[R] Partial Derivatives in R

[Paul Heinrich Dietrich]

Thank you for suggesting other functions, I will look into them.

When I read the deriv() function, it did mention partial, but I (being a
newbie) wasn't able to get partials for a simple MNL equation.  I'm sure I
did something wrong then, but here's what I tried the following and got
different answers, concluding prematurely maybe that deriv actually just
gives regular derivatives.  Thanks for looking:

### Variables for an observation

x01 <- rnorm(1,0,1)

x02 <- rnorm(1,0,1)

### Parameters for an observation

b00.1 <- rnorm(1,0,1)

b00.2 <- rnorm(1,0,1)

b00.3 <- 0

b01.1 <- rnorm(1,0,1)

b01.2 <- rnorm(1,0,1)

b01.3 <- 0

b02.1 <- rnorm(1,0,1)

b02.2 <- rnorm(1,0,1)

b02.3 <- 0

### Predicted Probabilities for an observation

phat1 <- 0.6

phat2 <- 0.3

phat3 <- 0.1



### Correct way to calculate a partial derivative
 for MNL
partial.b01.1 <- phat1 * (b01.1 - (b01.1*phat1+b01.2*phat2+b01.3*phat3))

partial.b01.2 <- phat2 * (b01.2 - (b01.1*phat1+b01.2*phat2+b01.3*phat3))

partial.b01.3 <- phat3 * (b01.3 - (b01.1*phat1+b01.2*phat2+b01.3*phat3))

partial.b01.1; partial.b01.2; partial.b01.3



partial.b02.1 <- phat1 * (b02.1 - (b01.1*phat1+b01.2*phat2+b01.3*phat3))

partial.b02.2 <- phat2 * (b02.2 - (b01.1*phat1+b01.2*phat2+b01.3*phat3))

partial.b02.3 <- phat3 * (b02.3 - (b01.1*phat1+b01.2*phat2+b01.3*phat3))

partial.b02.1; partial.b02.2; partial.b02.3



### Derivatives for MNL
 according to (my interpretation of) the deriv() function
dp1.dx <- deriv(phat1 ~ exp(b00.1+b01.1*x01+b02.1*x02) / 

	(exp(b00.1+b01.1*x01+b02.1*x02)+exp(b00.2+b01.2*x01+b02.2*x02)+

	exp(b00.3+b01.3*x01+b02.3*x02)), c("x01","x02"))

dp2.dx <- deriv(phat2 ~ exp(b00.2+b01.2*x01+b02.2*x02) / 

	(exp(b00.1+b01.1*x01+b02.1*x02)+exp(b00.2+b01.2*x01+b02.2*x02)+

	exp(b00.3+b01.3*x01+b02.3*x02)), c("x01","x02"))

dp3.dx <- deriv(phat3 ~ exp(b00.3+b01.3*x01+b02.3*x02) / 

	(exp(b00.1+b01.1*x01+b02.1*x02)+exp(b00.2+b01.2*x01+b02.2*x02)+

	exp(b00.3+b01.3*x01+b02.3*x02)), c("x01","x02"))

attr(eval(dp1.dx), "gradient")

attr(eval(dp2.dx), "gradient")

attr(eval(dp3.dx), "gradient")
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