我是否可以帮助我完成这个暂定（正在进行的）尝试来了解我对 ANOVA 和 REGRESSION 等价物的了解？我一直在尝试调和这两种方法的概念、命名法和语法。这个网站上有很多关于它们的共性的帖子，例如this或this，但是在开始时有一个快速的“你在这里”地图仍然很好。
我计划更新这篇文章，并希望得到帮助纠正错误。
单向方差分析：
Structure: DV is continuous; IV is ONE FACTOR with different LEVELS.
Scenario: miles-per-gal. vs cylinders
Note that Income vs Gender (M, F) is a t-test.
Syntax: fit <- aov(mpg ~ as.factor(cyl), data = mtcars); summary(fit); TukeyHSD(fit)
Regression: fit <- lm(mpg ~ as.factor(cyl), mtcars)
# with F dummy coded;
summary(fit); anova(fit)
双向方差分析：
Structure: DV is continuous; IV is > 1 FACTORS with different LEVELS.
Scenario: mpg ~ cylinders & carburators
Syntax: fit <- aov(mpg ~ as.factor(cyl) + as.factor(carb), mtcars);
summary(fit); TukeyHSD(fit)
Regression: fit <- lm(mpg ~ as.factor(cyl) + as.factor(carb), mtcars)
# with F dummy coded;
summary(fit); anova(fit)
双向因子方差分析：
Structure: All possible COMBINATIONS of LEVELS are considered.
Scenario: mpg ~ cylinders + carburetors + (4cyl/1,...8cyl/4)
Syntax: fit <- aov(mpg ~ as.factor(cyl) * as.factor(carb), mtcars);
summary(fit); TukeyHSD(fit)
Regression: fit <- lm(mpg ~ as.factor(cyl) * as.factor(carb), mtcars)
# with F dummy coded;
summary(fit); anova(fit)
安科瓦：
Structure: DV continuous ~ Factor and continuous COVARIATE.
Scenario: mpg ~ cylinders + weight
Syntax: fit <- aov(mpg ~ as.factor(cyl) + wt, mtcars); summary(fit)
Regression: fit <- lm(mpg ~ as.factor(cyl) + wt, mtcars)
# with F dummy coded;
summary(fit); anova(fit)
方差分析：
Structure: > 1 DVs continuous ~ 1 FACTOR ("One-way") or 2 FACTORS ("Two-way MANOVA").
Scenario: mpg and wt ~ cylinders
Syntax: fit <- manova(cbind(mpg,wt) ~ as.factor(cyl), mtcars); summary(fit)
Regression: N/A
曼科瓦：
Structure: > 1 DVs continuous ~ 1 FACTOR + 1 continuous (covariate) DV.
Scenario: mpg and wt ~ cyl + displacement (cubic inches)
Syntax: fit <- manova(cbind(mpg,wt) ~ as.factor(cyl) + disp, mtcars); summary(fit)
Regression: N/A
因子（或主题）方差分析：（代码here）
Structure: DV continuous ~ FACTOR with each level * with subject (repeated observations).
Extension paired t-test. Each subject measured at each level multiple times.
Scenario: Memory rate ~ Emotional value of words for Subjects @ Times
Syntax: fit <- aov(Recall_Rate ~ Emtl_Value * Time + Error(Subject/Time), data);
summary(fit); print(model.tables(fit, "means"), digits=3);
boxplot(Recall_Rate ~ Emtl_Value, data=data)
with(data, interaction.plot(Time, Emtl_Value, Recall_Rate))
with(data, interaction.plot(Subject, Emtl_Value, Recall_Rate))
NOTE: Data should be in the LONG FORMAT (same subject in multiple rows)
Regression: Mixed Effects
require(lme4); require(lmerTest)
fit <- lmer(Recall_Rate ~ Emtl_Value * Time + (1|Subject/Time), data);
anova(fit); summary(fit); coefficients(fit); confint(fit)
or
require(nlme)
fit <- lme(Recall_Rate ~ Emtl_Value * Time, random = ~1|Subject/Time, data)
summary(fit); anova(fit); coefficients(fit); confint(fit)
SPLIT-PLOT：（代码在这里）
Structure: DV continuous ~ FACTOR/-S with RANDOM EFFECTS and pseudoreplication.
Scenario: Harvest yield ~ Factors = Irrigation / Density of seeds / Fertilizer
& RANDOM EFFECTS (Blocks and plots of land):
Syntax: fit <- aov(yield ~ irrigation * density * fertilizer +
Error(block/irrigation/density), data); summary(fit)
Regression: Mixed Effects
require(lme4); require(lmerTest);
fit <- lmer(yield ~ irrigation * fertilizer +
(1|block/irrigation/density), data = splityield);
anova(fit); summary(fit); coefficients(fit); confint(fit)
or
library(nlme)
fit <- lme(yield ~ irrigation * variety, random=~1|field, irrigation)
summary(fit); anova(fit)
嵌套设计：（代码在这里）
Structure: DV continuous ~ FACTOR/-S with pseudoreplication.
Scenario: [Glycogen] ~ Factors = Treatment & RANDOM EFFECTS with Russian-doll effect:
Six rats (6 Livers)-> 3 Microscopic Slides/Liver-> 2 Readings/Slide).
Syntax: fit <- aov(Glycogen ~ Treatment + Error(Rat/Liver), data); summary(fit)
Regression: Mixed Effects
require(lme4); require(lmerTest)
fit <- lmer(Glycogen ~ Treatment + (1|Rat/Liver), rats);
anova(fit); summary(fit); coefficients(fit); confint(fit)
or
require(nlme)
fit<-lme(Glycogen ~ Treatment, random=~1|Rat/Liver, rats)
summary(fit); anova(fit); VarCorr(fit)
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