# Multinomial Logistic Discriminant Analysis

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Regression
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Multinomial Logistic Discriminant Analysis is estimated in Q when the Dependent question is a Pick One question with Variable Type of Categorical and contains three or more categories.

Multinomial Logistic Discriminant Analysis is more commonly referred to as Multonimial Logit (MNL), however, this is a different type of MNL model to the one most commonly used in the analysis of Experiments, which is why it is referred to as Multinomial Logistic Discriminant Analysis in Q.

See:

## Coefficients and related statistics

With Multinomial Logistic Discriminant Analysis, there are separate coefficients corresponding to all but the first category of the dependent question. Note that the Value Labels of the categories of the dependent question are in the first column:

3                  Constant                                        (intercept)           	 -8.153	1.330	 -6.131	   .000
3                  Satisfaction with fees (linear)                                       	  5.144	1.011	  5.086	   .000
3                  Satisfaction with interest rates (linear)                             	  3.980	 .962	  4.137	   .000
3                  Satisfaction with phone (linear)                                      	  3.150	 .952	  3.309	   .001
3                  Satisfaction with availability of ATMs (linear)                       	  2.071	 .875	  2.367	   .018
3                  Satisfaction with branch (categorical)           Very dissatisfied    	   .000	  NaN	    NaN	    NaN
3                                                                   2                    	  1.400	 .503	  2.784	   .005
3                                                                   3                    	  3.915	 .630	  6.210	   .000
3                                                                   4                    	  3.720	 .649	  5.734	   .000
3                                                                   5 + Very satisfied   	  3.189	 .710	  4.490	   .000
3                  Satisfaction with online (categorical)           Very dissatisfied + 2	   .000	  NaN	    NaN	    NaN
3                                                                   3                    	   .501	 .437	  1.147	   .252
3                                                                   4                    	   .879	 .457	  1.925	   .055
3                                                                   5 + Very satisfied   	  1.629	 .622	  2.619	   .009
4                  Constant                                        (intercept)           	  1.629	 .622	  2.619	   .009
4                  Satisfaction with fees (linear)                                       	-21.356	1.981	-10.779	   .000
4                  Satisfaction with interest rates (linear)                             	  9.755	1.141	  8.549	   .000
4                  Satisfaction with phone (linear)                                      	  8.034	1.088	  7.383	   .000
4                  Satisfaction with availability of ATMs (linear)                       	  7.197	1.079	  6.668	   .000
4                  Satisfaction with branch (categorical)           Very dissatisfied    	   .000	  NaN	    NaN	    NaN
4                                                                   2                    	  5.427	 .988	  5.495	   .000
4                                                                   3                    	  4.687	1.174	  3.992	   .000
4                                                                   4                    	  9.114	1.240	  7.348	   .000
4                                                                   5 + Very satisfied   	  9.404	1.260	  7.465	   .000
4                  Satisfaction with online (categorical)           Very dissatisfied + 2	   .000	  NaN	    NaN	    NaN
4                                                                   3                    	  8.907	1.291	  6.901	   .000
4                                                                   4                    	  1.160	 .508	  2.286	   .023
4                                                                   5 + Very satisfied   	  2.084	 .525	  3.971	   .000
5 + Very satisfied Constant                                        (intercept)           	  2.084	 .525	  3.971	   .000
5 + Very satisfied Satisfaction with fees (linear)                                       	  3.111	 .689	  4.516	   .000
5 + Very satisfied Satisfaction with interest rates (linear)                             	-30.131	2.167	-13.908	   .000
5 + Very satisfied Satisfaction with phone (linear)                                      	 13.357	1.271	 10.507	   .000
5 + Very satisfied Satisfaction with availability of ATMs (linear)                       	 11.739	1.200	  9.780	   .000
5 + Very satisfied Satisfaction with branch (categorical)           Very dissatisfied    	   .000	  NaN	    NaN	    NaN
5 + Very satisfied                                                  2                    	 10.697	1.215	  8.801	   .000
5 + Very satisfied                                                  3                    	  8.473	1.095	  7.736	   .000
5 + Very satisfied                                                  4                    	  2.182	1.187	  1.838	   .066
5 + Very satisfied                                                  5 + Very satisfied   	  8.506	1.118	  7.606	   .000
5 + Very satisfied Satisfaction with online (categorical)           Very dissatisfied + 2	   .000	  NaN	    NaN	    NaN
5 + Very satisfied                                                  3                    	 10.094	1.143	  8.831	   .000
5 + Very satisfied                                                  4                    	  9.977	1.186	  8.410	   .000
5 + Very satisfied                                                  5 + Very satisfied   	  1.419	 .598	  2.373	   .018



In additional the standard Regression Outputs, multinomial logistic discriminant analysis also produces a table of t-statistics to assist in variable selection:

T-Statistics
2 + Very dissatisfied	    3	     4	5 + Very satisfied
Constant                                        (intercept)           	                  .00	-6.13	  2.62	              3.97
Satisfaction with fees (linear)                                       	                  .00	 5.09	-10.78	              4.52
Satisfaction with interest rates (linear)                             	                  .00	 4.14	  8.55	            -13.91
Satisfaction with phone (linear)                                      	                  .00	 3.31	  7.38	             10.51
Satisfaction with availability of ATMs (linear)                       	                  .00	 2.37	  6.67	              9.78
Satisfaction with branch (categorical)           Very dissatisfied    	                  .00	  NaN	   NaN	               NaN
2                    	                  .00	 2.78	  5.50	              8.80
3                    	                  .00	 6.21	  3.99	              7.74
4                    	                  .00	 5.73	  7.35	              1.84
5 + Very satisfied   	                  .00	 4.49	  7.47	              7.61
Satisfaction with online (categorical)           Very dissatisfied + 2	                  .00	  NaN	   NaN	               NaN
3                    	                  .00	 1.15	  6.90	              8.83
4                    	                  .00	 1.93	  2.29	              8.41
5 + Very satisfied   	                  .00	 2.62	  3.97	              2.37