Policlorodibenzo- p-dioxinas y dibenzofuranos (PCDD/Fs)

After looking at the distribution of the mean frequencies of drug use in the sample (see Chapter 4), it is clear that the aggregate development of such behavior follows a curvilinear trajectory. Although aggregate measures of cross-sectional data do not always correspond to individual longitudinal data, this is a clue that a curvilinear term could be necessary in the LGM equation. In order to test this supposition, I compare three main modeling options with different restrictions on the random effects: (a) a LGM with only intercept, (b) a LGM with intercept and slope, and (c) a LGM with also a curvilinear slope in its equation. The first model assumes only a constant starting value and neither linear nor curvilinear development; the trajectory is thus a straight horizontal line with an estimated intercept (mean value at time point 1). The second model includes a slope term in the equation, thus allowing for variability in the steepness of the estimated line; here the behavior can be represented by an increasing or decreasing line with a specific intercept. The last model, although less parsimonious, introduces a quadratic term. The estimated developmental trajectory is now allowed to assume a curvilinear form and thus has developmental changes over time. All the above mentioned models are nested within each other. They differ only in the applied restrictions on some model parameters5_{. Table}

5.5 sums up the goodness of fit of the models and lays the basis for a comparison.

5_{In model (a), for instance, the linear and the quadratic slopes are fixed at zero.}

Table 5.5: LGM models comparison

Random eff.

Est. par.

Loglikelihood

CFI

Adj. BIC

RMSEA

I

7

1318.16 (0.000)

0.313

16797.42

0.254

IS

10

366.34 (0.000)

0.812

15858.11

0.152

ISQ

16

10.64 (0.030)

0.997

15527.43

0.033

As outlined above there are two main general aspects to consider when analyzing model fit; there are in fact measures that can be used to determine the model-fit of a specific model, and those that can be used to compare nested models with each other. In the first case, looking at first at the loglikelihood statistics, it can be noticed that its value sharply decreases as more growth parameters are added. Similarly, the CFI gets closer to the value of 1 as a curvilinear model is specified. The value of the RMSEA shows similar patterns, and only in the quadratic model it shows an acceptable value smaller than 0.05. Thus, by looking at every single model, the specification of a quadratic slope seems to improve the model-fit statistics to an acceptable level. A similar trend can be observed when comparing the models against each other. The BIC shows its smaller value for the quadratic solution, suggesting again that this is the best choice among the three. Thus, as anticipated by the aggregate mean values, a curvilinear trajectory seems to better represent the average longitudinal development of drug use in our sample.

Figure 5.5: Latent growth model for drug use

The development6 _{presented in Picture 5.5 shows how drug use consumption among}

youths in Duisburg increases constantly at the first three time points and stabilizes at

6_{The development of marijuana use shown in Picture 5.5 is represented by both the}

5.3. Results

the last two. At the last measurement point the frequency of drug use seems to slowly decrease, suggesting that substance use at this age either stabilizes or starts to decrease at the end of adolescence. The interpretation of the actual frequencies reported on the y-axis is not straightforward. As anticipated before, by using the natural logarithmus of the observed frequencies strongly increases the malleability of the data at the cost of direct interpretability of the results. Although the focus of this analysis should remain on the development itself and less on the simple frequencies, the logarithmized values on the y-axis can again be transformed into frequencies by simply calculating the exponential of the logged frequencies. The intercept, which represents the mean starting point of the individual trajectories, has a value of 0.083, which corresponds approximately to 1. This means that on average at time point one the sampled youths have used at least once marijuana in the last twelve months. Similarly, at time point four, when the subjects are 16 years old and the consumption of illicit substances reach a peak, the average logged value is about 0.4, i.e., the reported use increases to 1.5 times. Furthermore, all three developmental parameters show a significant variance (0.142 for the intercept, 0.261 for the slope, and 0.009 for the quadratic term), suggesting important heterogeneity within the sample concerning the developmental trajectory. The overall picture for this first analysis shows a general reduced use of illicit drugs in the sample. This behavior remains constant across the observed time span, although a small increase can be observed especially in the first three years. This is confirmed by the results of the descriptive statistics; the number of drug users in our sample is fairly small (see Section 4.2) and among these, only few seem to report heavy use or abuse of any sort. The majority of the sample can be described as either abstainers or simply experimental/occasional marijuana users. However, the presence of significant variability for all three developmental parameters also suggests that some subjects deviate from this developmental pattern. Descriptive statistics have also revealed that “heavy users” exist in the sample. The simplified representation of the whole sample by a single curve might ignore these subjects who are of great sociological interest. Can a single trajectory represent all, or do some specific groups of users exist which share a different development? This question can be answered by means of mixture models.