R原始数据帧图与摘要数据帧图的不同趋势线

我很难用平均值和95%置信区间（藻类覆盖率与珊瑚繁殖率之比）来创建一个汇总数字

数据库

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数据，而不对此进行过多研究-您如何期望它是相同的？您的数据摘要方法1是独特的，它提供了x和y的错误范围。线性回归直线法2不同，它给出了残差平方和最小的直线。需要误差范围，因为两个轴都代表平均值。我的困惑是，如果你取每个站点x避难所治疗组合的平均值并绘制一条趋势线，它不应该与原始数据趋势线相同吗？据我所知，所有的方法都是用来计算斜率系数的。这似乎是对多元线性回归方法的误解，而不是对混合回归的误解。使用多个参数拟合时，您可能会看到预期结果的反转。这是因为在多维空间中拟合平均子空间。你在2维中看到了负斜率，但在更高的维中，负部分实际上是由其他变量解释的。因此，考虑到所有其他变量，“藻类”的剩余效应实际上是积极的。我们只能看到3个维度（如果真的很好的话，可能是4到5个维度），但这并不全是视觉上的。
data <- structure(list(`Module #` = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 
2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 
4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 6L, 6L, 6L, 6L, 6L, 7L, 7L, 
7L, 7L, 7L, 7L, 8L, 8L, 8L, 8L, 8L, 8L, 9L, 9L, 9L, 9L, 9L, 9L, 
10L, 10L, 10L, 10L, 10L, 10L, 11L, 11L, 11L, 11L, 11L, 11L, 12L, 
12L, 12L, 12L, 12L, 12L), .Label = c("111", "112", "113", "114", 
"115", "116", "211", "212", "213", "214", "215", "216"), class = "factor"), 
    TimeStep = structure(c(1L, 2L, 5L, 6L, 9L, 10L, 1L, 2L, 5L, 
    6L, 9L, 10L, 1L, 2L, 5L, 6L, 9L, 10L, 1L, 2L, 5L, 6L, 9L, 
    10L, 1L, 2L, 5L, 6L, 9L, 10L, 1L, 2L, 5L, 6L, 9L, 10L, 1L, 
    2L, 5L, 6L, 9L, 10L, 1L, 2L, 5L, 6L, 9L, 10L, 1L, 2L, 5L, 
    6L, 9L, 10L, 1L, 2L, 5L, 6L, 9L, 10L, 1L, 2L, 5L, 6L, 9L, 
    10L, 1L, 2L, 5L, 6L, 9L, 10L), .Label = c("1", "2", "3", 
    "4", "5", "6", "7", "8", "9", "10", "11", "12"), class = "factor"), 
    Site_long = structure(c(2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
    2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
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    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L), .Label = c("Hanauma Bay", "Waikiki"), class = "factor"), 
    Shelter = structure(c(2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 
    1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 
    2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 
    2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 
    1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 
    1L, 1L, 1L), .Label = c("Low", "High"), class = c("ordered", 
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    17, 17, 18, 18, 19, 19, 17, 17, 18, 18, 19, 19, 17, 17, 18, 
    18, 19, 19), Season = c("summer", "fall", "summer", "fall", 
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    "summer", "fall", "summer", "fall", "summer", "fall", "summer", 
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    "summer", "fall", "summer", "fall", "summer", "fall", "summer", 
    "fall", "summer", "fall", "summer", "fall", "summer", "fall", 
    "summer", "fall", "summer", "fall", "summer", "fall", "summer", 
    "fall", "summer", "fall", "summer", "fall", "summer", "fall", 
    "summer", "fall", "summer", "fall", "summer", "fall", "summer", 
    "fall", "summer", "fall", "summer", "fall"), `Taxonomic Code` = c("PR", 
    "PR", "PR", "PR", "PR", "PR", "PR", "PR", "PR", "PR", "PR", 
    "PR", "PR", "PR", "PR", "PR", "PR", "PR", "PR", "PR", "PR", 
    "PR", "PR", "PR", "PR", "PR", "PR", "PR", "PR", "PR", "PR", 
    "PR", "PR", "PR", "PR", "PR", "PR", "PR", "PR", "PR", "PR", 
