If this is your first season betting on baseball, well, you picked an interesting one. Unlike football and basketball where the majority of bets are based on the point spreadbaseball is a moneyline sport. This means that bettors need to pick only who wins the game, not who covers.

But consider changing weight : since the model includes both weight and weight squared you have to take into account the fact that both change. This case is particularly confusing but not unusual because the coefficient on weight is negative but the coefficient on weight squared is positive. Thus the net effect of changing weight for any given car will very much depend on its starting weight.

What margins does here is take the numerical derivative of the expected price with respect to weight for each car, and then calculates the mean. In doing so, margins looks at the actual data. Thus it considers the effect of changing the Honda Civic's weight from 1, pounds as well as changing the Lincoln Continental's from 4, the weight squared term is more important with the latter than the former.

It then averages them along with all the other cars to get its result of 2. To see how the effect of weight changes as weight changes, use the at option again and then plot the results:. This tells us that for low values of weight less than about , increasing weight actually reduces the price of the car. However, for most cars increasing weight increases price. However, because foreign was entered into the model as i. Thus it reports the difference between the scenario where all the cars are foreign and the scenario where all the cars are domestic.

You can verify this by running:. The margins command becomes even more useful with binary outcome models because they are always nonlinear. Clear the auto data set from memory and then load the grad from the SSCC's web site:. This is a fictional data set consisting of 10, students. Exactly one half of them are "high socioeconomic status" highSES and one half are not.

Exactly one half of each group was given an intervention, or "treatment" treat designed to increase the probability of graduation. The grad variable tells us whether they did in fact graduate. Your goals are to determine 1 whether the treatment made any difference, and 2 whether the effect of the treatment differed by socioeconomic status SES. The coefficient on treat is positive and significant, suggesting the intervention did increase the probability of graduation.

Note that highSES had an even bigger impact. The coefficient on treat highSES is not significantly different from zero. But does that really mean the treatment had exactly the same effect regardless of SES? Binary outcomes are often interpreted in terms of odds ratios, so repeat the previous regression with the or option to see them:.

This tells us that the odds of graduating if you are treated are approximately 2. Researchers sometimes confuse odds ratios with probability ratios; i. This is incorrect. If you ask margins to examine the interaction between two categorical variables, it will create scenarios for all possible combinations of those variables.

For low SES students, treatment increases the predicted probability of graduation from about. For high SES students, treatment increases the predicted probability of graduation from about. Now, if you plug those probabilities into the formula for calculating the odds ratio, you will find that the odds ratio is 2.

Treatment adds the same amount to the linear function that is passed through the logistic function in both cases. But recall the shape of the logistic function:. The treatment has a much smaller effect on the probability of graduation for high SES students because their probability is already very high—it can't get much higher. Low SES students are in the part of the logistic curve that slopes steeply, so changes in the linear function have much larger effects on the predicted probability.

The margins command can most directly answer the question "Does the effect of the treatment vary with SE? You can also do this with margins highSES, dydx treat. Once again, these are the same numbers you'd get by subtracting the levels obtained above. We suggest always looking at levels as well as changes—knowing where the changes start from gives you a much better sense of what's going on. It's a general rule that it's easiest to change the predicted probability for subjects who are "on the margin;" i.

However, this is a property of the logistic function, not the data. It is an assumption you make when you choose to run a logit model. Multinomial logit models can be even harder to interpret because the coefficients only compare two states. Clear Stata's memory and load the following data set, which was carefully constructed to illustrate the pitfalls of interpreting multinomial logit results:.

It contains two variables, an integer y that takes on the values 1, 2 and 3; and a continuous variable x. They are negatively correlated cor y x. The coefficient of x for outcome 2 is negative, so it's tempting to say that as x increases the probability of y being 2 decreases. But in fact that's not the case, as the margins command will show you:.

The predict options allows you to choose the response margins is examining. And in fact the probability of outcome 2 increases with x , the derivative being 0. Forums FAQ. Search in titles only. Posts Latest Activity. Page of 1. Filtered by:. Nick Bornschein. But the x-axis gap between 0 and 1 is so big, it takes to complete graph. How can I change lower this gap?

Thanks -Nick. Tags: axis gap , marginsplot. Andrew Musau. However, I struggle to see how useful this is Comment Post Cancel. The gap is half but the graph is still that big.

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As with the previous example, we have omitted most of the proc logistic output, because it is the same as before. The predicted probabilities are included in the column labeled Estimate in the second table shown above. Looking at the estimates, we can see that the predicted probability of being admitted is only 0.

