FORMULA STRUCTURE AND SYNTAX IN R.  JEFF GILL.

GENERAL STRUCTURE:

	OV ~ EV1 + EV2

	- the tilde is a function that saves the formula as an unevaluated expression: formula object.
	- note that no actual "adding" is being done here in the arithmetic sense.
	- a constant is automatically implied, same as:

		OV ~ 1 + EV1 + EV2.

          but we can explicitly exclude the constant by:

		OV ~ -1 + EV1 + EV2.
		OV ~  0 + EV1 + EV2.

LINEAR IMPLEMENTATION:

	osha.df <- read.table("http://jgill.wustl.edu/data/osha2.dat",header=TRUE)

	osha.ols <- lm(INSPT ~ AP + DI,data=osha.df)

	osha.ols <- lm(INSPT ~ I(AP) + DI,data=osha.df)
	summary(osha.ols)

	kitchen.sink <- lm(as.vector(osha.df[,3]) ~ as.matrix(osha.df[,-3]))

INLINE MATH FORMULAS:

	log(OV) ~ EV1 + EV2

	OV ~ exp(EV1) + cos(EV2)

	OV ~ I(EV1/2) + sqrt(EV2 - mean(EV2))

	osha.ols <- lm(INSPT ~ AP + (DI>40) ,data=osha.df)

	osha.ols <- lm(INSPT ~ AP + cut(DI,3) ,data=osha.df)
	
INTERACTIONS:

	OV ~ EV1 + EV2 + EV1:EV2
	OV ~ EV1 * EV2

	osha.ols <- lm(INSPT ~ AP * DI, data=osha.df)

	osha.ols <- lm(INSPT ~ AP * DI * SIC1, data=osha.df)

NESTING:
	
	OV ~ EV1 + county %in% state
	OV ~ EV1 + state/county

	osha.ols <- lm(INSPT ~ D1 + D2 %in% D1, data=osha.df)
	osha.ols <- lm(INSPT ~ D1 + D1:D2, data=osha.df)
	osha.ols <- lm(INSPT ~ D1/D2, data=osha.df)
	
SPECIAL CHARACTERS (+ - : * / . ^):

	- the "." is a default:

 	  osha.ols <- lm(INSPT ~ ., data=osha.df)

	- the "^" gives all factors crossed to the order specified:

 	  osha.ols <- lm(INSPT ~ (as.factor(D2)+as.factor(IP))^2, data=osha.df)
	
UPDATE FUNCTION:

	osha.ols <- lm(INSPT ~ AP + DI + SIC1, data=osha.df)
	osha.ols <- update(osha.ols, . ~ . -AP)

	osha.ols <- lm(INSPT ~ AP + DI + SIC1, data=osha.df)
	osha.ols <- update(osha.ols, . ~ . +R0)
	osha.ols$call

PARENTHESES:

	OV ~ EV1/(EV2 : EV3)
	OV ~ EV1/EV2 : EV3

	osha.ols <- lm(INSPT ~ SIC1*(D2 + D1 %in% D2), data=osha.df)
	osha.ols <- lm(INSPT ~ SIC1*D2 + D1 %in% D2, data=osha.df)

FACTORS:

	osha.df$D2 <- factor(osha.df$D2)
        levels(osha.df$D2) <- c("Winter","Spring","Summer","Fall")

	osha.ols <- lm(INSPT ~ D2 + SIC1, data=osha.df)

	osha.df$D2<- factor(as.ordered(osha.df$D2))
	contrasts(osha.df$D2) <- contr.treatment(base=4,n=4)

	osha.ols <- lm(INSPT ~ D2 + SIC1, data=osha.df)
	osha.ols <- lm(INSPT ~ D2/D1, data=osha.df)

CONTRASTS:

	options()$contrasts
	options(contrasts=c("contr.treatment","contr.helmert"))

	- HELMERT: the difference between negative higher levels where abs(row)=#cats
	- POLYNOMIAL: linear, quadratic, cubic,... terms in hypothetical underlying
	    numeric variable that takes on equally spaced values for the
            levels of the factor.

	N <- factor(Nlevs <- c("men","women"))

	contr.sum(N)
	contr.treatment(N)
	contr.helmert(N)
	contr.poly(N)

	N <- factor(Nlevs <- c(1,4,8))

	contr.sum(N)
	contr.treatment(N)
	contr.poly(N)
	contr.helmert(N)
	contr.helmert(4)
	contr.helmert(5)

	- LOOK AT CONSEQUENCES FOR A SIMPLE LINEAR MODEL

	Y <- rnorm(100); X1 <- rgamma(100,3,2); X2 <- factor(rbinom(100,2,.6))
	contrasts(X2) <- contr.sum(3)
	summary(lm(Y~X1+X2))

	contrasts(X2) <- contr.treatment(3)
	summary(lm(Y~X1+X2))

	contrasts(X2) <- contr.poly(3)
	summary(lm(Y~X1+X2))

	contrasts(X2) <- contr.helmert(3)
	summary(lm(Y~X1+X2))

FIXING A TERM FOR MODEL COMPARISON (GLM ONLY):

	teach.df <- read.table("http://jgill.wust.edu/data/spector.mazzeo.data",
		col.names=c("GPA","TUCE","PSI","GRADE"))

	teach.logit.fit <- glm(GRADE ~ GPA + TUCE + PSI, family=binomial(link=logit), 
		data = teach.df)
	summary(teach.logit.fit)

	teach.logit.fit <- glm(GRADE ~ offset(GPA) + TUCE + PSI, family=binomial(link=logit), 
		data = teach.df)
	summary(teach.logit.fit)