I'm having some difficulty with running a logistic regression in R using glm. There are two ways to pass the binary response variable into glm to perform a logistic regression. You can pass the data to glm in a serial data format (e.g. one row per observation, the response variable either being a 0 or a 1, and the independent variable taking on whatever value you have for it), or you can pass it in as a table, with a minimum of three columns: the first column indicating the number of trials, the second column indicating the number of successes, and the third being the independent variable.
When I use glm using the latter data format (e.g. a data frame with three columns), I get the expected output, but when I enter the data using the former (i.e. serial data format) I don't get the expected answer.
Here's an example
prices <- c(89.99, 99.99, 149.99)
non_purchases <- c(11907, 2024, 5046)
purchases <- c(1369, 215, 31)
trials <- cbind(non_purchases, purchases)
model <- glm(trials ~ prices, family=binomial(link="logit"))
> summary(model)
Call:
glm(formula = trials ~ prices, family = binomial)
Deviance Residuals:
1 2 3
1.332 -4.440 1.553
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.923863 0.241677 -7.96 1.71e-15 ***
prices 0.044995 0.002593 17.35 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 715.832 on 2 degrees of freedom
Residual deviance: 23.897 on 1 degrees of freedom
AIC: 49.228
Number of Fisher Scoring iterations: 4
I get the expected value out in this case, however with serial data
> head(atable)
ordered sale_price
1 0 149.99
2 0 149.99
3 0 149.99
4 0 149.99
5 0 149.99
6 0 149.99
> summary(atable)
ordered sale_price
Min. :0.00000 Min. : 89.99
1st Qu.:0.00000 1st Qu.: 89.99
Median :0.00000 Median : 89.99
Mean :0.07843 Mean :105.87
3rd Qu.:0.00000 3rd Qu.: 99.99
Max. :1.00000 Max. :149.99
> conv_model <- glm(ordered ~ sale_price, family=binomial(link="logit"), data=atable)
> summary(conv_model)
Call:
glm(formula = ordered ~ sale_price, family = binomial(link = "logit"),
data = atable)
Deviance Residuals:
Min 1Q Median 3Q Max
-0.4743 -0.4743 -0.4743 -0.1209 3.1376
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.549136 0.095341 5.76 8.43e-09 ***
sale_price -0.019949 0.001002 -19.90 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 11322 on 20591 degrees of freedom
Residual deviance: 10623 on 20590 degrees of freedom
AIC: 10627
Number of Fisher Scoring iterations: 7
And just to show that it's the same data
> table(atable$ordered, atable$sale_price)
89.99 99.99 149.99
0 11907 2024 5046
1 1369 215 31
The output I get is totally different, and I'm totally confused. Can anyone help me out? I assume I'm doing something simple
I think your issue is that you are switching the definition of "success".
From ?glm (emphasis mine)
For binomial and quasibinomial families the response can also be specified as... a two-column matrix with the columns giving the numbers of successes and failures.
So the first column is "successes". In your code, you use cbind(non_purchases, purchases), which makes non_purchases the "success" column. But in your table, non-purchases are coded as 0 for failure. With the code below, we get identical results:
prices <- c(89.99, 99.99, 149.99)
non_purchases <- c(11907, 2024, 5046)
purchases <- c(1369, 215, 31)
trials <- cbind(non_purchases, purchases)
dd = data.frame(
price = c(rep(prices, non_purchases), rep(prices, purchases)),
purchase = c(rep(0, sum(non_purchases)), rep(1, sum(purchases)))
)
coef(glm(purchase ~ price, data = dd, family = "binomial"))
# (Intercept) price
# 1.92386320 -0.04499477
coef(glm(cbind(purchases, non_purchases) ~ prices, family = "binomial"))
# (Intercept) price
# 1.92386320 -0.04499477