模型摘要中有序和无序因子与数值预测变量的解释 [英] Interpretation of ordered and non-ordered factors, vs. numerical predictors in model summary
问题描述
我已经安装了一个模型，其中:
I have fitted a model where:
Y ~ A + A^2 + B + 混合效果(C)
Y ~ A + A^2 + B + mixed.effect(C)
Y 是连续的A 是连续的B 实际上指的是 DAY，目前看起来像这样:
Y is continuous A is continuous B actually refers to a DAY and currently looks like this:
Levels: 1 < 2 < 3 < 4 < 5 < 6 < 7 < 8 < 9 < 11 < 12
我可以轻松更改数据类型，但我不确定将 B 视为数字、因子或有序因子是否更合适.AND 当被视为数字或有序因子时，我不太确定如何解释输出.
I can easily change the data type, but I'm not sure whether it is more appropriate to treat B as numeric, a factor, or as an ordered factor. AND when treated as numeric or ordered factor, I'm not quite sure how to interpret the output.
当作为有序因子处理时，summary(my.model) 输出如下:
When treated as an ordered factor, summary(my.model) outputs something like this:
Linear mixed model fit by REML ['lmerMod']
Formula: Y ~ A + I(A^2) + B + (1 | mixed.effect.C)
Fixed effects:
Estimate Std. Error t value
(Intercept) 19.04821 0.40926 46.54
A -151.01643 7.19035 -21.00
I(A^2) 457.19856 31.77830 14.39
B.L -3.00811 0.29688 -10.13
B.Q -0.12105 0.24561 -0.49
B.C 0.35457 0.24650 1.44
B^4 0.09743 0.24111 0.40
B^5 -0.08119 0.22810 -0.36
B^6 0.19640 0.22377 0.88
B^7 0.02043 0.21016 0.10
B^8 -0.48931 0.20232 -2.42
B^9 -0.43027 0.17798 -2.42
B^10 -0.13234 0.15379 -0.86
什么是 L、Q 和 C?我需要知道每增加一天 (B) 对响应 (Y) 的影响.如何从输出中获取此信息?
What are L, Q, and C? I need to know the effect of each additional day (B) on the response (Y). How do I get this information from the output?
当我将 B 视为.numeric 时，我会得到类似这样的输出:
When I treat B as.numeric, I get something like this as output:
Fixed effects:
Estimate Std. Error t value
(Intercept) 20.79679 0.39906 52.11
A -152.29941 7.17939 -21.21
I(A^2) 461.89157 31.79899 14.53
B -0.27321 0.02391 -11.42
要获得每增加一天 (B) 对响应 (Y) 的影响，我是否应该将 B 乘以 B(天数)的系数?不知道如何处理这个输出...
To get the effect of each additional day (B) on the response (Y), am I supposed to multiply the coefficient of B times B (the day number)? Not sure what to do with this output...
推荐答案
这不是一个真正的混合模型特定问题，而是一个关于 R 中模型参数化的一般问题.
This is not really a mixed-model specific question, but rather a general question about model parameterization in R.
让我们尝试一个简单的例子.
Let's try a simple example.
set.seed(101)
d <- data.frame(x=sample(1:4,size=30,replace=TRUE))
d$y <- rnorm(30,1+2*d$x,sd=0.01)
x 作为数字
这只是做一个线性回归:x 参数表示 y 每单位变化 x 的变化；截距指定 y 在 x=0 处的预期值.
x as numeric
This just does a linear regression: the x parameter denotes the change in y per unit of change in x; the intercept specifies the expected value of y at x=0.
coef(lm(y~x,d))
## (Intercept) x
## 0.9973078 2.0001922
x 作为(无序/正则)因子
coef(lm(y~factor(x),d))
## (Intercept) factor(x)2 factor(x)3 factor(x)4
## 3.001627 1.991260 3.995619 5.999098
截距指定在因子的基线水平(x=1)中y的期望值；其他参数指定当 x 取其他值时 y 的预期值之间的差异.
The intercept specifies the expected value of y in the baseline level of the factor (x=1); the other parameters specify the difference between the expected value of y when x takes on other values.
coef(lm(y~ordered(x),d))
## (Intercept) ordered(x).L ordered(x).Q ordered(x).C
## 5.998121421 4.472505514 0.006109021 -0.003125958
现在截距指定了 mean 因子水平上的 y 值(介于 2 和 3 之间)；L(线性)参数给出了线性趋势的度量(不是很确定我可以解释特定值...)，Q和 C 指定二次项和三次项(在这种情况下接近于零，因为模式是线性的)；如果有更多级别，高阶对比度将编号为 5、6、...
Now the intercept specifies the value of y at the mean factor level (halfway between 2 and 3); the L (linear) parameter gives a measure of the linear trend (not quite sure I can explain the particular value ...), Q and C specify quadratic and cubic terms (which are close to zero in this case because the pattern is linear); if there were more levels the higher-order contrasts would be numbered 5, 6, ...
coef(lm(y~factor(x),d,contrasts=list(`factor(x)`=MASS::contr.sdif)))
## (Intercept) factor(x)2-1 factor(x)3-2 factor(x)4-3
## 5.998121 1.991260 2.004359 2.003478
这种对比将参数指定为连续级别之间的差异，这些参数都是(大约)2的常数值.
This contrast specifies the parameters as the differences between successive levels, which are all a constant value of (approximately) 2.
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