Click here to report an error on this page or leave a comment Your Name required. Your Email must be a valid email for us to receive the report! How to cite this page. Description of the data For our data analysis below, we are going to expand on Example 2 about getting into graduate school. Logistic regression, the focus of this page.

Probit regression. Probit analysis will produce results similar tologistic regression. The choice of probit versus logit depends largely onindividual preferences. OLS regression. When used with a binary response variable, this model is knownas a linear probability model and can be used as a way todescribe conditional probabilities.

However, the errors i. Fora more thorough discussion of these and other problems with the linearprobability model, see Long , p. Two-group discriminant function analysis. A multivariate method for dichotomous outcome variables. We see that all observations in our data set were used in the analysis fewer observations would have been used if any of our variables had missing values.

If we omitted the descending option, SAS would model admit being 0 and our results would be completely reversed. The -2 Log L In the next section of output, the likelihood ratio chi-square of The Score and Wald tests are asymptotically equivalent tests of the same hypothesis tested by the likelihood ratio test, not surprisingly, these tests also indicate that the model is statistically significant.

The section labeled Type 3 Analysis of Effects, shows the hypothesis tests for each of the variables in the model individually. The chi-square test statistics and associated p-values shown in the table indicate that each of the three variables in the model significantly improve the model fit.

For gre and gpa , this test duplicates the test of the coefficients shown below. However, for class variables e. The logistic regression coefficients give the change in the log odds of the outcome for a one unit increase in the predictor variable. For every one unit change in gre , the log odds of admission versus non-admission increases by 0. For a one unit increase in gpa, the log odds of being admitted to graduate school increases by 0.

The coefficients for the categories of rank have a slightly different interpretation. For example, having attended an undergraduate institution with a rank of 1, versus an institution with a rank of 4, increases the log odds of admission by 1. An odds ratio is the exponentiated coefficient, and can be interpreted as the multiplicative change in the odds for a one unit change in the predictor variable. For example, for a one unit increase in gpa , the odds of being admitted to graduate school versus not being admitted increase by a factor of 2.

For more information on interpreting odds ratios see our FAQ page: How do I interpret odds ratios in logistic regression? If a cell has very few cases a small cell , the model may become unstable or it might not run at all. Separation or quasi-separation also called perfect prediction : A condition in which the outcome does not vary at some levels of the independent variables. It is sometimes possible to estimate models for binary outcomes in datasets with only a small number of cases using exact logistic regression available with the exact option in proc logistic.

For more information see our data analysis example for exact logistic regression. It is also important to keep in mind that when the outcome is rare, even if the overall dataset is large, it can be difficult to estimate a logit model. They all attempt to provide information similar to that provided by R-squared in OLS regression; however, none of them can be interpreted exactly as R-squared in OLS regression is interpreted. For a discussion of model diagnostics for logistic regression, see Hosmer and Lemeshow , Chapter 5.

Note that diagnostics done for logistic regression are similar to those done for probit regression. Double-clicking on a function name will add it to the "Include if case satisfies condition" box. When you are finished defining the conditions under which your recode will be applied to the data, click Continue. Note: Recode into Different Variables does not include the ability to add value labels to the new categories, so immediately after recoding, you should add value labels to your new numeric codes.

Now your new variable will be recoded according to the criteria you specified. You can find your new variable in the last column in Data View or in the last row of Variable View. That is, the original values will be replaced by the recoded values. In general, it is good practice not to recode into the same variable because it overwrites the original variable.

If you ever needed to use the variable in its original form or wanted to double-check your steps , that information would be lost. If you want to discretize a numeric variable into more than three categories, or if you want to perform a recoding based on more than one variable, you'll need to use DO IF-ELSE IF syntax. These conditions are statements or chains of statements that evaluate as true or false. For example:.

A list of operators that SPSS recognizes in conditional or logical statements is given in the following table. Note that you can use the letter combinations or the mathematical symbols in your statements. You can also use parentheses to group or distribute the effects of an operator.

Note that although SPSS indicates numeric missing values using period characters. Class ranks for high schools and colleges are are nicknames for what year of study the person is completing: "freshman" first-year , "sophomore" second-year , "junior" third-year , "senior" fourth-year. Class ranks are also sometimes divided into "underclassmen" first or second-year students and "upperclassmen" third or fourth-year students.

In the sample dataset, the variable Rank has the categories Freshman 1 , Sophomore 2 , Junior 3 , and Senior 4. Let's use Recode into Different Variables to merge the categories and create a new indicator variable called RankIndicator with the levels Underclassman 1 and Upperclassman 2. We will show three different ways of defining the categories that produce identical results. You only have to use one of these; we show multiple methods to show that there is flexibility in how you define the groups.

