为何GLM模型预测值未呈现曲线，而是三段直线？

我编写了一段脚本，用于构建GLM模型并将数据集归一化至0-1区间，随后绘图展示变量间关系。处理多个数据集时，绘图均为曲线（如下左图），但针对某一特定数据集，绘图却呈现三段直线（如下右图）。我猜测这与predict函数中的newdata参数有关，但无法确定。

原代码 #

# turn off scientific notation
options(scipen = 999)

# recreating the data
IV_BP <- structure(list(Breakpoints = c("Min", "BP1", "BP2", "BP3", "BP4", "Max"),
                        SES = c(-1.8, -0.3, -0.1, 0.1, 0.3, 0.8),
                        Normalised_value = c(0,0.2, 0.4, 0.6, 0.8, 1)),
                   class = "data.frame", row.names = c(NA, -6L))

IV_df <- structure(list(SES = c(-0.006, 0.078, 0.028, -0.066, 0.041, -0.025, 
                                0.006, -0.021, -0.013, -0.145, -0.065, 0.026, 0.068, -0.22, 0.138, 
                                0.019, 0.174, 0.107, 0.339, 0.219, 0.093, -0.057, -0.19, 0.01, 
                                0.085, -0.011, -0.075, -0.113, -0.019, 0.141, -0.045, -0.258, 
                                -0.02, -0.178, -0.142, -0.067, 0.1, -0.155, 0.007, -0.18, -0.258, 
                                -0.497)), class = "data.frame", row.names = c(NA, -42L))

# make glm
glmfit <- glm(Normalised_value~SES,data=IV_BP,family = quasibinomial())

# use glm to transform values
IV_df$CC_Transformed <- predict(glmfit,newdata=IV_df,type="response")

# make a graph
plot(IV_BP$SES, IV_BP$Normalised_value,
     xlab = "Socioeconomic Status Index Score",
     ylab = "Normalised Values",
     xlim = c(-2, 2),
     pch = 19,
     col = "blue",
     panel.first =
       c(abline(h = 0, col = "lightgrey"),
         abline(h = 0.2, col = "lightgrey"),
         abline(h = 0.4, col = "lightgrey"),
         abline(h = 0.6, col = "lightgrey"),
         abline(h = 0.8, col = "lightgrey"),
         abline(h = 1, col = "lightgrey"),
         lines(-2:2,predict(glmfit,newdata=data.frame(SES=-2:2),type="response"),
      col = "lightblue",
      lwd = 5)))

问题根本不是newdata参数的问题，而是绘图时生成预测点用的-2:2是整数序列，仅包含-2, -1, 0, 1, 2这5个离散点。用这么少的点连线，必然会呈现分段直线，而非平滑曲线。

要得到平滑的曲线，需要生成足够密集的连续x值。可以用seq(-2, 2, by = 0.01)生成从-2到2、步长0.01的密集序列，这样预测出的点数量足够多，连线后就是自然的平滑曲线。

# 关闭科学计数法
options(scipen = 999)

# 重建数据
IV_BP <- structure(list(Breakpoints = c("Min", "BP1", "BP2", "BP3", "BP4", "Max"),
                        SES = c(-1.8, -0.3, -0.1, 0.1, 0.3, 0.8),
                        Normalised_value = c(0,0.2, 0.4, 0.6, 0.8, 1)),
                   class = "data.frame", row.names = c(NA, -6L))

IV_df <- structure(list(SES = c(-0.006, 0.078, 0.028, -0.066, 0.041, -0.025, 
                                0.006, -0.021, -0.013, -0.145, -0.065, 0.026, 0.068, -0.22, 0.138, 
                                0.019, 0.174, 0.107, 0.339, 0.219, 0.093, -0.057, -0.19, 0.01, 
                                0.085, -0.011, -0.075, -0.113, -0.019, 0.141, -0.045, -0.258, 
                                -0.02, -0.178, -0.142, -0.067, 0.1, -0.155, 0.007, -0.18, -0.258, 
                                -0.497)), class = "data.frame", row.names = c(NA, -42L))

# 构建GLM模型
glmfit <- glm(Normalised_value~SES,data=IV_BP,family = quasibinomial())

# 用模型转换数值
IV_df$CC_Transformed <- predict(glmfit,newdata=IV_df,type="response")

# 绘图：生成密集x序列保证曲线平滑
x_seq <- seq(-2, 2, by = 0.01)
plot(IV_BP$SES, IV_BP$Normalised_value,
     xlab = "社会经济地位指数得分",
     ylab = "归一化值",
     xlim = c(-2, 2),
     pch = 19,
     col = "blue",
     panel.first =
       c(abline(h = 0, col = "lightgrey"),
         abline(h = 0.2, col = "lightgrey"),
         abline(h = 0.4, col = "lightgrey"),
         abline(h = 0.6, col = "lightgrey"),
         abline(h = 0.8, col = "lightgrey"),
         abline(h = 1, col = "lightgrey"),
         lines(x_seq,predict(glmfit,newdata=data.frame(SES=x_seq),type="response"),
               col = "lightblue",
               lwd = 5)))

内容的提问来源于stack exchange，提问作者Xandian97