    "PR", "PR", "PR", "PR", "PR", "PR", "PR", "PR", "PR", "PR", 
    "PR", "PR", "PR", "PR", "PR", "PR", "PR", "PR", "PR", "PR", 
    "PR", "PR", "PR", "PR", "PR", "PR", "PR", "PR", "PR", "PR", 
    "PR"), Settlement_Area_final = c(2, 2, 1.75902336, 2, 2, 
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    1.51804672, 1.75902336, 1.75902336, 1.51804672, 1.75902336, 
    2, 2, 2, 1.51804672, 1.667940557, 1.404193216, 2, 2, 2, 2, 
    2, 1.46300425, 2, 2, 2, 2, 2, 2, 1.75902336, 1.75902336, 
    1.75902336, 1.75902336, 1.614808922, 2, 1.75902336, 1.75902336, 
    2, 0.9487792, 1.37951168, 1.409872614, 1.75902336, 1.51804672, 
    1.75902336, 1.75902336, 1.743842893, 1.607218688, 1.75902336, 
    1.51804672, 1.366242048, 1.290339712, 1.206847142, 1.561677286
    ), recruits_new = c(0, 0, 1, 0, 0, 4, 0, 0, 0, 1, 2, 1, 4, 
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    2, 1, 0, 2, 2, 0, 4, 1, 1, 4, 8, 2, 3, 2, 1, 4, 8, 5, 4, 
    2, 1), coral_count_new = c(2, 2, 7, 7, 9, 13, 0, 0, 2, 3, 
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    21, 18, 18, 0, 1, 5, 9, 10, 8, 0, 0, 2, 0, 3, 3, 0, 0, 1, 
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    20, 29, 31, 4, 13, 27, 26, 15, 10), percent_recruits = c(0, 
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    0.185185185185185, 0.153846153846154, 0.133333333333333, 
    0.1), recruits_per_meter_squared = c(0, 0, 0.56849728249203, 
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    0, 0, 0, 0, 0.56849728249203, 1.13699456498406, 0.56849728249203, 
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    5.26993003219295, 3.65967363346732, 3.09995884246644, 1.65721070249674, 
    0.640337161182224), Date_new.x = structure(c(17301, 17387, 
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    18135, 17288, 17386, 17687, 17783, 18044, 18142, 17288, 17386, 
    17687, 17783, 18044, 18135, 17288, 17386, 17680, 17783, 18037, 
    18142, 17288, 17386, 17683.5, 17783, 18044, 18135), class = "Date"), 
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    17288, 17386, 17687, 17783, 18037, 18135, 17288, 17386, 17687, 
    17783, 18044, 18142, 17288, 17386, 17687, 17783, 18044, 18135, 
    17288, 17386, 17680, 17783, 18037, 18142, 17288, 17386, 17683.5, 
    17783, 18044, 18135), class = "Date"), Site = c("WAI", "WAI", 
    "WAI", "WAI", "WAI", "WAI", "WAI", "WAI", "WAI", "WAI", "WAI", 
    "WAI", "WAI", "WAI", "WAI", "WAI", "WAI", "WAI", "WAI", "WAI", 
    "WAI", "WAI", "WAI", "WAI", "WAI", "WAI", "WAI", "WAI", "WAI", 
    "WAI", "WAI", "WAI", "WAI", "WAI", "WAI", "WAI", "HAN", "HAN", 
    "HAN", "HAN", "HAN", "HAN", "HAN", "HAN", "HAN", "HAN", "HAN", 
    "HAN", "HAN", "HAN", "HAN", "HAN", "HAN", "HAN", "HAN", "HAN", 
    "HAN", "HAN", "HAN", "HAN", "HAN", "HAN", "HAN", "HAN", "HAN", 
    "HAN", "HAN", "HAN", "HAN", "HAN", "HAN", "HAN"), Treatment = c("OPE", 
    "OPE", "OPE", "OPE", "OPE", "OPE", "CLO", "CLO", "CLO", "CLO", 
    "CLO", "CLO", "OPE", "OPE", "OPE", "OPE", "OPE", "OPE", "CLO", 
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1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 