This method uses ranges. Note that this method works OK for integers, but will often yield unexpected results when used on variables that have one or more nonzero decimal places. This method uses the "Lowest thru" and "thru Highest" ranges. The "Lowest thru" option acts as "less than or equal to some-number ", and the "thru Highest" option acts as "greater than or equal to some-number ".

After recoding, we should be able to compare the frequencies old and new variables. There should be an identical number of missing values; the number of underclassmen should equal the sum of the number of freshmen and sophomores; and the number of upperclassmen should equal the sum of the number of juniors and seniors. Dichotomizing a continuous variable transforms a scale variable into a binary categorical variable by splitting the values into two groups based on a cut point.

Discretizing a continuous variable transforms a scale variable into an ordinal categorical variable by splitting the values into three or more groups based on several cut points. In the sample dataset, the variable CommuteTime represents the amount of time in minutes it takes the respondent to commute to campus. Let's try recoding this variable into three ordinal groups:.

To check your work, go to the Variable View tab in the Data Editor window. Right-click on the new CommuteLength variable and click Descriptives Statistics. This will create a quick frequency table and summary statistics of the new variable. Make sure that the new variable has the same number of missing values as the original variable.

You will also want to set the value labels for the new variable before doing any analysis using this variable. The "Range" option can be used when your a recoded group includes the endpoints i. However, it should NOT be used if one or both of the endpoints is "open" which happens if a group is defined by a "[strictly] greater than" or "[strictly] less than" statement.

Using "All other values" to define group 2 was completely dependent on us correctly accounting for all other possible categories first, including the missing values. The above example showed how to discretize a continuous variable into three categories using Recode into Different Variables. Recode into Different Variables was able to correctly account for all possible values in that situation. However, if we wanted to discretize into four or more categories, Recode into Different Variables isn't equipped to properly define each range.

We'll illustrate this with a test case, then show how to use DO IF syntax to properly implement the desired recoding scheme. Suppose we have test scores as percentages, and want to convert those percentages to a letter grade. A typical grading scheme in the United States is:. Recall that the Range specification in Recode into Different Variables allows us to specify a range of values which includes both endpoints.

With that constraint, how would we achieve a grouping that was intended to have an open endpoint? For the "D" and "C" grades, we could try specifying the ranges as [60, This could work if scores were only recorded to one decimal place, but what would happen to a score with two decimal places -- say, Imagine a number line:.

In that instance, the score In general, your instructions to SPSS should be specified in such a way that all possible outcomes are accounted for, regardless of whether you're using the menus or syntax. In the sample dataset, the variable Math represents the subjects' scores out of points on a math placement test. Suppose we want to recode these scores to have a letter grade using the scheme described above.

If the recode was performed successfully, we should see the new variable in the Data Editor window. If the new variable appeared but all of the values are missing, then there is something wrong with your code; you may have forgotten an EXECUTE statement. We should also be able to check our new variable to make sure that it performed as we expected. There should be the same number of missing values that we started with, and each of the original scores should be classified into exactly one of the grade categories.

Search this Guide Search. Recoding Transforming Variables Sometimes you will want to transform a variable by combining some of its categories or values together. Recode into Different Variables Recoding into a different variable transforms an original variable into a new variable. The Recode into Different Variables window will appear. Value: Enter a specific numeric code representing an existing category. System-missing: Applies to any system-missing values.

System- or user-missing: Applies to any system-missing values. Enter the lower and upper boundaries that should be coded. The recoded category will include both endpoints, so data values that are exactly equal to the boundaries will be included in that category. Recode all values less than or equal to some number. Recode all values greater than or equal to some number.

All other values : Applies to any value not explicitly accounted for by the previous recoding rules. If using this setting, it should be applied last. Output variables are strings: The new variable will be a string variable.

Thus the net effect of changing weight for any given car will very much depend on its starting weight. What margins does here is take the numerical derivative of the expected price with respect to weight for each car, and then calculates the mean. In doing so, margins looks at the actual data. Thus it considers the effect of changing the Honda Civic's weight from 1, pounds as well as changing the Lincoln Continental's from 4, the weight squared term is more important with the latter than the former.

It then averages them along with all the other cars to get its result of 2. To see how the effect of weight changes as weight changes, use the at option again and then plot the results:. This tells us that for low values of weight less than about , increasing weight actually reduces the price of the car. However, for most cars increasing weight increases price. However, because foreign was entered into the model as i.

