Mental health and wellbeing among adolescents in Scotland: profile and trends

Appendix F: Regression

Interpreting Logistic Regression models

Table F1a shows the output for the logistic regression model for girls in 2013 in relation to borderline/abnormal versus normal score for three components of SDQ - emotion, conduct and hyperactivity components of SDQ. The first two columns indicate the different predictor factors included in the model. All variables have been treated as categorical variables.

Logistic regression models compare different categories against a reference category. In Table F1a, large urban area has been set as the reference category for the urban/rural classification, and the other categories are a series of comparisons with this category.

The columns headed 'Sig.', shows whether the factor is significant. A value of less than 0.05 in these columns suggests that this factor is significant. In Table F1a, the figure for 'other urban areas' (vs. large urban areas) for the emotion components is less than 0.05, it follows that - after controlling for the effect of all other factors in the model - the likelihood among people living in other urban areas of having an abnormal/borderline score for emotion is different from the likelihood among those in large urban areas. Significant factors are highlighted in yellow in the tables.

The column headed 'Beta' indicates the direction of the effect. A positive value indicates that those in the category are more likely to have an abnormal/borderline SDQ score and vice versa. For example, those in other urban areas were more likely than those in large urban areas to have an abnormal/borderline score for emotion.

The column headed "Exp(B)" gives the odds ratio. This indicates the size of the effect. The further above 1 that the odds ratio is, the greater the increase in likelihood of using at least one substance. The further below 1, the greater the decrease in the likelihood of using at least one substance. A value of 1 for the odds ratio means that a factor has no effect. (The odds ratio is the inverse natural log of the Beta value. For example, the 'other urban areas' compared to 'large urban areas' in the emotion component of Table F1a, the beta value is 0.25. The inverse of the natural log of 0.25 - Exp(0.25) - is 1.28. This is the odds ratio.)

In the following tables, where a factor is significant, we have colour coded the odds ratios to give an indication of the size of the effect.

Figure F1: Key to colour coding of log odds

Note that for factors that are significant, it follows that ranges of likely values for the odds ratio (the values within the associated confidences internals) will all be either above or all below 1. The 95% confidence intervals can be calculated by taking the inverse of the natural log of the Beta values plus/minus 1.96 * of the standard error. This calculation is shown below for the upper and lower confidence intervals of the odds ratios of 'other urban areas' compared to 'large urban areas' in the emotion component:

• Upper and lower CIs of odds ratio = inverse of natural log of Beta +/- 1.96 * se.
• Beta = 0.25 and se is 0.05.
• So inverse of the natural log of 0.25 +/- 1.96 * 0.05.
  = inverse of natural log of 0.10 and of 0.35
  = 1.16 and 1.42.

Table F1a: Logistic regression model of girls in 2013: borderline/abnormal versus normal score for the emotion, conduct and hyperactivity components of SDQ

Table F1b: Logistic regression model of girls in 2013: borderline/abnormal versus normal scores for the peer and pro-social components of SDQ and SDQ overall.

Table F2a: Logistic regression model of boys in 2013: borderline/abnormal versus normal score for the emotion, conduct and hyperactivity components of SDQ

Table F2b: Logistic regression model of boys in 2013: borderline/abnormal versus normal score for the peer and pro-social components of SDQ and SDQ overall.

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