ANLY505 - Intro to Stan

Week 4

Intro to STAN Homework Part #1

After our Intro to Stan lecture I think it would be valuable to have you go through a similar exercise. Let’s test a second research question.

Research question: Is sea ice extent declining in the Southern Hemisphere over time? Is the same pattern happening in the Antarctic as in the Arctic? Fit a Stan model to find out!

Make sure you follow the steps we used in class.

What do your Stan model results indicate so far?

1. Load and Inspect Data

#place the code here

seaice_load <- read.csv("seaice.csv")
head(seaice_load)

##   year extent_north extent_south
## 1 1979       12.328       11.700
## 2 1980       12.337       11.230
## 3 1981       12.127       11.435
## 4 1982       12.447       11.640
## 5 1983       12.332       11.389
## 6 1984       11.910       11.454

2. Plot the data

#plot data

plot(extent_south ~ year, pch = 14, data = seaice_load)

3. Run a general linear model using lm()

#write the code

lin_model <- lm(extent_south~year, data=seaice_load)
summary(lin_model)

## 
## Call:
## lm(formula = extent_south ~ year, data = seaice_load)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.23372 -0.18142  0.01587  0.18465  0.88814 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)  
## (Intercept) -14.199551  10.925576  -1.300   0.2018  
## year          0.012953   0.005468   2.369   0.0232 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3843 on 37 degrees of freedom
## Multiple R-squared:  0.1317, Adjusted R-squared:  0.1082 
## F-statistic: 5.611 on 1 and 37 DF,  p-value: 0.02318

4. Index the data, re-run the lm(), extract summary statistics and turn the indexed data into a dataframe to pass into Stan

#write the code here


x<- I(seaice_load$year-1978)
y<- seaice_load$extent_south

lin_model2 <- lm(y ~ x)
summary(lin_model2)

## 
## Call:
## lm(formula = y ~ x)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.23372 -0.18142  0.01587  0.18465  0.88814 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 11.421555   0.125490  91.015   <2e-16 ***
## x            0.012953   0.005468   2.369   0.0232 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3843 on 37 degrees of freedom
## Multiple R-squared:  0.1317, Adjusted R-squared:  0.1082 
## F-statistic: 5.611 on 1 and 37 DF,  p-value: 0.02318

alpha<- summary(lin_model2)$coeff[1]
beta<- summary(lin_model2)$coeff[2]
sigma <- sigma(lin_model2)
seaice_data <- list(N=nrow(seaice_load), y=y, x=x)

5. Write the Stan model

#write the code

 write("// Stan model for simple linear regression

data {
 int < lower = 1 > N; // Sample size
 vector[N] x; // Predictor
 vector[N] y; // Outcome
}

parameters {
 real alpha; // Intercept
 real beta; // Slope (regression coefficients)
 real < lower = 0 > sigma; // Error SD
}

model {
 y ~ normal(alpha + x * beta , sigma);
}

generated quantities {
} // The posterior predictive distribution",

"stan_model1.stan")


stan_model1 <- "stan_model1.stan"

6. Run the Stan model and inspect the results

#code here


#(fit <- stan(file = stan_model1, data = seaice_data, iter = 1000, chains = 4, cores = 2, thin = 1))

*******my system is not able to finish this run and it is restarting my R session.

7. Extract the posterior estimates into a list so we can plot them

#code here
#list_post <- extract(fit)

8. Compare your results to our results to “lm”

#code here

9. Plot multiple estimates from the posterior

#code here