Comparing Linear, Ridge, and Lasso Regression Models
Zhanchao Yang
This document demonstrates the application of Population Dynamics Foundation Model (PDFM) embeddings to predict Zillow Home Value Index (ZHVI) data. PDFM embeddings are 330-dimensional vector representations that capture complex spatial and demographic patterns.
Ridge and Lasso regression are particularly useful when working with high-dimensional embeddings (330 features) because they:
# Data manipulation and analysis
library(tidyverse)
library(readr)
# Geospatial data handling
library(sf)
library(leaflet)
# Machine learning and modeling
library(caret)
library(MASS) # For stepwise regression
library(glmnet) # For Ridge and Lasso regression
# Model evaluation
library(Metrics)
library(ggplot2)
# For table formatting
library(knitr)
library(kableExtra)
# Set random seed for reproducibility
set.seed(42)# constuct correct State FIPS code and Municipal FIPS code with leading zeros
zhvi_df <- zhvi %>%
mutate(
StateCodeFIP = str_pad(as.character(StateCodeFIPS), width = 2, side = "left", pad = "0"),
MunicipalCodeFIP = str_pad(as.character(MunicipalCodeFIPS), width = 3, side = "left", pad = "0")
)
# Create place identifier
zhvi_df <- zhvi_df %>%
mutate(
place = paste0("geoId/", StateCodeFIP, MunicipalCodeFIP)
)Note: The place column creates a unique identifier for each county by combining state and municipal FIPS codes, which will be used to join with geospatial and embedding data.
# Create interactive map with Leaflet
pal <- colorNumeric(
palette = "Blues",
domain = viz_gdf[[target_date]],
na.color = "transparent"
)
leaflet(viz_gdf) %>%
addTiles() %>%
addPolygons(
fillColor = ~pal(get(target_date)),
fillOpacity = 0.7,
color = "white",
weight = 1,
popup = ~paste0(
"<strong>", RegionName, ", ", State, "</strong><br>",
"Home Value: $", format(get(target_date), big.mark = ",")
)
) %>%
addLegend(
position = "bottomright",
pal = pal,
values = ~get(target_date),
title = "Zillow Home Median Value",
opacity = 1
)