Multinomial Logistic Regression with One Dichotomous and One Continuous Predictor Variable

hello this is dr. Grande welcome to my video on conducting a multinomial logistic regression in SPSS so a multinomial logistic regression is a statistic which allows us to calculate the probability of group membership so I'll demonstrate that using these fictitious data in the data view in SPSS so my first variables ID so I have 40 participants in this study and then I have an independent variable it has two levels experimental and treatment as usual and then I have some measure of motivation with one representing not much motivation or almost no motivation to change and ten representing a great deal of motivation to change so let's say that the participants that we're working with with these fictitious data would be struggling with substance use my motivations a construct we often try to measure when dealing with substance use so we're going to look at this experimental treatment we have and we're going to consider that as a predictor of group membership and the level of motivation to stop using substances as a predictor and then we have an outcome and I'll show you that looks like which is the code writes all zeros and ones and twos for for outcome and all zeroes and ones for program but you see there's three levels you have no improvement that's represented by zero as an outcome some improvement and significant improvement so this would be a case where due to some limitation we really couldn't use an instrument that measures on the scale level of measurement but we have to use in this case an ordinal level of measurement where you just have significant we have been the finding that you'd want that that would be the most desirable outcome then some improvement would be the next most desirable and then the least desirable of course would be if there was no improvement right so we want the participants to improve but we only have these three categories to go by in terms of measurement so we're using program and motivation to predict membership in one of these three categories so we first start with analyze and we'll go to regression and then we want multinomial logistic regression now if we only had two possible outcomes we would use binary logistic regression but in this case since we have more than two it's multinomial and here's the dialogue and of course the dependent here is going to be the outcome and we move that over you're going to need to set the reference category while potentially unless the last category is what you want and this case I want the first category to be the reference category and the first category as I mentioned is no improvement which is zero so zero is no improvement one is some improvement and two is significant improvement so I want some improvement and significant improvement to be compared to no improvement therefore the reference category here will be the first category if I left the default which is last category that would set the reference at significant improvement and if I wanted some improvement to be the reference category I would have to go into custom and actually type in one because that's the value assigned to some improvement but as I said in this case I'll be using the first category which is no improvement I continue on these buttons to the right and we'll be making any changes in the model for statistics I'm going to add cell probabilities goodness-of-fit and information criteria I'm going to click OK or continue in this case and then under criteria I'm going to leave this as default click continue options again default and then save I am going to make some changes here these are actually quite useful variables that you can create as part of running the multinomial logistic regression so I'm going to actually click all of them alright so estimated response probabilities predicted category predicted category probability and actual category probability and click continue and now we need to choose our factors and our covariance so in a multinomial logistic regression factors would be a categorical or ordinal right so in this case program we have two programs experimental and treatment as usual that's a nominal variable a nominal level of measurement so I'm going to move that over to factor but motivation is a scale from 1 to 10 all right so that's in this case that's a scale level measurement so I'm going to move that to covariant so as you can see the multinomial logistic regression dialog will accept both nominal and ordinal levels of measurement variables measured as nominal ordinal and variables measured with the scale level measurement but there's a different list box for that labeled covariant then I'm going to click okay this is actually going to run the multinomial logistic regression and you can see already off the bat we have this warning there's their 25 cells with zero frequencies and this is not unusual for design like this because I have 10 possible outcomes for the motivation variable because it's scale and then you have the two possible programs so every combination was not represented that's why you have this morning it shouldn't be ignored but you should understand that's quite common to have that particular warning and then we can see the different percentages and the number for each of these levels of outcome and a program and you can see I have no missing values as we move down to model fitting information we do want this to be statistically significant alpha equaling 0.2 05.02.2013 5 level on both Pearson and deviance in the pseudo R square it's the second value 'enter prett here Oh point three eight four is 38 four percent so thirty-eight point four percent of the variances explained that's fairly good and then moving down to likelihood ratio tests again in this case we are looking for significant value we do not have it for motivation is not statistically significant point zero five four is greater than point zero five but for program we do have a statistically significant result and then we'll take a look at the parameter estimates and you can see there are several values here you have beta and the Wold statistic and significance then you have this one exp B right and this is the odds ratio so there's a few things to consider here the first thing you want to keep in mind is that these two outcomes some improvement and significant improvement are both compared to the reference category I mentioned earlier which I set as the first category which was no improvement so all these values represent a comparison between the some improvement level and some improvement outcome the significant improvement outcome and no improvement it does not show you the relationship here between some improvement and significant improvement in order to see that you need to change the reference category and rerun the statistic so let's take a look so as we look through some improvement and we take a look at the values we have motivation we can see we did not have a statistically significant result here all right this there's no statistical significance here if we want to interpret the odds ratio anyway this would be 0.92 1 which is a value less than 1 and what this would mean precisely would be that as