Tabulate coefficients from lm

Question

I have 10 linear models where I only need some information, namely: r-squared, p-value, coefficients of slope and intercept. I managed to extract these values (via ridiculously

Answer 1

Consider building a matrix of lm results. First create a defined function to handle your generalized data frame model build with results extraction. Then, call by which can subset your data frame by a factor column and pass each subset into defined method. Finally, rbind all grouped matrices together for a singular output

lm_results <- function(df) {

  model <- lm(Qend ~ Rainfall, data = df)
  res <- summary(model)

  p <- res$fstatistic

  c(gradient = res$coefficients[2,1],
    intercept = res$coefficients[2,2],
    r_sq = res$r.squared,
    adj_r_sq = res$adj.r.squared,
    f_stat = p[['value']],
    p_value = unname(pf(p[1], p[2], p[3], lower.tail=FALSE))
  )
}

matrix_list <- by(d, d$group, lm_results)

final_matrix <- do.call(rbind, matrix_list)

---

To demonstrate on random, seeded data

set.seed(12262018)
data_tools <- c("sas", "stata", "spss", "python", "r", "julia")

d <- data.frame(
  group = sample(data_tools, 500, replace=TRUE),
  int = sample(1:15, 500, replace=TRUE),
  Qend = rnorm(500) / 100,
  Rainfall = rnorm(500) * 10
)

Results

mat_list <- by(d, d$group, lm_results)

final_matrix <- do.call(rbind, mat_list)
final_matrix

#             gradient    intercept        r_sq     adj_r_sq    f_stat    p_value
# julia  -1.407313e-04 1.203832e-04 0.017219149  0.004619395 1.3666258 0.24595273
# python -1.438116e-04 1.125170e-04 0.018641512  0.007230367 1.6336233 0.20464162
# r       2.031717e-04 1.168037e-04 0.041432175  0.027738349 3.0256098 0.08635510
# sas    -1.549510e-04 9.067337e-05 0.032476668  0.021355710 2.9203121 0.09103619
# spss    9.326656e-05 1.068516e-04 0.008583473 -0.002682623 0.7618853 0.38511469
# stata  -7.079514e-05 1.024010e-04 0.006013841 -0.006568262 0.4779679 0.49137093

Answer 2

Using library(data.table) you can do

d <- fread("example.csv")
d[, .(
  r2         = (fit <- summary(lm(Qend~Rainfall)))$r.squared,
  adj.r2     = fit$adj.r.squared,
  intercept  = fit$coefficients[1,1], 
  gradient   = fit$coefficients[2,1],
  p.value    = {p <- fit$fstatistic; pf(p[1], p[2], p[3], lower.tail=FALSE)}),
  by  = CatChro]

#    CatChro         r2       adj.r2   intercept     gradient      p.value
# 1:    A3G1 0.03627553  0.011564648 0.024432020 0.0001147645 0.2329519751
# 2:    A3D1 0.28069553  0.254054622 0.011876543 0.0004085644 0.0031181110
# 3:    A3G2 0.06449971  0.041112205 0.026079409 0.0004583538 0.1045970987
# 4:    A3D2 0.03384173  0.005425311 0.023601325 0.0005431693 0.2828170556
# 5:    A3G3 0.07587433  0.054383038 0.043537869 0.0006964512 0.0670399684
# 6:    A3D3 0.04285322  0.002972105 0.022106960 0.0001451185 0.3102578215
# 7:    A3G4 0.17337420  0.155404076 0.023706652 0.0006442175 0.0032431299
# 8:    A3D4 0.37219027  0.349768492 0.009301843 0.0006614213 0.0003442445
# 9:    A3G5 0.17227383  0.150491566 0.025994831 0.0006658466 0.0077413595
#10:    A3D5 0.04411669 -0.008987936 0.014341399 0.0001084626 0.3741011769

Answer 3

Here in only a couple of lines:

library(tidyverse)
library(broom)
# create grouped dataframe:
df_g <- df %>% group_by(CatChro)
df_g %>% do(tidy(lm(Qend ~ Rainfall, data = .))) %>% 
   select(CatChro, term, estimate) %>% spread(term, estimate) %>% 
   left_join(df_g %>% do(glance(lm(Qend ~ Rainfall, data = .))) %>%
   select(CatChro, r.squared, adj.r.squared, p.value), by = "CatChro")

And the result will be:

# A tibble: 10 x 6
# Groups:   CatChro [?]
   CatChro `(Intercept)` Rainfall r.squared adj.r.squared  p.value
   <chr>           <dbl>    <dbl>     <dbl>         <dbl>    <dbl>
 1 A3D1          0.0119  0.000409    0.281        0.254   0.00312 
 2 A3D2          0.0236  0.000543    0.0338       0.00543 0.283   
 3 A3D3          0.0221  0.000145    0.0429       0.00297 0.310   
 4 A3D4          0.00930 0.000661    0.372        0.350   0.000344
 5 A3D5          0.0143  0.000108    0.0441      -0.00899 0.374   
 6 A3G1          0.0244  0.000115    0.0363       0.0116  0.233   
 7 A3G2          0.0261  0.000458    0.0645       0.0411  0.105   
 8 A3G3          0.0435  0.000696    0.0759       0.0544  0.0670  
 9 A3G4          0.0237  0.000644    0.173        0.155   0.00324 
10 A3G5          0.0260  0.000666    0.172        0.150   0.00774 

So, how does this work?

