线性回归斜率综述

Question

新的R用户在这里。

我有一个大约400个站点的数据集，我试图得到每个站点的p和回归斜率的标准差。

我已经用下面的方法获得了一部分，但我不知道如何接近问题的最后一部分，以拟合一个线性回归到每个站点，得到直线的斜率，并创建另一个列与每一个站点的斜率。

我很感激你的帮助！

# Sample df
df <- data.frame(site.id=c("1", "1", "2", "2", "3", "3"), year=c("2019", "2020", "2019", "2020", "2019", "2020"), p=c(107, 101, 114, 117, 97, 89)
    print(df)

# Summarize
    df.sum <- df %>%
    group_by(site.id) %>%
      summarise(p.sd=sd(p))
    print(df.sum)

Answer 1

尝试以下两种方法之一：

# 1
df %>%
  mutate(year = as.numeric(year)) %>%
  group_by(site.id) %>%
  summarise(p.sd = sd(p), slope = cov(p, year) / var(year))

# 2
df %>%
  mutate(year = as.numeric(year)) %>%
  group_by(site.id) %>%
  summarise(p.sd = sd(p), slope = coef(lm(p ~ year))[[2]])

如果我们知道每个site.id都有2行，这在示例数据中是这样的，那么这也可以：

# 3 - only if every site.id has exactly 2 rows
df %>%
  mutate(year = as.numeric(year)) %>%
  group_by(site.id) %>%
  summarise(p.sd = sd(p), slope = diff(p) / diff(year))

如果我们知道每个site.id正好有2行和连续的年份，那么diff(年份)等于1，这在示例数据中是这样的，那么它可以简化为：

# 4 - only if every site.id has exactly 2 rows & consecutive years
df %>%
  group_by(site.id) %>%
  summarise(p.sd = sd(p), slope = diff(p))

备注

我们使用了这个问题上的输入：

df <- data.frame(site.id=c("1", "1", "2", "2", "3", "3"), 
  year = c("2019", "2020", "2019", "2020", "2019", "2020"),
  p = c(107, 101, 114, 117, 97, 89))

Answer 2

# Sample df
df <- data.frame(site.id = c(1, 1, 2, 2, 3, 3), 
                 year = c(2019, 2020, 2019, 2020, 2019, 2020), 
                 p = c(107, 101, 114, 117, 97, 89))

# split by site.id, fit lm and extract slope coefficient
regression_slopes_list <- split(df, df$site.id) |> 
  lapply(function(x) { 
    lm(p ~ year, data = x)$coefficients[ 2 ] |> 
      as.numeric() 
  })

# transform list to data.frame
slopes_df <- data.frame(slope = unlist(regression_slopes_list), 
                        site.id = names(regression_slopes_list))

# get sd by site.id
sd_df <- tapply(df$p, df$site.id, sd) |> 
  as.data.frame() |> 
  `colnames<-`('sd')
sd_df$site.id <- rownames(sd_df)

# merge data.frame with slope data with sample df
df <- merge(df, slopes_df, by = 'site.id') |> 
  merge(sd_df, by = 'site.id')

print(df)