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 continuousA is continuousB 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.
这篇关于模型摘要中有序和无序因子与数值预测变量的解释的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持！