Multinomial Regression in Excel with UNISTAT

The UNISTAT statistics add-in extends Excel with Multinomial Regression capabilities.

For further information visit UNISTAT User's Guide section 7.2.7. Multinomial Regression.

Here we provide a sample output from the UNISTAT Excel statistics add-in for data analysis.

Multinomial Regression

Regression Results

Valid Number of Cases: 54, 0 Omitted
Dependent Variable: Period
Base Category: 1

	Coefficient	Standard Error	Wald Statistic	Probability	Lower 95%	Upper 95%
Period = 2 Constant	3.8133	1.7428	4.7874	0.0287	0.3974	7.2292
Score	-0.0818	0.0358	5.2104	0.0225	-0.1519	-0.0116
Noise = High	0.4319	0.7490	0.3325	0.5642	-1.0362	1.8999
Period = 3 Constant	7.7488	2.0964	13.6626	0.0002	3.6400	11.8576
Score	-0.1924	0.0503	14.6346	0.0001	-0.2910	-0.0938
Noise = High	1.1811	0.9236	1.6352	0.2010	-0.6292	2.9914

-2 Log likelihood:
Initial Model	118.6501
Final Model	91.6682
Pseudo R-squared:
McFadden	0.2274
Adjusted McFadden	0.1768
Cox & Snell	0.3933
Nagelkerke	0.4424
Likelihood Ratio Statistic:
Chi-Square Statistic	26.9820
Degrees of Freedom	4
Right-Tail Probability	0.0000

Relative Risk Ratio

	Relative Risk Ratio	Standard Error	Lower 95%	Upper 95%
Period = 2 Score	0.9215	0.0330	0.8590	0.9885
Noise = High	1.5402	1.1536	0.3548	6.6855
Period = 3 Score	0.8249	0.0415	0.7475	0.9104
Noise = High	3.2579	3.0091	0.5330	19.9132

Correlation Matrix of Regression Coefficients

	Period = 2 Constant	Score	Noise = High	Period = 3 Constant	Score	Noise = High
Period = 2 Constant	1.0000	-0.9548	0.0421	0.6820	-0.5699	0.0475
Score	-0.9548	1.0000	-0.2573	-0.6379	0.5703	-0.1609
Noise = High	0.0421	-0.2573	1.0000	0.0434	-0.1441	0.5618
Period = 3 Constant	0.6820	-0.6379	0.0434	1.0000	-0.9475	0.1186
Score	-0.5699	0.5703	-0.1441	-0.9475	1.0000	-0.3417
Noise = High	0.0475	-0.1609	0.5618	0.1186	-0.3417	1.0000

Covariance Matrix of Regression Coefficients

	Period = 2 Constant	Score	Noise = High	Period = 3 Constant	Score	Noise = High
Period = 2 Constant	3.0375	-0.0596	0.0550	2.4918	-0.0500	0.0765
Score	-0.0596	0.0013	-0.0069	-0.0479	0.0010	-0.0053
Noise = High	0.0550	-0.0069	0.5610	0.0682	-0.0054	0.3886
Period = 3 Constant	2.4918	-0.0479	0.0682	4.3948	-0.0999	0.2297
Score	-0.0500	0.0010	-0.0054	-0.0999	0.0025	-0.0159
Noise = High	0.0765	-0.0053	0.3886	0.2297	-0.0159	0.8531

Classification by Group

Observed/Predicted	1	2	3
1	12	4	2
	66.67%	22.22%	11.11%
2	7	5	6
	38.89%	27.78%	33.33%
3	0	5	13
	0.00%	27.78%	72.22%

Correctly Classified	55.56%

Classification by Case

	Actual Group	Misclassified	Estimated Group	Probability
1	1	*	2	0.4327
2	1		1	0.4552
3	1		1	0.6290
4	2	*	3	0.4842
5	2	*	1	0.4283
6	2	*	1	0.5585
7	3		3	0.8105
8	3		3	0.5819
9	3	*	2	0.4383
10	1	*	3	0.6426
11	1	*	3	0.4509
12	1	*	2	0.4383
13	2	*	3	0.7703
14	2	*	3	0.5819
15	2		2	0.4417
16	3		3	0.8596
17	3		3	0.7238
18	3		3	0.4509
19	1		1	0.6290
20	1		1	0.7292
21	1		1	0.8653
22	2	*	1	0.5828
23	2	*	1	0.4817
24	2	*	1	0.8072
25	3		3	0.4842
26	3	*	2	0.4417
27	3	*	2	0.4383
28	1		1	0.5226
29	1		1	0.4715
30	1		1	0.7532
31	2	*	3	0.7332
32	2	*	3	0.4669
33	2	*	1	0.5473
34	3		3	0.8895
35	3		3	0.7781
36	3		3	0.4341
37	1	*	2	0.4600
38	1	*	2	0.4493
39	1		1	0.6395
40	2	*	3	0.5954
41	2		2	0.4336
42	2		2	0.4585
43	3		3	0.7982
44	3		3	0.6822
45	3	*	2	0.4336
46	1		1	0.6606
47	1		1	0.7364
48	1		1	0.9221
49	2		2	0.4562
50	2		2	0.4508
51	2	*	1	0.6808
52	3		3	0.5642
53	3		3	0.6256
54	3	*	2	0.4418

