What would you do? Higher R without interaction terms

Question

I'm working with RStudio. I've searched, but I haven't been able to find anyone with this problem. I'm dealing with a dataset that has many variables, and I've found that the model I've created with interaction terms has a lower R and R squared than the model without the interaction terms. What would you do in this case? Datasets: https://www.kaggle.com/arashnic/fitbit I used sleepDay_merged.csv and dailyActivity_merged.csv

# Installing packages
install.packages("pacman")

pacman::p_load(tidyverse, lubridate, janitor, DataExplorer, venn, e1071, olsrr,ggiraphExtra)

daily_sleep <- read_csv("sleepDay_merged.csv")
head(daily_sleep)

# Cleaning and mutating, data frames, and preparing for merge.
daily_sleep <- daily_sleep %>%
  clean_names() %>% 
  mutate(date = mdy(sleep_day))

daily_activity <- read_csv("dailyActivity_merged.csv")
head(daily_activity)
glimpse(daily_activity)


daily_activity <- daily_activity %>% 
  clean_names() %>% 
  mutate(id = as.factor(id), date = mdy(activity_date), day = weekdays(date))
head(daily_activity)

sleep_activity <- merge(daily_activity, daily_sleep)
sleep_activity <- sleep_activity[c(1,2,4,5,8:10,12:16,17,20,21)]
head(sleep_activity)
str(sleep_activity)
usage <- daily_activity %>%
    group_by(id,date) %>% 
  summarise(day,sum_minutes = sum(lightly_active_minutes)+sum(fairly_active_minutes)+
              sum(very_active_minutes)) %>% 
  mutate(usage_level = case_when(
    sum_minutes >= 0 & sum_minutes <= 183 ~ "Low Usage",
    sum_minutes >138 & sum_minutes <= 358.8 ~ "Moderate Usage",
    sum_minutes > 358.8 | sum_minutes <= 552.0 ~ "High Usage"))
head(usage)
summary(usage)

usage_day <- usage %>% group_by(day) %>% summarise(sum_minutes,usage_level)

usage_day$day <- ordered(usage_day$day, 
                         levels=c("Monday", "Tuesday", "Wednesday", "Thursday", 
                                         "Friday", "Saturday", "Sunday"))

# Transforming sleep_activity data
sleep_activity %>% plot_histogram(ncol = 5, ggtheme = theme_light())
sleep_activity_filtered <- merge(sleep_activity,usage)
sleep_activity_filtered <- sleep_activity_filtered[!(sleep_activity_filtered$sedentary_minutes <5),]
head(sleep_activity_filtered)
# Transforming skewed data with log transformations
sleep_activity_filtered <- sleep_activity_filtered %>% 
  mutate(log_moderately_active_distance = log(moderately_active_distance+1),
         log_very_active_distance = log(very_active_distance+1),
         log_very_active_minutes = log(very_active_minutes+1),
         log_fairly_active_minutes = log(fairly_active_minutes+1))
colnames(sleep_activity_filtered)
sleep_activity_filtered <- sleep_activity_filtered %>%
  select(-c("moderately_active_distance",
            "very_active_minutes",
            "very_active_distance",
            "fairly_active_minutes"))

# Merging final data frames.
new_data <- sleep_activity_filtered %>% 
  select(-c("id"))

Regular multiple linear regression model:

multi_model <- lm(calories ~., data = new_data)
summary(multi_model)
mutli_step <- ols_step_both_p(multi_model, pent = 0.05, prem = 0.1, details = TRUE)

Model Summary                           
-----------------------------------------------------------------
R                       0.923       RMSE                 292.130 
R-Squared               0.851       Coef. Var             12.175 
Adj. R-Squared          0.847       MSE                85339.931 
Pred R-Squared          0.829       MAE                  215.072 

Multiple Linear Regression with Interaction terms:

interaction <- lm(calories ~ date + day + sedentary_minutes + (total_minutes_asleep *
               total_time_in_bed) + (total_steps*total_distance * light_active_distance *
               lightly_active_minutes) + (total_steps * total_distance *
               log_moderately_active_distance *
               log_fairly_active_minutes) +
               (total_steps * total_distance * log_very_active_distance *
               log_very_active_minutes), data = new_data )
summary(interaction)
int_step_model <- ols_step_both_p(interaction, pent = 0.5, prem = 0.1, details = TRUE)
step_model$interaction
plot(int_step_model, interaction, print_plot = TRUE)

Model Summary                            
------------------------------------------------------------------
R                       0.871       RMSE                  373.020 
R-Squared               0.758       Coef. Var              15.546 
Adj. R-Squared          0.750       MSE                139143.659 
Pred R-Squared          0.736       MAE                   293.464 
------------------------------------------------------------------

Answer 1

I'm dealing with a dataset that has many variables, and I've found that the model I've created with interaction terms has a lower R and R squared than the model without the interaction terms.

This is completely unsurprising since more variables will reduce the RSS, even if they are not truly associated with the outcome.

What would you do in this case?

Its a bit late to do this now, but if you're going to compare models like this you need to pre-specify the comparison and then perform an F test between the two models.

As of now, you're doing something like stepwise regression, and stepwise is known to be a poor method for model selection let alone inference. I would encourage you to search this forum for mentions of stepwise and read some of the more popular answers.