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Imagine a situation: We have historical records (20 years) of three mines. Does the presence of silver increases the probability of finding gold in next year? How to test such question?


enter image description here

Here is example data:

mine_A <- c("silver","rock","gold","gold","gold","gold","gold",
            "rock","rock","rock","rock","silver","rock","rock",
            "rock","rock","rock","silver","rock","rock")
mine_B <- c("rock","rock","rock","rock","silver","rock","rock",
            "silver","gold","gold","gold","gold","gold","rock",
            "silver","rock","rock","rock","rock","rock")
mine_C <- c("rock","rock","silver","rock","rock","rock","rock",
            "rock","silver","rock","rock","rock","rock","silver",
            "gold","gold","gold","gold","gold","gold")
time <- seq(from = 1, to = 20, by = 1)

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  • 1
    $\begingroup$ You may be interested in calculating transition matrices. $\endgroup$
    – Andy W
    Apr 27, 2015 at 11:54
  • $\begingroup$ Hi @AndyW! Thank you for comment. I am familiar with transition matrices package:makkovchain - markovchainFit(). May I use the probability values from transition matrix as p-values? Is there any way how to test hypothesis: "There exist a "silver-gold" relationship." (p-value = xx)? $\endgroup$ Apr 27, 2015 at 12:10
  • 1
    $\begingroup$ @LadislavNado transition probabilities cannot be interpreted as p-values (they do not tell you anything about rejecting any H0), see stats.stackexchange.com/questions/31/… for learning more on p-values. $\endgroup$
    – Tim
    Apr 27, 2015 at 12:58
  • 1
    $\begingroup$ I see a problem with the way you have extracted your data. Consider your "silver: no" & "gold: yes" scenario, you should also be counting your consecutive runs of "gold" since that meets the logic criteria. $\endgroup$
    – user32490
    Apr 27, 2015 at 16:05
  • 1
    $\begingroup$ With the one cell corrected from 1 to 14, the model changes to: Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) -1.2528 0.8018 -1.562 0.118 as.factor(c(0, 1))1 0.3655 0.8624 0.424 0.672 $\endgroup$
    – user32490
    Apr 27, 2015 at 16:27

1 Answer 1

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My best try: ...usage of transition matrices suggested by @AndyW is probably not the solution I am looking for (based on @Tim's comment). So I've tried a different approach. I found this link which deals with how to do logistic regression where response variable y and a predictor variable x are both binary.

According to example I should create 2 × 2 table based on my data:

               gold (yes)  gold (no)
silver (yes)       2           7
silver (no)       14          34

How I extracted the values: enter image description here

And construct a model:

response <- cbind(yes = c(2, 14), no = c(7, 34))

mine.logistic <- glm(response ~ as.factor(c(0,1)),
                      family = binomial(link=logit))

summary(mine.logistic)
# Coefficients:
#                     Estimate Std. Error z value Pr(>|z|)
# (Intercept)          -1.2528     0.8018  -1.562    0.118
# as.factor(c(0, 1))1   0.3655     0.8624   0.424    0.672

Is it a good solution? Does the p-value (0.673) mean that presence of silver no not increase the probability of finding gold?

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  • $\begingroup$ How did you generate these nice charts? Tikz? $\endgroup$ Apr 29, 2015 at 15:59
  • $\begingroup$ Hi @ssdecontrol! Charts were made by hand in Inkscape. $\endgroup$ Apr 29, 2015 at 16:00
  • $\begingroup$ Yes, that's a decent interpretation. Also, if you just look at the rows of your 2x2 table, on the top row (silver: yes) you have 9 cases, 2 of which had gold, so given silver probability of gold next year is 2/9 = 0.222. On the bottom row (silver: no) you have 48 cases, 14 of which had gold next year, so given no silver probability of gold is 14/(14+34) = 0.292. Given all that, it looks like silver hurts your chance of finding gold, though from your p-values not "statistically significantly". $\endgroup$ Apr 29, 2015 at 16:39
  • $\begingroup$ Also be mindful of your coding, you start with yes = c(2, 14), no = c(7, 34), which means your putting Silver:yes first. So when you do as.factor(c(0, 1)) the 0 corresponds to silver: yes, which is your reference level and thus your intercept. The 0.67 p-value corresponds to the small positive bump you get in probability of finding gold moving from silver:yes to silver:no. $\endgroup$ Apr 29, 2015 at 16:42
  • $\begingroup$ One last comment: you are using transition matrices. Your 2, 7, 14, 34 matrix is a transition matrix. $\endgroup$ Apr 29, 2015 at 16:43

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