Response to another student discussion: Odds in logistic regression
DIRECTIONS:
Respond to another student discussion on odds in logistic regression.Respond by evaluating the learner's response. Do you agree or disagree? Why? Do you consider this a good answer to the question? Why or why not?
PLEASE CITE REFERENCES
Robert Laukaitis
U05D1 - Interpretation of Odds - R. Laukaitis 
Top of Form
U05D1 – Binary Logistic Regression
Odds in logistic regression represent the probability of an event occurring compared to the probability of an event not occurring (George & Mallery, 2013; Warner, 2013). In order to provide an example, an article provided by Szumilas (2010) summarized the following scenario:
186 of the 263 adolescents previously judged as having experienced a suicidal behaviour requiring immediate psychiatric consultation did not exhibit suicidal behaviour (non-suicidal, NS) at six months follow-up. Of this group, 86 young people had been assessed as having depression at baseline. Of the 77 young people with persistent suicidal behaviour at follow-up (suicidal behaviour, SB), 45 had been assessed as having depression at baseline. (para. 6)
The hypotheses for this example might state:
H0: There is no relationship between depression and suicidal behavior in young people.
Ha: There is a relationship between depression and suicidal behavior in young people.
Calculations
The scenario data was recreated in SPSS (IBM, 2016) and analyzed. Warner (2013) suggested that starting with an odds ratio table would help present data that could help make a decision about H0. Table 1 represents the 2×2 odds ratio table to begin the analysis.
| Table 1 | |||
| Odds example | |||
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| Suicidal Behavior (SB) (Y=0) | Non-suicidal Behavior (NS) (Y=1) | Total (N) |
| Depression (X=0) | 45 (34.4%) | 32 (24.2%) | 77 |
| No Depression (X=1) | 86 (65.6%) | 100 (75.8%) | 186 |
| Total (N) | 131 | 132 | 263 |
| Odds for suicidal behavior with depression, suicidal behavior without depression, non-suicidal behavior with depression and non-suicidal behavior without depression. | |||
The odds in Table 1 were calculated by calculating the odds that an individual with depression (n=131) had suicidal behavior: 45/131= 34.4%. Next, those with no depression is assumed by calculating the remaining balance of those having suicidal behavior: 1 (100%)-.344 (34.4%) = .656 (65.6%). The same approach was used to calculate those with non-suicidal behavior: 32/132=.242 (24.2%) with the residual representing those with non-suicidal behavior and no diagnosis of depression: 1 (100%)-.242 (24.2%)=.758 (75.8%). Table 2 represents the χ2 test for independence between the frequency of participants having depression and those having suicidal behaviors. In Table 2, the Pearson χ2 results indicated that there was not a significant relationship between those participants diagnosed with depression and exhibiting suicidal behaviors ( χ 2 (1) = 3.245, p > 0.05). Therefore, H0 is accepted.
| Table 2 | |||||
| Chi-Square Tests | |||||
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| Value | df | Asymp. Sig. (2-sided) | Exact Sig. (2-sided) | Exact Sig. (1-sided) |
| Pearson Chi-Square | 3.245a | 1 | .072 |
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| Continuity Correctionb | 2.775 | 1 | .096 |
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| Likelihood Ratio | 3.256 | 1 | .071 |
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| Fisher's Exact Test |
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| .079 | .048 |
| Linear-by-Linear Association | 3.232 | 1 | .072 |
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| N of Valid Cases | 263 |
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| a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 38.35. | |||||
| b. Computed only for a 2×2 table | |||||
In order to understand the effect size, phi (φ) was calculated to determine the goodness of fit (Warner, 2013). The effect size was calculated as Cramer's V. According to Warner (2013), the effect size is equal to:
In this case, the df = 1 with φ = .111 represents a relatively small effect size.
| Table 3 | |||||
| Symmetric Measures | |||||
|
| Value | Approx. Sig. | |||
| Nominal by Nominal | Phi | .111 | .072 | ||
| Cramer's V | .111 | .072 | |||
| N of Valid Cases | 263 |
| |||
Odds versus Odds Ratio
Warner (2013) suggested that the concept of odds represented the probability of an event occurring and the probability of an event not occurring. Using the example in Table 1, the odds of an individual being diagnosed with depression and displaying suicidal behavior: 34.4%/65.6% ≈ 1:2. The odds of an individual being diagnosed with depression and not displaying suicidal behavior: 24.2/75.8 ≈ 1:3. This indicated that an individual being diagnosed with depression was 1.5 times more likely to display suicidal behavior than an individual not diagnosed with depression. However, Warner (2013) odds ratio for depression is calculated using the depression row (X=0) and the non-depression row (X=1). These two numbers computed as a ratio represent the odds ratio:
| (X=0;Y=0)/(X=0;Y=1) |
| (X=1;Y=0)/(X=1;Y=1) |
This would be calculated as 45/32 86/100 = 1.41 .86 = 1.64 his would indicate that a one unit increase in those diagnosed with depression displaying suicidal behavior is equal to 1.64 unit increase in those not diagnosed with depression exhibiting suicidal behavior.
References
IBM. (2016). Statistical Package for the Social Sciences (SPSS) software. Retrieved Feb 28, 2016, from www.IBM.com: http://www-01.ibm.com/software/analytics/spss/
Szumilas, M. (2010). Explaining odds ratios. Journal of the Canadian Academy of Child and Adolescent Psychiatry, 19(3), 227-229. Retrieved from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2938757/
Warner, R. M. (2013). Applied statistics: From bivariate through multivariate techniques (2nd ed.). Thousand Oaks, CA: Sage. Retrieved from http://online.vitalsource.com/books/9781452268705
