Model Fitting

data("nyc_airbnb")

nyc_airbnb = 
  nyc_airbnb %>% 
  mutate(stars = review_scores_location / 2) %>% 
  rename(
    boro = neighbourhood_group,
    neighborhood = neighbourhood) %>% 
  filter(boro != "Staten Island") %>% 
  dplyr::select(price, stars, boro, neighborhood, room_type)

Fit the first linear model:

fit = lm(price ~ stars + boro, data = nyc_airbnb)

summary(fit)
## 
## Call:
## lm(formula = price ~ stars + boro, data = nyc_airbnb)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -169.8  -64.0  -29.0   20.2 9870.0 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    -70.414     14.021  -5.022 5.14e-07 ***
## stars           31.990      2.527  12.657  < 2e-16 ***
## boroBrooklyn    40.500      8.559   4.732 2.23e-06 ***
## boroManhattan   90.254      8.567  10.534  < 2e-16 ***
## boroQueens      13.206      9.065   1.457    0.145    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 181.5 on 30525 degrees of freedom
##   (9962 observations deleted due to missingness)
## Multiple R-squared:  0.03423,    Adjusted R-squared:  0.03411 
## F-statistic: 270.5 on 4 and 30525 DF,  p-value: < 2.2e-16
coef(fit)
##   (Intercept)         stars  boroBrooklyn boroManhattan    boroQueens 
##     -70.41446      31.98989      40.50030      90.25393      13.20617

Tidy the results:

fit %>% 
  broom::tidy() %>% 
  mutate(
    term = str_replace(term, "boro", "Boro:") 
  ) %>% 
  knitr::kable()
term estimate std.error statistic p.value
(Intercept) -70.41446 14.020697 -5.022180 0.0000005
stars 31.98989 2.527500 12.656733 0.0000000
Boro:Brooklyn 40.50030 8.558723 4.732049 0.0000022
Boro:Manhattan 90.25393 8.567490 10.534465 0.0000000
Boro:Queens 13.20617 9.064879 1.456850 0.1451682

Take a look at factors…

nyc_airbnb = 
  nyc_airbnb %>% 
  mutate(
    boro = fct_infreq(boro),  # reorder factor levels based on their frequencies
    room_type = fct_infreq(room_type))

fit = lm(price ~ stars + boro, data = nyc_airbnb)
fit %>% broom::glance()
## # A tibble: 1 x 11
##   r.squared adj.r.squared sigma statistic   p.value    df  logLik    AIC
##       <dbl>         <dbl> <dbl>     <dbl>     <dbl> <int>   <dbl>  <dbl>
## 1    0.0342        0.0341  182.      271. 6.73e-229     5 -2.02e5 4.04e5
## # … with 3 more variables: BIC <dbl>, deviance <dbl>, df.residual <int>

Diagnostics

modelr::add_residuals(nyc_airbnb, fit) %>% 
  ggplot(aes(x = boro, y = resid)) + 
  geom_violin() +
  ylim(-500, 500)
## Warning: Removed 10202 rows containing non-finite values (stat_ydensity).

nyc_airbnb %>% 
  modelr::add_residuals(fit) %>% 
  ggplot(aes(x = stars, y = resid)) + 
  geom_point() +
  ylim(-500, 500)
## Warning: Removed 10202 rows containing missing values (geom_point).

modelr::add_predictions(nyc_airbnb, fit)
## # A tibble: 40,492 x 6
##   price stars boro  neighborhood room_type        pred
##   <dbl> <dbl> <fct> <chr>        <fct>           <dbl>
## 1    99     5 Bronx City Island  Private room     89.5
## 2   200    NA Bronx City Island  Private room     NA  
## 3   300    NA Bronx City Island  Entire home/apt  NA  
## # … with 4.049e+04 more rows

Nesting

nyc_airbnb %>% 
  lm(price ~ stars * boro + room_type * boro, data = .) %>% 
  broom::tidy() %>% 
  knitr::kable(digits = 3)
term estimate std.error statistic p.value
(Intercept) 95.694 19.184 4.988 0.000
stars 27.110 3.965 6.838 0.000
boroBrooklyn -26.066 25.080 -1.039 0.299
boroQueens -4.118 40.674 -0.101 0.919
boroBronx -5.627 77.808 -0.072 0.942
room_typePrivate room -124.188 2.996 -41.457 0.000
room_typeShared room -153.635 8.692 -17.676 0.000
stars:boroBrooklyn -6.139 5.237 -1.172 0.241
stars:boroQueens -17.455 8.539 -2.044 0.041
stars:boroBronx -22.664 17.099 -1.325 0.185
boroBrooklyn:room_typePrivate room 31.965 4.328 7.386 0.000
boroQueens:room_typePrivate room 54.933 7.459 7.365 0.000
boroBronx:room_typePrivate room 71.273 18.002 3.959 0.000
boroBrooklyn:room_typeShared room 47.797 13.895 3.440 0.001
boroQueens:room_typeShared room 58.662 17.897 3.278 0.001
boroBronx:room_typeShared room 83.089 42.451 1.957 0.050 
nest_lm_res =
  nyc_airbnb %>% 
  nest(data = -boro) %>% 
  mutate(models = map(data, ~lm(price ~ stars + room_type, data = .x)),
         models = map(models, broom::tidy)) %>% 
  dplyr::select(-data) %>% 
  unnest(models)
manhattan_airbnb =
  nyc_airbnb %>% 
  filter(boro == "Manhattan")

manhattan_nest_lm_res =
  manhattan_airbnb %>% 
  nest(data = -neighborhood) %>% 
  mutate(models = map(data, ~lm(price ~ stars + room_type, data = .x)),
         models = map(models, broom::tidy)) %>% 
  dplyr::select(-data) %>% 
  unnest(models)

manhattan_nest_lm_res %>% 
  filter(str_detect(term, "room_type")) %>% 
  ggplot(aes(x = neighborhood, y = estimate)) + 
  geom_point() + 
  facet_wrap(~term) + 
  theme(axis.text.x = element_text(angle = 80, hjust = 1))