Exercise 1 Descriptive statistics INPUT Variable: Names are - PDF document

1 Exercise 1 Descriptive statistics INPUT Variable: Names are mahcig01 MeHGsx1 DePicSTS ZDePicSAS DeNamVTS ZDeNamVAS mdhgsx1 sw4emo sw4con sw4hyp sw4peer sw4pros sw5emo sw5con sw5hyp sw5peer sw5pros male pregsmok missingd; USEVAR are sw4emo sw4con sw4hyp sw4peer sw4pros sw5emo sw5con sw5hyp sw5peer sw5pros male pregsmok ZDePicSAS ZDeNamVAS ; CATEGORICAL are sw4emo sw4con sw4hyp sw4peer sw4pros sw5emo sw5con sw5hyp sw5peer sw5pros male pregsmok ; Missing are all (-999) ; Analysis: Type = basic ; Exercise 1: OUTPUT (abridged) SUMMARY OF ANALYSIS Number of groups 1 Number of observations 2624 Observed dependent variables Continuous ZDEPICSAS ZDENAMVAS Binary and ordered categorical (ordinal) SW4EMO SW4CON SW4HYP SW4PEER SW4PROS SW5EMO

2 SW5CON SW5HYP SW5PEER SW5PROS MALE PREGSMOK SUMMARY OF MISSING DATA PATTERNS MISSING DATA PATTERNS (x = not missing) 1 SW4EMO x SW4CON x SW4HYP x SW4PEER x SW4PROS x SW5EMO x SW5CON x SW5HYP x SW5PEER x SW5PROS x MALE x PREGSMOK x ZDEPICSA x ZDENAMVA x SUMMARY OF CATEGORICAL DATA PROPORTIONS SW4EMO Category 1 0.938 Category 2 0.039 Category 3 0.023 SW4CON Category 1 0.711 Category 2 0.162 Category 3 0.127 SW4HYP Category 1 0.832 Category 2 0.072 Category 3 0.095 SW4PEER Category 1 0.854 Category 2 0.082 Category 3 0.064 SW4PROS Category 1 0.903 Category 2 0.068 Category 3 0.029 SW5EMO

3 Category 1 0.929 Category 2 0.039 Category 3 0.032 SW5CON Category 1 0.767 Category 2 0.133 Category 3 0.101 SW5HYP Category 1 0.816 Category 2 0.075 Category 3 0.109 SW5PEER Category 1 0.874 Category 2 0.063 Category 3 0.063 SW5PROS Category 1 0.929 Category 2 0.054 Category 3 0.016 MALE Category 1 0.500 Category 2 0.500 PREGSMOK Category 1 0.792 Category 2 0.208 MEANS/INTERCEPTS/THRESHOLDS MALE$1 PREGSMOK ZDEPICSA ZDENAMVA ________ ________ ________ ________ 1 0.000 0.814 0.024 0.022 1. How many observations are in the dataset? 2624 2. What is the proportion of males and females? 50% / 50% 3. What is the proportion of children whose mother reported smoking during pregnancy? 21% 4. What are the means of the Picture Similarity and the Naming vocabulary z scores? 0.024 ; 0.022 5. Are there missing data in any of these variables ? NO

4 EXERCISE 2 INPUT 2-class model (abridged) Variable: Names are mahcig01 MeHGsx1 DePicSTS ZDePicSAS DeNamVTS ZDeNamVAS mdhgsx1 sw4emo sw4con sw4hyp sw4peer sw4pros sw5emo sw5con sw5hyp sw5peer sw5pros male pregsmok missingd; USEVAR are sw4emo sw4con sw4hyp sw4peer sw4pros; CATEGORICAL are sw4emo sw4con sw4hyp sw4peer sw4pros; Missing are all (-999) ; classes are x(2); !estimates a latent categorical variable with two classes, !the indicators are sw4emo-sw4pros, specified in categorical option of variable Analysis: Type = MIXTURE ; ! invokes a mixture model algorithm OUTPUT: TECH1 TECH10 TECH11 TECH14; PLOT:Type is PLOT3; series is sw4emo (1) sw4con (2) sw4hyp (3) sw4peer (4) sw4pros (5); DEFINE: CUT sw4emo-sw4pros (0); !creates binary variables using 0 as cut-point OUTPUT (abridged) RANDOM STARTS RESULTS RANKED FROM THE BEST TO THE WORST LOGLIKELIHOOD VALUES Final stage loglikelihood values at local maxima, seeds, and initial stage start numbers: -5066.709 195873 6 -5066.709 253358 2 -------------------------------------------------------------------------------------------------------

5 The best loglikelihood is replicated and no error messages or warnings. Appears to be a trustworthy-enough solution. ------------------------------------------------------------------------------------------------------- FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES BASED ON THE ESTIMATED MODEL Latent Classes 1 566.72122 0.21598 2 2057.27878 0.78402 ------------------------------------------------------------------------------------------------------- 22% of individuals are in latent class 1 and 78% are in latent class 2, based on estimated model RESULTS IN PROBABILITY SCALE Latent Class 1 SW4EMO Category 1 0.812 0.023 35.084 0.000 Category 2 0.188 0.023 8.123 0.000 SW4CON Category 1 0.190 0.060 3.136 0.002 Category 2 0.810 0.060 13.400 0.000 SW4HYP Category 1 0.489 0.047 10.367 0.000 Category 2 0.511 0.047 10.843 0.000 SW4PEER Category 1 0.660 0.031 21.150 0.000 Category 2 0.340 0.031 10.914 0.000 SW4PROS Category 1 0.758 0.026 29.003 0.000 Category 2 0.242 0.026 9.249 0.000 Latent Class 2 SW4EMO