Probabilities

	1	2	3
1	0.2456	0.4327	0.3217
2	0.4552	0.4170	0.1279
3	0.6290	0.3251	0.0459
4	0.1413	0.3745	0.4842
5	0.4283	0.4258	0.1459
6	0.5585	0.3689	0.0726
7	0.0235	0.1661	0.8105
8	0.0953	0.3229	0.5819
9	0.2700	0.4383	0.2917
10	0.0716	0.2858	0.6426
11	0.1595	0.3896	0.4509
12	0.3744	0.4383	0.1873
13	0.0328	0.1969	0.7703
14	0.0953	0.3229	0.5819
15	0.2952	0.4417	0.2631
16	0.0140	0.1264	0.8596
17	0.0453	0.2309	0.7238
18	0.1595	0.3896	0.4509
19	0.6290	0.3251	0.0459
20	0.7292	0.2504	0.0203
21	0.8653	0.1312	0.0035
22	0.5828	0.3547	0.0625
23	0.4817	0.4066	0.1116
24	0.8072	0.1842	0.0086
25	0.1413	0.3745	0.4842
26	0.2952	0.4417	0.2631
27	0.3744	0.4383	0.1873
28	0.5226	0.3972	0.0803
29	0.4715	0.4221	0.1064
30	0.7532	0.2329	0.0139
31	0.0389	0.2280	0.7332
32	0.1399	0.3932	0.4669
33	0.5473	0.3833	0.0693
34	0.0083	0.1021	0.8895
35	0.0281	0.1939	0.7781
36	0.1576	0.4083	0.4341
37	0.3147	0.4600	0.2253
38	0.3928	0.4493	0.1579
39	0.6395	0.3230	0.0375
40	0.0826	0.3220	0.5954
41	0.1971	0.4336	0.3694
42	0.3404	0.4585	0.2011
43	0.0237	0.1781	0.7982
44	0.0531	0.2647	0.6822
45	0.1971	0.4336	0.3694
46	0.6606	0.3074	0.0320
47	0.7364	0.2471	0.0165
48	0.9221	0.0771	0.0008
49	0.2650	0.4562	0.2788
50	0.2413	0.4508	0.3078
51	0.6808	0.2920	0.0272
52	0.0949	0.3409	0.5642
53	0.0716	0.3029	0.6256
54	0.4192	0.4418	0.1390

Index Values

	1	2	3
1	0.0000	0.5663	0.2698
2	0.0000	-0.0877	-1.2698
3	0.0000	-0.6600	-2.6169
4	0.0000	0.9751	1.2320
5	0.0000	-0.0059	-1.0773
6	0.0000	-0.4147	-2.0396
7	0.0000	1.9561	3.5414
8	0.0000	1.2204	1.8094
9	0.0000	0.4846	0.0774
10	0.0000	1.3839	2.1943
11	0.0000	0.8934	1.0396
12	0.0000	0.1576	-0.6924
13	0.0000	1.7926	3.1565
14	0.0000	1.2204	1.8094
15	0.0000	0.4028	-0.1151
16	0.0000	2.2014	4.1187
17	0.0000	1.6291	2.7716
18	0.0000	0.8934	1.0396
19	0.0000	-0.6600	-2.6169
20	0.0000	-1.0687	-3.5791
21	0.0000	-1.8863	-5.5036
22	0.0000	-0.4965	-2.2320
23	0.0000	-0.1694	-1.4622
24	0.0000	-1.4775	-4.5414
25	0.0000	0.9751	1.2320
26	0.0000	0.4028	-0.1151
27	0.0000	0.1576	-0.6924
28	0.0000	-0.2743	-1.8735
29	0.0000	-0.1108	-1.4886
30	0.0000	-1.1736	-3.9904
31	0.0000	1.7695	2.9376
32	0.0000	1.0337	1.2056
33	0.0000	-0.3561	-2.0660
34	0.0000	2.5053	4.6697
35	0.0000	1.9330	3.3225
36	0.0000	0.9520	1.0132
37	0.0000	0.3797	-0.3340
38	0.0000	0.1344	-0.9113
39	0.0000	-0.6831	-2.8358
40	0.0000	1.3607	1.9754
41	0.0000	0.7885	0.6283
42	0.0000	0.2980	-0.5264
43	0.0000	2.0148	3.5150
44	0.0000	1.6060	2.5527
45	0.0000	0.7885	0.6283
46	0.0000	-0.7648	-3.0282
47	0.0000	-1.0918	-3.7980
48	0.0000	-2.4817	-7.0696
49	0.0000	0.5432	0.0509
50	0.0000	0.6250	0.2434
51	0.0000	-0.8466	-3.2207
52	0.0000	1.2790	1.7830
53	0.0000	1.4425	2.1678
54	0.0000	0.0527	-1.1037