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How to Interpret Probability Models

Statistical analysis in the social sciences and other quantitative fields requires the interpretation of probability models in many instances. The most common methodology used by social scientists is Ordinary Least Squares (OLS). However, OLS is methodologically unfeasible when the dependent variable is a dummy. When this is the case, logit models are preferred. While different from interpreting OLS, it is not difficult to understand logit models, which express data in S-shaped curves as predicted probabilities.

Things You'll Need

Data set with regression matrix

Instructions

How to Set Up a Logit Model
- 1
  Write down the formulas you will use to set up your model as follows:
  
  Y* = b0 + b1X1 + b2X2 + ...
  
  Pr(Y = 1) = ( 1)/(1+exp?(-Y*))
- 2
  Pr(Y = 1) indicates the probability that Y =1, with Y indicating some event. Imagine that Y is the likelihood that a citizen will vote. If Pr(Y = 1) = .5, then you know that there is a .5 probability that the citizen will vote. Hence, Pr(Y = 1) is always a value between 0 and 1.
- 3
  The coefficients (b0, b1, b2, etc) will be expressed as signs either positive or negative and correspond to your independent variables (the variables which act upon your dependent variable). If one of these coefficients has a negative sign, a larger corresponding X means that there will be a lower Y*, and hence a decreased Pr(Y = 1).
How to Interpret a Logit Model
- 4
  In logit models, the dependent variable is a dummy. That is, it expresses an either/or type of event expressed as a likelihood. A logit model with likelihood of voting as the dependent variable would ascribe either a "0" or a "1" to each alternative as follows:
  
  "0" = did not vote
  
  "1" = voted
  
  The dependent variable is situated on the y-axis, which runs on a scale with 0 at its lowest point and 1 at its highest point.
  
  Simulate this example by drawing an xy graph with the y-axis described above.
- 5
  Create an x-axis which describes level of education. Place five hash marks on the scale and label them beginning with 1 at the hash closest the intersect and ending with 5 at the point furthest from the intersect, where 1 = some high school, 2 = high school, 3 = some undergraduate, 4 = undergraduate, and 5 = beyond undergraduate.
- 6
  Draw and S shaped curve so that the highest point on the curve (the top of the S) is situated above the 5 on the x-axis and across from a point just below the 1 on the y-axis and the lowest point is above the 1 on the x-axis and across from a point just above the 0 on the y-axis.
- 7
  To interpret this curve, go up an imaginary vertical line from any given point on the x-axis to the place where the imaginary line meets the S curve. Then imagine another line running horizontally from that intersect to the y-axis. This intersect reveals the probability that a citizen with "x" level of education has a "y" probability of voting (i.e., a citizen with some undergraduate experience has a .43 probability of voting)

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