3L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 6L, 6L, 
6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 7L, 8L, 8L, 8L, 8L, 8L, 8L, 9L, 
9L, 9L, 9L, 9L, 9L, 10L, 10L, 10L, 10L, 10L, 10L, 11L, 11L, 11L, 
11L, 11L, 11L, 12L, 12L, 12L, 12L, 12L, 12L), .Label = c("111", 
"112", "113", "114", "115", "116", "211", "212", "213", "214", 
"215", "216"), class = "factor"), TimeStep = structure(c(1L, 
2L, 5L, 6L, 9L, 10L, 1L, 2L, 5L, 6L, 9L, 10L, 1L, 2L, 5L, 6L, 
9L, 10L, 1L, 2L, 5L, 6L, 9L, 10L, 1L, 2L, 5L, 6L, 9L, 10L, 1L, 
2L, 5L, 6L, 9L, 10L, 1L, 2L, 5L, 6L, 9L, 10L, 1L, 2L, 5L, 6L, 
9L, 10L, 1L, 2L, 5L, 6L, 9L, 10L, 1L, 2L, 5L, 6L, 9L, 10L, 1L, 
2L, 5L, 6L, 9L, 10L, 1L, 2L, 5L, 6L, 9L, 10L), .Label = c("1", 
"2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12"), class = "factor"), 
    Site_long = structure(c(2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
    2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
    2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L), .Label = c("Hanauma Bay", "Waikiki"), class = "factor"), 
    Shelter = structure(c(2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 
    1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 
    2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 
    2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 
    1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 
    1L, 1L, 1L), .Label = c("Low", "High"), class = c("ordered", 
    "factor")), Year = c(17, 17, 18, 18, 19, 19, 17, 17, 18, 
    18, 19, 19, 17, 17, 18, 18, 19, 19, 17, 17, 18, 18, 19, 19, 
    17, 17, 18, 18, 19, 19, 17, 17, 18, 18, 19, 19, 17, 17, 18, 
    18, 19, 19, 17, 17, 18, 18, 19, 19, 17, 17, 18, 18, 19, 19, 
    17, 17, 18, 18, 19, 19, 17, 17, 18, 18, 19, 19, 17, 17, 18, 
    18, 19, 19), Season = c("summer", "fall", "summer", "fall", 
    "summer", "fall", "summer", "fall", "summer", "fall", "summer", 
    "fall", "summer", "fall", "summer", "fall", "summer", "fall", 
    "summer", "fall", "summer", "fall", "summer", "fall", "summer", 
    "fall", "summer", "fall", "summer", "fall", "summer", "fall", 
    "summer", "fall", "summer", "fall", "summer", "fall", "summer", 
    "fall", "summer", "fall", "summer", "fall", "summer", "fall", 
    "summer", "fall", "summer", "fall", "summer", "fall", "summer", 
    "fall", "summer", "fall", "summer", "fall", "summer", "fall", 
    "summer", "fall", "summer", "fall", "summer", "fall", "summer", 
    "fall", "summer", "fall", "summer", "fall"), .rows = structure(list(
        1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 11L, 12L, 13L, 
        14L, 15L, 16L, 17L, 18L, 19L, 20L, 21L, 22L, 23L, 24L, 
        25L, 26L, 27L, 28L, 29L, 30L, 31L, 32L, 33L, 34L, 35L, 
        36L, 37L, 38L, 39L, 40L, 41L, 42L, 43L, 44L, 45L, 46L, 
        47L, 48L, 49L, 50L, 51L, 52L, 53L, 54L, 55L, 56L, 57L, 
        58L, 59L, 60L, 61L, 62L, 63L, 64L, 65L, 66L, 67L, 68L, 
        69L, 70L, 71L, 72L), ptype = integer(0), class = c("vctrs_list_of", 
    "vctrs_vctr", "list"))), row.names = c(NA, 72L), class = c("tbl_df", 
"tbl", "data.frame"), .drop = TRUE), class = c("grouped_df", 
"tbl_df", "tbl", "data.frame"))