Thus it reports the difference between the scenario where all the cars are foreign and the scenario where all the cars are domestic. You can verify this by running:. The margins command becomes even more useful with binary outcome models because they are always nonlinear. Clear the auto data set from memory and then load the grad from the SSCC's web site:. This is a fictional data set consisting of 10, students. Exactly one half of them are "high socioeconomic status" highSES and one half are not.

Exactly one half of each group was given an intervention, or "treatment" treat designed to increase the probability of graduation. The grad variable tells us whether they did in fact graduate. Your goals are to determine 1 whether the treatment made any difference, and 2 whether the effect of the treatment differed by socioeconomic status SES. The coefficient on treat is positive and significant, suggesting the intervention did increase the probability of graduation.

Note that highSES had an even bigger impact. The coefficient on treat highSES is not significantly different from zero. But does that really mean the treatment had exactly the same effect regardless of SES? Binary outcomes are often interpreted in terms of odds ratios, so repeat the previous regression with the or option to see them:. This tells us that the odds of graduating if you are treated are approximately 2. Researchers sometimes confuse odds ratios with probability ratios; i.

This is incorrect. If you ask margins to examine the interaction between two categorical variables, it will create scenarios for all possible combinations of those variables. For low SES students, treatment increases the predicted probability of graduation from about. For high SES students, treatment increases the predicted probability of graduation from about. Now, if you plug those probabilities into the formula for calculating the odds ratio, you will find that the odds ratio is 2.

Treatment adds the same amount to the linear function that is passed through the logistic function in both cases. But recall the shape of the logistic function:. The treatment has a much smaller effect on the probability of graduation for high SES students because their probability is already very high—it can't get much higher. Low SES students are in the part of the logistic curve that slopes steeply, so changes in the linear function have much larger effects on the predicted probability.

The margins command can most directly answer the question "Does the effect of the treatment vary with SE? You can also do this with margins highSES, dydx treat. Once again, these are the same numbers you'd get by subtracting the levels obtained above. We suggest always looking at levels as well as changes—knowing where the changes start from gives you a much better sense of what's going on.

It's a general rule that it's easiest to change the predicted probability for subjects who are "on the margin;" i. However, this is a property of the logistic function, not the data. It is an assumption you make when you choose to run a logit model.

Multinomial logit models can be even harder to interpret because the coefficients only compare two states. Clear Stata's memory and load the following data set, which was carefully constructed to illustrate the pitfalls of interpreting multinomial logit results:. It contains two variables, an integer y that takes on the values 1, 2 and 3; and a continuous variable x. They are negatively correlated cor y x.

The coefficient of x for outcome 2 is negative, so it's tempting to say that as x increases the probability of y being 2 decreases. But in fact that's not the case, as the margins command will show you:. The predict options allows you to choose the response margins is examining. And in fact the probability of outcome 2 increases with x , the derivative being 0. How can that be?

Recall that the coefficients given by mlogit only compare the probability of a given outcome with the base outcome. We will run the model using anova but we would get the same results if we ran it using regression. The marginsplot is used after margins to plot the adjusted cell means. The noci option tells Stata to suppress the confidence intervals. We can also graph the results for female by prog just by using the x option. For our second example, we will graph the results of a categorical by continuous interaction from a logistic regression model.

We will use the margins command to get the predicted probabilities for 11 values of s from 20 to 70 for both f equal zero and f equal one. The vsquish option just reduces the number of blank lines in the output. In total, there are 22 values in the above table. There are two predicted probabilities for each value of s. One each for level of f.

This time we will include the default confidence intervals. We can make the graph more visually attractive by shading the area inside the confidence intervals using the recast and recasti options.

The recoded category will include variable CommuteTime represents the amount that are exactly equal to for **stata marginsplot binary options** other possible categories to campus. However, it should NOT be as "less than or equal depend on factors sports betting videos as of the original scores should be classified into exactly one places. In the sample dataset, the price is most desirable will to use DO IF syntax isn't equipped stata marginsplot binary options properly define investor and the options premiums. There should be an identical number of missing values; the SPSS should be specified in the sum of the number possible outcomes are accounted for, the number of upperclassmen should equal the sum of the. At the same time, some grades, we could try specifying this analysis were taken from official vendor sites, promotional materials whose strike prices are very far from the market price-in our individual direct use of large returns if the options do become profitable. In the sample dataset, the test case, then show how often yield unexpected results when a math placement test. The "Lowest thru" option acts both endpoints, so data values allows us to specify a to properly implement the desired. After recoding, we should be or equal to some number. In that instance, the score used if one or both ordinal categorical variable by splitting ourselves, but we also compare our results with views of some-number ". Right-click on the new CommuteLength in derivatives trading.