Title: Presentation of results
Course: UGQuants (SSPS) > Section: Logistic Regression

Presentation of results

Once you have produced a statistically robust and theoretically coherent model, there remains only the work of reporting it properly. Just as there are 'good table manners', so too there are pieces of information that ought to be included in any report of a logistic regression analysis to allow others to reach an independent evaluation of its quality.

You certainly need to report the Exp(B) coefficients and we would recommend reporting the 95% confidence intervals for them as well. You should also report how well the overall model performed, for example using the Nagelkerke R squared and/or the reduction in the -2LL for the model, as well as the Hosmer-Lemeshow goodness of fit test results. It is also a good idea to give some empirical examples and interpretations of the meaning of your findings, perhaps including a cross tabulation, so that those unfamiliar with the language of odds can follow your analysis.

Here are two examples of how this might be done.

Example 1

Kassim, H.; Peterson, J.; Bauer, M.; Connolly, S.; Dehousse, R.; Hooghe, L. and Thompson, A. (2013). The European Commission of the Twenty-First Century. Oxford University Press, Oxford.

Footnotes were given to explain the findings:

1 | One scale point increase in socio-cultural conservatism decreases the odds of being a CM supporter by 6.5% (95%CI: 2.7% to 10.1%), holding all other variables constant.
2 | Those whose reasons for joining the Commission included wishing to build Europe have increased odds of being a CM supporter of 96.2% (95%CI: 58.5% to 142.9%), holding all other variables constant.
3 | One scale point increase in economic support for markets decreases the odds of being a CM supporter by 5.2% (95%CI: 0% / 9.9%), holding all other variables constant.
4 | A one per cent increase in the proportion of protestants in a country shows a 0.36% decrease in the odds of support for CM (95%CI: 0.05% to 0.56%), holding all other variables constant.
5 | A one scale point increase in the index of multi-level governance in a country shows a 1.4% increase in the odds of support for CM (95%CI: 0% to 2.4%), holding all other variables constant.

[p142]

Table 5.1: Personal and national characteristics supporting the Community Method

 | Model 1 | Model 2
 | B (SE) | >Wald | Odds ratio (95%CI) | B (SE) | Wald | Odds ratio (95%CI)
Personal
Commitment to Europe (ref cat: no) | 0.728 (0.108) | 45.45*** | 2.072 (1.676:2.561) | 0.674 (0.109) | 37.946*** | 1.963 (1.584:2.432)
Socio-cultural philosophy index | -0.061 (0.020) | 9.32** | 0.941 (0.905:0.978) | -0.067 (0.020) | 10.876** | 0.935 (0.899:0.973)
Economic philosophy index | -0.066 (0.025) | 6.89** | 0.936 (0.891:0.983) | -0.053 (0.026) | 4.275* | 0.949 (0.902:0.997)
National
Protestantism (proportion) |  |  |  | -0.438 (0.195) | 5.035* | 0.645 (0.440:0.946)
Index of multi-level governance |  |  |  | 0.014 (0.005) | 6.853** | 1.014 (1.004:1.025)
Reduction in -2LL | 63.77*** |  |  | 77.147*** |  |
Nagelkerke R² | 0.048 |  |  | 0.058 |  |
Hosmer and Lemeshow test (sig) | 0.803 |  |  | 0.989 |  |
n (unweighted) | 1794 |  |  | 1794 |  |

*** p<0.001; ** p<0.01; * p<0.05

Notes: The multilevel modelling, carried out using MLwiN (v2.02) with Markov Chain Monte Carlo methods to allow Bayesian estimates, shows that no additional variance is found between countries once adjustment is made for the fixed variables, implying that a logistic regression would offer an equivalent analysis. The table shows the results of the hierarchical logistic regression run in SPSS (v17). Model 1 considers the personal characteristics only, while Model 2 adds the national characterstics.

Example 2

Bikker AP and Thompson AGH (2006). Predicting and comparing patient satisfaction in four different modes of health care across a nation. Social Science and Medicine, 63 (6), 1671-1683.

[p1681]

Table 4: Predictors of global satisfaction with each service

General Practice

(n=1192)
Domiciliary care

(n=158)
Outpatients

(n=519)
Inpatient

(n=252)
-2LL | 1035.161 | 100.546 | 424.484 | 198.646
Model chi square | 611.378^** | 95.122^** | 294.677^** | 150.684^**
% correct predictions | 79.8 | 88.0 | 80.9 | 83.3
Random estimate | 53.5 | 69.0 | 51.3 | 50.4
Nagelkerke R^2 | 0.536 | 0.637 | 0.578 | 0.600
Hosmer & Lemeshow goodness of fit (sig) | 0.367 | 0.337 | 0.070 | 0.188
Odds Ratios (95%CI)
Age | 1.17^* (1.05/1.31) | 1.42^* (1.00/2.13) | 1.17 (0.99/1.38) | 1.16 (0.88/1.54)
Female | 1.33 (.096/1.85) | 1.41 (0.38/5.16) | 0.83 (0.50/1.37) | 2.84^* (1.24/6.47)
Health Status

(Good = 1)
Fairly good | 0.88 (0.62/1.25) | 1.15 (0.32/4.14) | 0.79 (0.45/1.38) | 2.21 (0.93/5.26)
Not very good | 1.02 (0.64/1.63 | 1.94 (0.49/7.60) | 0.98 (0.51/1.88) | 0.82 (0.32/2.11)
Education

(Post-school higher qualifications = 1)
Formal school qualifications | 0.82 (0.58/1.18) | 0.66 (0.17/2.60) | 0.82 (0.46/1.46) | 1.75^ (0.74/4.17)
No formal qualifications | 0.80 (0.52/1.23) | 0.40 (0.09/1.83) | 1.16 (0.58/2.29) | 2.17 (0.79/5.94)
Improvement of service | 0.59^** (0.50/0.68) | 0.33^** (0.18/0.59) | 0.53^** (0.42/0.67) | 0.44^** (0.31/0.62)
Interpersonal care and information | 6.05^** (4.82/7.60) | 11.42^** (4.61/28.27) | 7.79^** (5.25/11.58) | 7.15^** (4.14/12.33)
Physical facilities | 1.34^** (1.14/1.57) |  | 2.19^** (1.67/2.87) | 1.97^** (1.32/2.94)
Time | 2.37^** (2.00/2.82) | 0.99 (0.57/1.73) |  |
Access | 1.36^** (1.16/1.58) |  | 1.69^** (1.33/2.17) | 1.11 (0.76/1.62)
Quality of food |  |  |  | 2.05^** (1.34/3.14)
Constant | 0.59^* | 0.74 | 0.49 | 0.12^*

^*p < 0.05, ^**p< 0.001