT JOIN: returns all rows from the left table, even if there are no matches in the right table.

RIGHT JOIN: returns all rows from the right table, even if there are no matches in the left table.

FULL JOIN: returns rows when there is a match in one of the tables.

SELF JOIN: is used to join a table to itself as if the table were two tables, temporarily renaming at least one table in the SQL statement.

CARTESIAN JOIN: returns the Cartesian product of the sets of records from the two or more joined tables.

Weekly R-Tips: Visualizing Predictions

Lets say that we estimated a linear regression model on time series data with lagged predictors. The goal is to estimate sales as a function of inventory, search volume, and media spend from two months ago. After using the lm function to perform linear regression, we predict sales using values from two month ago.

frmla <- sales ~ inventory + search_volume + media_spend
mod <- lm(frmla, data=dat)
pred = predict(mod, values, interval="predict") 

If this model is estimated weekly or monthly, we will eventually want to understand how well our model did in predicting actual sales from month to month. To perform this task, we must regularly maintain a spreadsheet or data structure (RDS object) with actual predicted sales figures for each time period. That data can be used to create line graphs that visualize both the actual versus predicted values.

Here is what the original spreadsheet looked like.

Screenshot from 2016-02-05 16:41:22

Transform that data into long format using whatever package you prefer.

mydat = melt(d1)

This will provide a data frame with three columns.

Screenshot from 2016-02-04 15:04:36

We can utilize the ggplot2 package to create visualizations.

ggplot(mydat, aes(Month, value, group=variable, colour=variable)) +
  geom_line(lwd=1.05) + geom_point(size=2.5) + 
  ggtitle("Sales (01/2010 to 05/2015)") +
  xlab("Date") + ylab("Sales") + ylim(0,30000) + xlab(" ") + ylab(" ") +  
  theme(legend.title=element_blank()) + xlab(" ") + 
  theme(axis.text.x=element_text(colour="black")) +
  theme(axis.text.y=element_text(colour="black")) +
  theme(legend.position=c(.4, .85))


Above is an example of what the final product could look like. Visualizing predicted against actual values is an important component of evaluating the quality of a model. Furthermore, having such visualization will be of value when interacting with business audiences and “selling” your analysis.