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Multiple Correspondence Analysis (MCA)
As the ‘don’t know’ category was chosen quite frequently by respondents, list-wise deletion would have resulted in a reduction of the sample size of all three surveys from a total of 6806 observations to 3541 observations. Furthermore, since we do not know whether the ‘don’t know’ response simply indicates a neutral attitude, list-wise deletion with respect to this category may result in (perhaps heavy) uncontrollable bias of the sample. We, therefore, used homogeneity analysis, a form of principal component analysis for categorical data, which provides both optimal quantifications for the item categories and scores for the observations maximizing internal consistency [1-5].The six categories (from the 5-point Likert scale and the ‘don’t know’ category) were treated as nominal. The relative location of the category quantifications provide the information to evaluate the meaning of all response categories with respect to a low dimensional space. Like ordinary principle component analysis (PCA), homogeneity analysis (also called MCA – Multiple Correspondence Analysis) yieldsobject scores (dimensions) for each respondent, which than will be employed in our Age-Period-Cohort analyses. The stability of the solution could be challenged by the number of ‘don’t know’ answers given by individual respondents – in ten items this can be a maximum of ten ‘don’t knows’. We evaluated the stability of our solution dependent on the amount of 'don´t know' answers by means of "naïve resampling” [6-8], drawing 1000 samples of the size N with replacement. We do not employ this method to estimated confidence regions [9] but rather to evaluate the precision of the category quantifications in a 2-dimensional space. Analyses were carried out by means of the modulmca for Stata [10].
The 2-dimensional solutions were stable when including respondents with up to eight (out of ten) ‘don’t know’ answers, so we used a final sample excluding only respondents showing more than eight ‘don’t know’ answers, resulting in 6338 interviews remaining for further analysis. We use the first dimension, where higher values indicate a more positive attitude towards psychotropic drugs. We standardized this score for our analyses with zero mean and unit variance. According to this analysis, ‘don’t know’ responses can be considered as indicating a critical appraisal of psychotropic drugs and not an indifferent attitude. The optimal quantification of the ‘don’t know’ category yielded a classification between the categories 1 and 2 (agreement) for the items representing unwanted effects, and between 4 and 5 (no agreement) for the items representing wanted effects (see SFigure 1). This is consistent with earlier findings [11]. For a comparison of the first and second dimension for up to eight and up to ten ‘don’t knows’ see SFigures 1-3.
Age-Period-Cohort Analysis with Partial Least Square Regression (PLS)
In PLS components are extracted that are weighted combinations of the original variables. The aim is to maximize the covariance between the outcome and those weighted components. As a result, the first component has a greater covariance with the outcome than the second and so on. The regression coefficients for the three variables age, period and cohort can directly be obtained from their weights in each component.For more detailed information on the identification problem in APC analyses and the application of PLS see Jiang et al. [12] and Tu et al.[13]. Since PLS penalizes variables according to their variance when extracting the components, covariates were scaled to have unit variance and zero mean.In all PLS analyses, we used a model with two PLS components because it showed a better model fit than a one-component model.Adding a third component didn’t increase the model fit (STable1). We thus report results for the two-components linear PLS models only
Sensitivity analyses
First, we reduced the sample, leaving only those individuals that had no ‘don’t know’ answer (N=3541). For these individuals we used the first axis of the object score and also calculated a conventional sum score. In a second sensitivity analysis we used the second dimension of the full sample (up to ten ‘don’t know’ answers) as a contrast. When adding cases with only ‘don’t know’ responses, the first dimension of the MCA separates don’t know answers from all other responses, while the second dimension separates all six response categories similar to the first dimension when using only cases with <8 don’t know answers (SFigure 3). All analyses were performed using the statistical software R (version 3.0.2, with the pls package.