module_recruitment <- data$`Module #`
data$Site_long <- as.factor(data$Site_long)
data$Shelter <- factor(data$Shelter, levels = c("Low", "High"), ordered = TRUE) 
# factorize variables

recruitment_lm_A <- lmer(recruits_per_meter_squared ~ combined_cover + Site_long*Shelter + (1|Year/Season), data = data, na.action = "na.fail")
summary(recruitment_lm_A)

std.dev.pop <- function(x) sqrt(sum((x - mean(x))^2)/(length(x)))
std.error.pop <- function(x) (std.dev.pop(x))/(sqrt(length(x)))
#standard error function for error bars

## Summary Database
recruit_algae_data_PR_1_10_summary <- data %>% group_by(Site_long, Shelter) %>% 
  summarise(mean_recruit = mean(recruits_per_meter_squared),
            sd_recruit = std.dev.pop(recruits_per_meter_squared),
            lower_recruit = mean(recruits_per_meter_squared) - 1.96*std.error.pop(recruits_per_meter_squared),
            upper_recruit = mean(recruits_per_meter_squared) + 1.96*std.error.pop(recruits_per_meter_squared),
            mean_algae = mean(combined_cover),
            sd_algae = std.dev.pop(combined_cover),
            lower_algae = mean(combined_cover) - 1.96*std.error.pop(combined_cover),
            upper_algae = mean(combined_cover) + 1.96*std.error.pop(combined_cover),
            sample_size = n())

## Plot Code
recruit_algae_data_PR_1_10_plot <- ggplot(data = recruit_algae_data_PR_1_10_summary, aes(x = mean_algae, y = mean_recruit, fill = interaction(Site_long, Shelter), shape = interaction(Site_long, Shelter))) + 
  geom_point(aes(size = 5)) +
  stat_smooth(method=lm, aes(fill = NULL, shape = NULL)) +
  geom_line(aes(linetype = Shelter)) +
  scale_linetype_manual(values=c("dashed", "solid")) +
  scale_shape_manual(name = 'Site x Shelter', values = c(21, 24, 21, 24), labels = c("Hanauma Bay - Low", "Waikiki - Low", "Hanauma Bay - High", "Waikiki - High")) +
  scale_fill_manual(name = "Site x Shelter", values = c(NA, NA, 1, 1), labels = c("Hanauma Bay - Low", "Waikiki - Low", "Hanauma Bay - High", "Waikiki - High")) +
  guides(size = FALSE, linetype = FALSE,  shape = guide_legend(override.aes = list(size = 4))) +
  geom_errorbar(aes(ymin = lower_recruit, ymax = upper_recruit), width = 0) + 
  geom_errorbarh(aes(xmin = lower_algae, xmax = upper_algae), height = 0) +
  labs(x = "Mean benthic algal % cover", y = expression(paste("Coral recruitment per m"^"2"))) +
  theme_bw() + 
  theme(panel.border = element_blank(), 
        panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank(), 
        axis.line = element_line(colour = "black"), 
        axis.title = element_text(size = rel(1)), 
        axis.text.y = element_text(angle = 90), 
        axis.text = element_text(size = 16), 
        legend.text = element_text(size = rel(1.5)), 
        legend.title = element_text(size = rel(1.5)), 
        legend.position = "none", 
        plot.title = element_text(size = 20, hjust = 0.5, vjust = -1.5))

rawplot <- ggplot(data = data, aes(x = combined_cover, y = recruits_per_meter_squared)) +
  geom_point(aes(size = 5)) +
  geom_smooth(method = "lm")