6 Category 1 0.973 0.006 159.352 0.000 Category 2 0.027 0.006 4.497 0.000 SW4CON Category 1 0.855 0.017 49.465 0.000 Category 2 0.145 0.017 8.403 0.000 SW4HYP Category 1 0.927 0.011 88.091 0.000 Category 2 0.073 0.011 6.941 0.000 SW4PEER Category 1 0.908 0.010 90.681 0.000 Category 2 0.092 0.010 9.232 0.000 SW4PROS Category 1 0.943 0.007 130.536 0.000 Category 2 0.057 0.007 7.941 0.000 Individuals in class 1 have a higher probability of borderline /abnormal scores (category 2) in the SDQ scales compared to individual in latent class 2. The conditional probability of abnormal scores is particularly high for the conduct problems scale for individuals in class 1 (0.81). Individuals in class 2 have, in general, low probabilities of reporting abnormal scores in the SDQ scales. Class 1 can be identified as the “problem” class and class 2 as the “difficulty” class. ---------------------------------------------------------------------------------------------------------- PARAMETRIC BOOTSTRAPPED LIKELIHOOD RATIO TEST FOR 1 (H0) VERSUS 2 CLASSES H0 Loglikelihood Value -5301.974 2 Times the Loglikelihood Difference 470.531 Difference in the Number of Parameters 6 Approximate P-Value 0.0000 Successful Bootstrap Draws 5 WARNING: THE BEST LOGLIKELIHOOD VALUE WAS NOT REPLICATED IN 5 OUT OF 5 BOOTSTRAP DRAWS. THE P-VALUE MAY NOT BE TRUSTWORTHY DUE TO LOCAL MAXIMA. INCREASE THE NUMBER OF RANDOM STARTS USING THE LRTSTARTS OPTION. ---------------------------------------------------------------------------------------------------------- The low p value indicates that the model with one less class (1-class model) is rejected in favour of the estimated 2-class model. However, the warning message suggests increasing the random starts of the bootstrapped test. The default for LRTSTARTS = 0 0 20 5; More thorough is LRTSTARTS = 2 1 50 15; This would be added in the ANALYSIS: command. INPUT 3-class model (abridged) Variable: Names are mahcig01 MeHGsx1 DePicSTS ZDePicSAS DeNamVTS ZDeNamVAS mdhgsx1 sw4emo sw4con sw4hyp sw4peer sw4pros sw5emo sw5con sw5hyp sw5peer sw5pros male pregsmok missingd; USEVAR are sw4emo sw4con sw4hyp sw4peer sw4pros;

7 CATEGORICAL are sw4emo sw4con sw4hyp sw4peer sw4pros; Missing are all (-999) ; classes are x(3); !estimates a latent categorical variable with three classes, !the indicators are sw4emo-sw4pros, specified in categorical option of variable Analysis: Type = MIXTURE ; ! invokes a mixture model algorithm OUTPUT: TECH1 TECH10 TECH11 TECH14; PLOT:Type is PLOT3; series is sw4emo (1) sw4con (2) sw4hyp (3) sw4peer (4) sw4pros (5); DEFINE: CUT sw4emo-sw4pros (0); !creates binary variables using 0 as cut-point OUTPUT (abridged) RANDOM STARTS RESULTS RANKED FROM THE BEST TO THE WORST LOGLIKELIHOOD VALUES Final stage loglikelihood values at local maxima, seeds, and initial stage start numbers: -5049.029 608496 4 -5049.946 253358 2 WARNING: WHEN ESTIMATING A MODEL WITH MORE THAN TWO CLASSES, IT MAY BE NECESSARY TO INCREASE THE NUMBER OF RANDOM STARTS USING THE STARTS OPTION TO AVOID LOCAL MAXIMA. WARNING: THE BEST LOGLIKELIHOOD VALUE WAS NOT REPLICATED. THE SOLUTION MAY NOT BE TRUSTWORTHY DUE TO LOCAL MAXIMA. INCREASE THE NUMBER OF RANDOM STARTS. ------------------------------------------------------------------------------------------------------- The log-likelihood is not replicated. Furthermore, the software provides warnings. Increase the start values and the number of iterations in the initial stage: ---------------------------------------------------------------------------------------------------------- Type = MIXTURE ; STARTS = 300 10; STITERATIONS = 20; ---------------------------------------------------------------------------------------------------------- Which provides this solution: ---------------------------------------------------------------------------------------------------------- RANDOM STARTS RESULTS RANKED FROM THE BEST TO THE WORST LOGLIKELIHOOD VALUES Final stage loglikelihood values at local maxima, seeds, and initial stage start numbers: