Estimate many Similar Models (and Plot Results)

Estimate_Similar_Models.md

Estimate Many Similar Models and Display Coefficients

Ryan T. Moore 14 October 2016

The Problem

You want to estimate a set of similar models, and display the coefficients in a plot. For example, you want to estimate

y = a + b*x1
y = a + c*x2
y = a + d*x3

and display b, c, and d in a plot with confidence intervals.

The TL;DR Solution

Copy the function below (or from this PDF version) and run the function similar_models(), such as

similar_models(df, "y", c("x1", "x2", "x3"))

The Full Solution

Some required libraries:

library(ggplot2)
library(tidyr)
library(dplyr)

The Function

The function similar_models takes the data, the outcome, the set of related variables that you want to include, one-by-one, and any variables that you want to include in every model.

similar_models <- function(data, outcome, related_variables, always_include = NULL,
                           verbose = FALSE){
  
  ## Initialize storage:
  n_models <- length(related_variables)
  storage <- matrix(NA, n_models, 3)
  
  ## Loop over names
  for(model.idx in 1:n_models){
    if(verbose == TRUE){
      cat(paste("Starting ", related_variables[model.idx], "\n"))
    }
    ## Create string for formula:
    this_formula <- paste0(outcome, " ~ ", related_variables[model.idx])
    
    if(length(always_include) > 0){
      additional_terms <- ""
      for(always.idx in 1:length(always_include)){
        additional_terms <- paste(additional_terms, "+", always_include[always.idx])
      }
      
      this_formula <- paste(this_formula, additional_terms)
    }
    
    this_formula <- as.formula(this_formula)
    
    ## Estimate:
    lm_out <- lm(this_formula, data = data)
    ## Store coef and CI:
    results <- c(coef(lm_out)[2], confint(lm_out)[2, 1], confint(lm_out)[2, 2])
    storage[model.idx, ] <- results
  }
  
  storage <- as.data.frame(storage)
  ## Add variable names:
  storage$Variable <- related_variables
  names(storage)[1:3] <- c("Coefficient", "Lower", "Upper")
  
  ## Sort:
  storage$Variable <- factor(storage$Variable, 
                             levels = storage$Variable[order(storage$Coefficient)])

  return(storage)
}

Sample Data

Create some data with variables y, x1, x2, x3, and w:

set.seed(418)
n <- 100
df <- data.frame(x1 = rnorm(n), x2 = rnorm(n), x3 = rnorm(n), w = rnorm(n))
df <- df %>% mutate(y = x1 + 2*x2 + 3*x3 + 2*w + rnorm(n))

Estimate the Similar Models

Store the variable names as a vector of strings, then estimate the similar models in the equations above.

related_vars <- c("x1", "x2", "x3")

lm_results <- similar_models(df, "y", related_vars)

## Plot the results:
lm_results %>% ggplot(aes(x = Coefficient, y = Variable)) + 
  geom_point() + 
  geom_segment(aes(x = Lower, xend = Upper, y = Variable, yend = Variable))

Including other Predictors in Each Model

To estimates models like

y = a + b*x1 + e*w
y = a + c*x2 + e*w
y = a + d*x3 + e*w

specify the variable(s) you want to always include, such as w. You could include several, as c("w", "z", "q", ...).

lm_results_w <- similar_models(df, "y", related_vars, always_include = "w")

## Plot:
lm_results_w %>% ggplot(aes(x = Coefficient, y = Variable)) + 
  geom_point() + 
  geom_segment(aes(x = Lower, xend = Upper, y = Variable, yend = Variable))

Estimate_Similar_Models.Rmd

---
title: "Estimate Many Similar Models and Display Coefficients"
author: Ryan T. Moore
date: "14 October 2016"
output: rmarkdown::github_document
urlcolor: red
---

# The Problem

You want to estimate a set of similar models, and display the coefficients in a plot.  For example, you want to estimate

```
y = a + b * x1
y = a + c * x2
y = a + d * x3
```

and display `b`, `c`, and `d` in a plot with confidence intervals.

# The TL;DR Solution

Copy the function below (or from this [PDF version](http://www.ryantmoore.org/files/ht/htSimilarModels.pdf)) and run the function `similar_models()`, such as 

```r
similar_models(df, "y", c("x1", "x2", "x3"))
```

# The Full Solution

## Some required libraries:
```{r warning = FALSE, message=FALSE}
library(dplyr)
library(ggplot2)
library(tidyr)
```

## The Function 
The function `similar_models` takes the data, the outcome, the set of related variables that you want to include, one-by-one, and any variables that you want to include in every model.

```{r warning = FALSE}
similar_models <- function(data, outcome, related_variables, always_include = NULL,
                           verbose = FALSE){
  
  ## Initialize storage:
  n_models <- length(related_variables)
  storage <- matrix(NA, n_models, 3)
  
  ## Loop over names
  for(model.idx in 1:n_models){
    if(verbose == TRUE){
      cat(paste("Starting ", related_variables[model.idx], "\n"))
    }
    ## Create string for formula:
    this_formula <- paste0(outcome, " ~ ", related_variables[model.idx])
    
    if(length(always_include) > 0){
      additional_terms <- ""
      for(always.idx in 1:length(always_include)){
        additional_terms <- paste(additional_terms, "+", always_include[always.idx])
      }
      
      this_formula <- paste(this_formula, additional_terms)
    }
    
    this_formula <- as.formula(this_formula)
    
    ## Estimate:
    lm_out <- lm(this_formula, data = data)
    ## Store coef and CI:
    results <- c(coef(lm_out)[2], confint(lm_out)[2, 1], confint(lm_out)[2, 2])
    storage[model.idx, ] <- results
  }
  
  storage <- as.data.frame(storage)
  ## Add variable names:
  storage$Variable <- related_variables
  names(storage)[1:3] <- c("Coefficient", "Lower", "Upper")
  
  ## Sort:
  storage$Variable <- factor(storage$Variable, 
                             levels = storage$Variable[order(storage$Coefficient)])

  return(storage)
}
```

## Sample Data
Create some data with variables `y`, `x1`, `x2`, `x3`, and `w`:
```{r}
set.seed(418)
n <- 100
df <- data.frame(x1 = rnorm(n), x2 = rnorm(n), x3 = rnorm(n), w = rnorm(n))
df <- df %>% mutate(y = x1 + 2*x2 + 3*x3 + 2*w + rnorm(n))
```

## Estimate the Similar Models

Store the variable names as a vector of strings, then estimate the similar models in the equations above.
```{r warning = FALSE, message=FALSE}
related_vars <- c("x1", "x2", "x3")

lm_results <- similar_models(df, "y", related_vars)

## Plot the results:
lm_results %>% ggplot(aes(x = Coefficient, y = Variable)) + 
  geom_point() + 
  geom_segment(aes(x = Lower, xend = Upper, y = Variable, yend = Variable))
```

## Including other Predictors in Each Model

To estimates models like

```
y = a + b*x1 + e*w
y = a + c*x2 + e*w
y = a + d*x3 + e*w
```

specify the variable(s) you want to always include, such as `w`.  You could include several, as `c("w", "z", "q", ...)`.

```{r warning = FALSE}
lm_results_w <- similar_models(df, "y", related_vars, always_include = "w")

## Plot:
lm_results_w %>% ggplot(aes(x = Coefficient, y = Variable)) + 
  geom_point() + 
  geom_segment(aes(x = Lower, xend = Upper, y = Variable, yend = Variable))
```