Semiparametric Regression in R

A. INTRODUCTION When building statistical models, the goal is to define a compact and parsimonious mathematical representation of some data generating process. Many of these techniques require that one make assumptions about the data or how the analysis is specified. For example, Auto Regressive Integrated Moving Average (ARIMA) models require that the time series is weakly stationary or can be made so. Furthermore, ARIMA assumes that the data has no deterministic time trends, the variance of the error term is constant, and so forth. Assumptions are generally a good thing, but there are definitely situations in which one wants to free themselves from such “constraints.” In the context of evaluating relationships between one or more target variables and a set of explanatory variables, semiparametric regression is one such technique that provides the user with some flexibility in modeling complex data without maintaining stringent assumptions. With semiparametric regression, the goal is to develop a properly specified model that integrates the simplicity

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Using csvkit to Summarize Data: A Quick Example

As data analysts, we’re frequently presented with comma-separated value files and tasked with reporting insights. While it’s tempting to import that data directly into R or Python in order to perform data munging and exploratory data analysis, there are also a number of utilities to examine, fix, slice, transform, and summarize data through the command line. In particular, Csvkit is a suite of python based utilities for working with CSV files from the terminal. For this post, we will grab data using wget, subset rows containing a particular value, and summarize the data in different ways. The goal is to take data on criminal activity, group by a particular offense type, and develop counts to understand the frequency distribution. Lets start by installing csvkit. Go to your command line and type in the following commands. $ pip install csvkit One: Set the working directory. $ cd /home/abraham/Blog/Chicago_Analysis Two: Use the wget command to grab data and export it as a

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Examining Website Pathing Data Using Markov Chains

A markov model can be used to examine a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Let’s define a stochastic process  that takes on a finite number of possible values which are nonnegative integers. Each state, , represents it’s value in time period . If the probability of being in is dependent on , it’s refered to as the first-order Markov property. We are interested in estimating , which is the fixed probability that at time  will be followed by state . These step transition probabilities are calculated through the Chapman-Kolmogorov equations, which relates the joint probability distributions of different sets of coordinates on a stochastic process. Markov chains are generally represented as a state diagram or transition matrix where every row of the matrix, , is a conditional probability mass function. Let’s consider an example using website pathing data from an ecommerce website. The set

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Statistics Refresher

Let’s face it, a good statistics refresher is always worthwhile. There are times we all forget basic concepts and calculations. Therefore, I put together a document that could act as a statistics refresher and thought that I’d share it with the world. This is part one of a two part document that is still being completed. This refresher is based on Principles of Statistics by Balmer and Statistics in Plain English by Brightman. The Two Concepts of Probability Statistical Probability Statistical probability pertains to the relative frequency with which an event occurs in the long run. Example: Let’s say we flip a coin twice. What is the probability of getting two heads? If we flip a coin twice, there are four possible outcomes, . Therefore, the probability of flipping two heads is Inductive Probability Inductive probability pertains to the degree of belief which is reasonable to place on a proposition given evidence. Example: I’m certain that the answer to  is between and . The Two Laws

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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))) head(ddat) tail(ddat) 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 <-

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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

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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. 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. Transform that data into long format using whatever package you prefer. This will provide a data frame with three columns. We can utilize the ggplot2 package to create visualizations. Above

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Applied Statistical Theory: Quantile Regression

This is part two of the ‘applied statistical theory’ series that will cover the bare essentials of various statistical techniques. As analysts, we need to know enough about what we’re doing to be dangerous and explain approaches to others. It’s not enough to say “I used X because the misclassification rate was low.” Standard linear regression summarizes the average relationship between a set of predictors and the response variable. represents the change in the mean value of given a one unit change in . A single slope is used to describe the relationship. Therefore, linear regression only provides a partial view of the link between the response variable and predictors. This is often inadaquete when there is heterogenous variance between and . In such cases, we need to examine how the relationship between and changes depending on the value of . For example, the impact of education on income may be more pronounced for those at higher income levels than

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Applied Statistical Theory: Belief Networks

Applied statistical theory is a new series that will cover the basic methodology and framework behind various statistical procedures. As analysts, we need to know enough about what we’re doing to be dangerous and explain approaches to others. It’s not enough to say “I used X because the misclassification rate was low.” At the same time, we don’t need to have doctoral level understanding of approach X. I’m hoping that these posts will provide a simple, succinct middle ground for understanding various statistical techniques. Probabilistic grphical models represent the conditional dependencies between random variables through a graph structure. Nodes correspond to random variables and edges represent statistical dependencies between the variables. Two variables are said to be conditionally dependent if they have a direct impact on each others’ values. Therefore, a graph with directed edges from parent and child denotes a causal relationship. Two variables are conditionally independent if the link between those variables are conditional on another. For a

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Basic Forecasting

Forecasting refers to the process of using statistical procedures to predict future values of a time series based on historical trends. For businesses, being able gauge expected outcomes for a given time period is essential for managing marketing, planning, and finances. For example, an advertising agency may want to utilizes sales forecasts to identify which future months may require increased marketing expenditures. Companies may also use forecasts to identify which sales persons met their expected targets for a fiscal quarter. There are a number of techniques that can be utilized to generate quantitative forecasts. Some methods are fairly simple while others are more robust and incorporate exogenous factors. Regardless of what is utilized, the first step should always be to visualize the data using a line graph. You want to consider how the metric changes over time, whether there is a distinct trend, or if there are distinct patterns that are noteworthy. There are several key concepts that we should

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