The following creates a dataframe with all coefficients and the corresponding statistics (tidy turns the result of lm into a dataframe):

df_g %>%
  do(tidy(lm(Qend ~ Rainfall, data = .)))
A tibble: 20 x 6
Groups:   CatChro [10]
   CatChro term        estimate std.error statistic      p.value
   <chr>   <chr>          <dbl>     <dbl>     <dbl>        <dbl>
 1 A3D1    (Intercept) 0.0119   0.00358       3.32  0.00258     
 2 A3D1    Rainfall    0.000409 0.000126      3.25  0.00312     
 3 A3D2    (Intercept) 0.0236   0.00928       2.54  0.0157      
 4 A3D2    Rainfall    0.000543 0.000498      1.09  0.283       

I understand that you want to have the intercept and the coefficient on Rainfall as individual columns, so let's "spread" them out. This is achieved by first selecting the relevant columns, and then invoking tidyr::spread, as in

select(CatChro, term, estimate) %>% spread(term, estimate)

This gives you:

df_g %>% do(tidy(lm(Qend ~ Rainfall, data = .))) %>% 
  select(CatChro, term, estimate) %>% spread(term, estimate)
A tibble: 10 x 3
Groups:   CatChro [10]
   CatChro `(Intercept)` Rainfall
   <chr>           <dbl>    <dbl>
 1 A3D1          0.0119  0.000409
 2 A3D2          0.0236  0.000543
 3 A3D3          0.0221  0.000145
 4 A3D4          0.00930 0.000661

Glance gives you the summary statistics you are looking for, for each model one. The models are indexed by group, here CatChro, so it is easy to just merge them onto the previous dataframe, which is what the rest of the code is about.

Answer 4

Another solution, with lme4::lmList. The summary() method for objects produced by lmList does almost everything you want (although it doesn't store p-values, that's something I had to add below).

m <- lme4::lmList(Qend~Rainfall|CatChro,data=d)
s <- summary(m)
pvals <- apply(s$fstatistic,1,function(x) pf(x[1],x[2],x[3],lower.tail=FALSE))
data.frame(intercept=coef(s)[,"Estimate","(Intercept)"],
           slope=coef(s)[,"Estimate","Rainfall"],
           r.squared=s$r.squared,
           adj.r.squared=unlist(s$adj.r.squared),
           p.value=pvals)

Answer 5

Here is a base R solution:

data <- read.csv("./data/so53933238.csv",header=TRUE)

# split by value of CatChro into a list of datasets
dataList <- split(data,data$CatChro)

# process the list with lm(), extract results to a data frame, write to a list
lmResults <- lapply(dataList,function(x){
     y <- summary(lm(Qend ~ Rainfall,data = x))
     Intercept <- y$coefficients[1,1]
     Slope <- y$coefficients[2,1]
     rSquared <- y$r.squared
     adjRSquared <- y$adj.r.squared
     f <- y$fstatistic[1]
     pValue <- pf(y$fstatistic[1],y$fstatistic[2],y$fstatistic[3],lower.tail = FALSE)
     data.frame(Slope,Intercept,rSquared,adjRSquared,pValue)
})
lmResultTable <- do.call(rbind,lmResults)
# add CatChro indicators
lmResultTable$catChro <- names(dataList)

lmResultTable 

...and the output:

    > lmResultTable
            Slope   Intercept   rSquared  adjRSquared       pValue catChro
A3D1 0.0004085644 0.011876543 0.28069553  0.254054622 0.0031181110    A3D1
A3D2 0.0005431693 0.023601325 0.03384173  0.005425311 0.2828170556    A3D2
A3D3 0.0001451185 0.022106960 0.04285322  0.002972105 0.3102578215    A3D3
A3D4 0.0006614213 0.009301843 0.37219027  0.349768492 0.0003442445    A3D4
A3D5 0.0001084626 0.014341399 0.04411669 -0.008987936 0.3741011769    A3D5
A3G1 0.0001147645 0.024432020 0.03627553  0.011564648 0.2329519751    A3G1
A3G2 0.0004583538 0.026079409 0.06449971  0.041112205 0.1045970987    A3G2
A3G3 0.0006964512 0.043537869 0.07587433  0.054383038 0.0670399684    A3G3
A3G4 0.0006442175 0.023706652 0.17337420  0.155404076 0.0032431299    A3G4
A3G5 0.0006658466 0.025994831 0.17227383  0.150491566 0.0077413595    A3G5
>

To render the output in a tabular format in HTML, one can use knitr::kable().

library(knitr)
kable(lmResultTable[1:5],row.names=TRUE,digits=5) 

...which produces the following output after rendering the Markdown: