Multinomial Probit and Logit Models in SAS

this video will be about how to do the multinomial logit model the conditional logit model and the mixed logit model incest I put there with the multinomial probit model but I don't have a program for this yet so let's go ahead and look at the programs here's my sass program open and I have the program here for the multinomial logit model and i have the program already executed and the results are shown on the right so when we look at the data set this is the kind of data that we have it's data on fishing mode and the dependent variable would be mode so we have each row with an observation and individual making a choice on how to fish they have four choices beach pier private and charter and we see that the first person has picked charter the second person is pictorial the third person has picked private pier and so on there are two there is a variable that we will consider and this variable is income and notice that the income variable does not depend on whether on what alternative the individuals have chosen so let's close dataset and go back to the program we're reading in the data multinomial underscore fishing and if we look at the means for the data set for the variables mode and income mode would be our dependent variable income with the our independent variable so these are the frequencies for each of the four modes of fishing and this is the percent frequency so we see that the most chosen alternative is actually charter and then in private here I think SAS organized them alphabetically in as different modes so the multinomial logit model we will do this with pro kleh gistic s-- you're reading in the data and the model mode would be the dependent variable income would be the independent variable and link would be equal to gene logit and in this case SAS would automatically pick the reference category if you don't specify one and in this case you see how it says here logit a model use mode equal private as the reference category so it just picked the last one that it came alphabetically so we have four values here for the dependent variable and these are the parameter estimates so notice here that we have three sets of coefficients estimated for income because we have four alternatives we have three sets of coefficients and one thing that you can say is that in comparison to the reference category which is private those that have higher income are less likely to choose the beach option less likely to choose the charter option and less likely to choose the pier option for fishing so that's how you interpret these and also in comparison to the private you can see one of the odds ratio for when income increases for the likelihood of them selecting one of these options so these negative coefficients here correspond to odds ratios of less than one then the next procedure here that we have is if you specify the base outcome if you look at this procedure and the procedure above we have everything else the same except for the fact we're saying that class is mode that's our dependent variable and we're giving you for reference we will Pete pick the beach category and in this case you see how it says beach category would be chosen as the reference category and when you look at the results you see that now for income the beach category is not here because that's the reference category the one would just skip them for which the coefficients are normalized to equal to zero so the way to interpret that is that in comparison to the beach alternative people that have higher income are well this is not significant but they are less likely to select the Pier option and more likely to select the private option okay so this is how to do the multinomial logit model and i don't have a program for the probit model so next let's look at the conditional logit model in SAS and i have open here the program and I have already executed it so let's look again at the data and here we have data that is in what we call the long form versus the wide form so notice here that we have ID and this is the first person the second person the third person and so on and for each of them the fish mode is one of the four options so we are listing the four options for every single individual and the mode is which which option or alternative did this individual select so the first person selected charter the second person selected charter the third person selected private the fourth person selected pier and so on okay so here what we want to do is we would like to consider the effects of price and and catch rate on the likelihood of selecting a particular alternative and so we would use two independent variable one of them is a price and one of them is catch Q so price notice that each individual faces different prices for each of the options and the second individual faces different prices for their options and so on okay and then we also have the catch rate for each of the options differs now notice that if we have a variable that does not vary with the alternatives this variable like income is repeated for each of the option for each of the individuals across all the alternatives so income is exactly the same and it's repeated four times another way in which to specify the dependent variable with the long form is to put a dummy variable equal to one if this option is selected and zero otherwise so these are the four available options and the first person pick charter therefore this is the line under which we would have the dummy equals to one and the rest would be zero for the second person we have again charter so that option would be so that would be equal to one and the rest zero the third person is selected private so we would have this line right here it equals to one and the rest for this person would be equal to zero and so on so we would use this variable D I don't think you can see it that way if it's highlighted but we would use this variable D as the dependent variable here okay so let's go ahead and close the data and I had the windows rearranged a little bit okay so here's back we're back to the program and we have D is our dependent variable P and Q are our independent variables and you can see the mean for this point 25 because we have four options and they have to pick one of this four so that's why it's 0.1 point 25 that's the average price an average catch rate so you can also summarize the frequency for this D but again we have a quarter of them or equal to once and the rest are zero which is not surprising for this for the way the variable is defined so next we can use the procedure MDC to do the conditional logic model and here we specify model DS the dependent variable P and Q are the independent variable if you type equals C logic and the number of choice being four and you also have to say which one is your ID variable because for each ID or person the software needs to know which option they have picked so in this case we don't have income as the independent variable I don't think that this procedure here can put a variable that does not vary across alternatives so if we look at the output we only have the parameter estimates of P and Q so we have that higher price of an option leads to lower likelihood of it being selected and higher catch rate leads to higher likelihood of the option being selected but then again we don't have income as the independent variable so this differs a little bit then the results that I showed you in the example okay so the final thing that I wanted to show you is how to do the mixed logit model in SAS and I'm going to open and look at the data and this is the data set that I have so again it's completely it's a similar data set but we have eliminated here the charter option I don't know why it's just that's how the example came so we don't have four options here we just have three options that's not to say that you can't do it with four just this is the example now with three options so again we have the long form of specifying the data with each ID having three rows now one for each of the alternatives and here the alternatives specified and here's what what the third person pick private the fourth person pick P R the fifth person pick private and so on and now we also have P would be the price for each of the alternatives and you see that there is a different price for different options and we also have the catch rate which we have a different one for different options we will also use two dummy variables one of them would be dummy variable for beach which is equal to one if the option that we are considering is a beach so we would have one basically on every like third or fourth of the row and same for pier if the option here that you see here then you would have a one and zero otherwise so we would have these ones periodically and yes we would we would skip we would skip the private variable for for the analysis so next thing we can also define dummy variables for y beach which is the multiplication of incoming Beach and for wipe here which is the multiplication of income and pier and we would use those in the analysis as well so going back to the program one thing that we will have here is we can calculate the means for the for the variables and again you see for D the mean is point 33 because they could pick one of the three options and we have again the mean for the dummy variable of a beach and private a pointer 33% okay so then to do the mix logic model we again use the proc MVC model would be equal to D that's our dependent variable Q is the independent variable we have the dummy variables and we have also the interaction variables here and we have P which is the price that would be an independent variable we're also saying type equals mix logic the number of choices three mixed we would use a normal parameter and for that we would use P as the price so when you use this program in your own research what you need to put here is the dependent variable what you need to put here is all the independent variables including the one that for which we will consider the random parameters and one thing you need to change here is also put the name of the variable here for which we would consider these random parameters and also of course change the number of choices depending on on the problem the problem that you have so we need when we estimate the mixed logit model these are the results that we get higher higher catch rate would lead to higher likelihood of using of using that alternate then we have that dummy variable for beach is negative and significant and this one again is for private is negative and significant this is in comparison to the reference category that we had here then look at these parameters on the price price was our variable that had random parameters so this is price for mean and this is price the standard deviation of price and so if price increases of an alternative we have less likelihood or low likelihood of this alternative being selected which makes sense the more expensive it is less likelihood of being selected but we also have that as the standard deviation increases we have this likelihood in a increases as well and the way to interpret this this parameter here is that there is a considerable heterogeneity across individuals in terms of how they react what is the effect of the price on the likelihood of the alternative being selected so this is all I had on how to do the three models the multinomial logit model the conditional logic model and the mixed logit model in SAS thank you for watching

Channel: econometricsacademy

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Keywords: Conditional Logit Model in SAS, Logistic Regression, Econometrics Sas, SAS, Multinomial Logit Model in SAS, Logit Model, Mixed Logit Model in SAS, Econometrics, SAS software, Logit, Econometrics Academy

Id: Cdzoc8s1OtQ

Length: 16min 36sec (996 seconds)

Published: Sun Feb 10 2013