Sensitivity analysis 1: excluding all ‘don’t know’ answers
For the reduced sample excluding all respondents with ‘don’t know’ answers, similar results could be observed in terms of the direction and effect sizes. The variance explained was a little bit higher with 6.72%, indicating a better model fit. Again period showed the strongest effect with 0.101 points increase between 1990 and 2001 and 0.1185 between 1990 and 2011. This change between 2001 and 2011 was also significant when 2001 served as reference category. Age also showed a significant effect with a higher supporting attitude (increase of 0.028 points per decade). In this model birth cohort revealed no significant effect on the perception of medication.
Sensitivity analysis 2: Including all respondents (up to 10 ‘don’t knows)
As some kind of contrast we also report the PLS analysis for the second axis of the scores for the full sample (up to 10 ‘don’t know’ answers). These results were overall similar to the others (see STable2).
Sensitivity analysis 3: Sum-Score
Finally, the same pattern could be observed for the sum score with all items coded in such a way that higher scores indicate higher approval for psychotropic medication. This score ranged from 10 to 50 points with a mean of 27. The model explained 6.93% of the variance in the score representing approval for psychotropic medication. Period effect showed the strongest change of 2.060 score points increase between 1990 - 2001 and 2.394 between 1990 – 2011, also with a small but significant increase between 2001 and 2011. The age effect here was an increase of 0.573 points per decade which results in a score increase of 3.44 over the life span of 60 years. For birth cohort the effect was only 0.224 per decade (1.35 points over 60 years) but also significant.
References
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[10] StataCorp (2013) Stata Statistical Software: Release 13. College Station, TX
[11] Matschinger H, Angermeyer M (2006) The evaluation of “Don’t Know” responses by generalized canonical analysis. In: Blasius J, Greenacre M(eds) Multiple CorrespondenceAnalysis and relatedmethods. CRC Press, pp 275-288
[12] Jiang T, Gilthorpe MS, Shiely F, Harrington JM, Perry IJ, Kelleher CC, Tu YK (2013) Age-period-cohortanalysis for trends in body mass index in Ireland. BMC PublHealth. 13:889
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Table S1. Explained variance in X and Y of the PCA components for all models
Up to eight ‘don’t know’ responses (1st dimension of the MCA) / No ‘don’t know’ responses (1st dimension of the MCA) / Up to ten ‘don’t know’ responses (2nd dimension of the MCA) / Sum score of all ten items1 component / X: 19.4%
Y: 5.4% / X: 23.1%
Y: 6.3% / X: 22.9%
Y: 5.0% / X: 23.0%
Y: 6.5%
2 components / X: 60.7%
Y: 5.5% / X: 63.6%
Y:6.7% / X: 64.0%
Y: 6.7% / X: 63.7%
Y: 6.9%
3 components / X: 100%
Y: 5.5% / X: 100%
Y: 6.7% / X: 100%
Y: 6.7% / X: 100%
Y: 6.9%
X: covariates (age, period, cohort)
Y: outcome variable (object score / sum score)
Increasing the number of components in the model also increased the explained variance in X but the variance explained in Y reached its maximum with only using a 2-component model.
Figure S1: Dimension projection plots of all items (up to eight ‘don’t know’ responses). In the first dimension, which is used for the APC-analysis, ‘don’t know’ responses (6) indicate negative attitudes, because they are consistently localized on the ‘negative’ side of the undecided category (3), depending on item direction.
Figure S2:Dimension projection plots of all items (up to eight ‘don’t know’ responses). In the first dimension, ‘don’t know’ responses (6) indicate negative attitudes, because they are consistently localized on the ‘negative’ side of the undecided category (3), depending on item direction. The second dimension separates ‘don’t know’ responses from all other responses
Figure S3: Dimension projection plots of all items (up to ten ‘don’t know’ responses). In the first dimension, ‘don’t know’ responses (6) indicate negative attitudes, because they are consistently localized on the ‘negative’ side of the undecided category (3), depending on item direction. The second dimension separates ‘don’t know responses’ from all other responses.
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