motivation increases by a unit the odds of seeing the some improvement as compared to no improvement decreased by 7.9 percent and I obtained that value simply by taking 1 and subtracting 0.92 1 if we look at motivation here again we do not have a statistically significant result here but if we wanted to interpret the odds ratio its 1.2950 as motivation increases there'd be a twenty nine point five percent increase in the probability of realizing a significant improvement versus no improvement now with program we have a different finding right so you have program zero is the experimental treatment and program one is treatment as usual you can see the program one in both cases is set to zero so as we look over here we have statistical significance so we know there's a statistically significant relationship between the program and the outcome specifically the outcome of some improvement and a statistically significant relationship between the program and significant improvement remember both as compared to the reference category of no improvement and the case of some improvement and program you can see that the odds ratio is let's see 13 right so it's 13 times more likely for the experimental treatment to result in some improvement versus no improvement similarly the probability that somebody in the experimental treatment versus the treatment as usual will have an outcome and the significant improvement versus no improvement is 14 and a half times greater for the experimental treatment so just to give you some other examples of how these values or values like this in this column could be interpreted say this value instead of fourteen point five five was one point five right that would mean that the odds of somebody in the experimental treatment being the significant improvement versus no improvement category would be fifty percent greater than a participant in the treatment as usual and if this value were negative point five the probability would be fifty percent less or another way of putting that would would be they're half as likely to be in this significant improvement category versus no improvement as compared to the treatment as usual group so when interpreting the odds ratio in this column a value greater than one is equal to a greater probability value less than 1 is equal to smaller probability and the value of one means there's the same probability so in this case whether a participant was in the experimental or treatment as usual category they would have an equal probability of being in the significant improvement versus the no improvement outcome category the table below this is the observed and predicted frequencies and exceed offers every combination of the levels of motivation and the two levels of program and the outcome and gives you the observe predicted Pearson residual and in terms of percentage observed and predicted so this is a useful table to really drill down into the output and get more information about what is happening with the data the last thing I like to do with the multinomial logistic regression is to take a look at the saved variables these are actually quite helpful you might remember from the original dialogue I chose to save all the possible variables in that dialogue and you can see that there we have here in the first column the estimated cell probability for response category zero and this is the same thing for response category one and for two then we have in this column here the predicted response category so based on the model and using the multinomial logistic regression this is the category that SPSS predicted then we have the estimated classification probability for the predicted category and then the same for the actual category so this allows you to see the actual percentages used by SPSS to make the determination of the predicted outcome category and these will always add up to one hundred one hundred percent and you can see sometimes the model predicted the correct value and as in this case sometimes mile did not right so in this instance we had significant improvement the model predicted there was a 61 percent chance that would have some improvement and only 33 percent chance that we would have significant improvement of course a six percent chance of no improvement so you can see here in the predicted probability you can see the 61 but then for the actual category was 33 so when you see a difference like this you know that the model predicted the wrong outcome if the values are the same and greater than 0.5 you know that it had it did predict the correct category now the reason I say above 0.5 is like safe situation down here now now the model did predict the right value but you could have one value at 46% and another value at 46% which would leave the third category at 8% and the predicted the actual could be different but still be 46% you can see here the values are very close 49 and 45 and in this case the model actually predicted the wrong outcome there's no improvement it predicted some improvement so again if there's a difference between these two the model always predicted the incorrect outcome but if they're the same and not greater than 0.5 make sure to double-check that it had the correct outcome so other than the significance levels and the odds ratios and all the other output data I like to look at this column here and look for kind of high percentages when you see a lot of high percentages that's an indication when paired together with correct outcomes that's an indication that the model is working pretty well when you have a lot of low values and these are mostly lower values you can see there's quite a bit of disagreement between the outcome the predicted outcome and the actual outcome here so ideally we want a model that allows us to differentiate you know we have no course different probabilities but with a little more authority than say outcomes like these where the values are relatively close together what of course we'd want to find here instead would be kind of like a value here where you have eighty-three percent probability that it was going to be some improvement and only 11 four significant you know and six four no improvement Edie of course predicted it correctly with the eighty three percent so I recommend saving these variables as part of this procedure and taking a look at some of the cases and looking for trends and how accurate the model is and what the percentages look like relative to each other are they distinct you know far apart are they fairly close together I hope you found this video in conducting a multinomial logistic regression and SPSS to be helpful as always if you have any questions or concerns feel free to contact me I'll be happy to assist you

Channel: Dr. Todd Grande

Views: 37,766

Rating: 4.8222222 out of 5

Keywords: SPSS, multinomial logistic regression, logistic regression, dependent variable, independent variable, predictor variable, dichotomous, dichotomous variable, continuous variable, outcome variable, variable, model fitting, odds ratio, probability, group membership, predictor, counseling, Grande, Variables (Quotation Subject), Dichotomy, Regression Analysis

Id: Ti-8pBj4mXk

Length: 19min 19sec (1159 seconds)

Published: Thu Aug 27 2015