Results of the Latent Class Model

The AIC and BIC criteria were suggestive of five- and four-class in the acute and chronic phase. We used latent class regression with the selected number of class to explore the latent structure of PANSS. There are two types of parameters in the latent class model:

latent class probabilities and latent conditional probabilities. The results of the two phases were described as follows.

Results of the Acute Phase

Table 6 shows that the summarized results of the acute phase with the latent five-class model without covariates which was run by our program. The first class was the mixed class because of high conditional probabilities on the most positive, negative, and general psychopathological items of the PANSS. In the second class, the conditional probabilities of a positive item (P1), six negative items (N1-N6), and a general psychopathological item (G12) were greater than or equal to 0.8. Since the patients of the second class were diagnosed with the most negative symptoms, we labeled it as the negative class. In the third class, there were delusions (P1), conceptual disorganization (P2), hallucinatory behavior (P3), suspiciousness/persecution (P6), difficulty in abstract thinking (N5), un-usual thought content (G9) and lack of judgment and insight (G12) with high conditional

probabilities. These majority symptoms related with thought, therefore the disorganized thought was labeled to the third class. In the fourth class, the patients had the significant symptoms, delusions (P1), hallucinatory behavior (P3), suspiciousness/persecution (P6), unusual thought content (G9) and lack of judgment and insight (G12). Ninety percent of the patients in the fourth class had delusions (P1) symptom, therefore we labeled the fourth class as the delusion class. The fifth class could be labeled as the positive class, because the patients had the likelihood of eighty percent or higher to have six positive items (P1-P4, P6, P7) and the four general psychopathological items (G9, G12, G14, G15). In addition, five latent class probabilities of each class were about equal with the disorganized thought class (the third class) having the lowest prevalence 0.15.

In addition, we also performed the latent class model of the acute phase using Mplus version 3, and the results were concluded in Table 7. The first class was similar to the first class of results based on our program, and it was labeled as the mixed class. The second class was also similar to the second class of results based on our program, which had the high conditional probabilities on the blunted affect (N1), emotional withdrawal, passive/apathetic social withdrawal (N4), difficulty in abstract thinking (N5), and lack of judgment and insight (G12). We also labeled the negative class to the second class of resulting from Mplus. In the third class, the conditional probabilities of the delusions (P1), hallucinatory behavior (P3), suspiciousness/persecution (P6), unusual thought content (G9) and lack of judgment and insight (G12) were greater than eighty percent. It was similar to the third class of results based on our program, thus we also labeled it as the disorganized thought. In the fourth class, there were only two significant symptoms, delusions (P1) and lack of judgment and insight (G12). The delusion was labeled to the fourth class, which was similar to the fourth class of resulting from our program. In the fifth class, the conditional probabilities of four positive items (P1-P3, P7), five negative items (N1, N3-N6), and five general psychopathological items (G1, G7, G11, G12, G15) were greater than or equal to eighty percent. The patients of the fifth class were diagnosed

as having several positive, negative and general psychopathological symptoms. However, the number of symptoms diagnosed of the fifth class was less than of the mixed class, thus we labeled it as the a little mixed class. The fifth class resulting from our program was nested within the fifth class resulting from Mplus, where the conditional probabilities of negative items (N1, N3-N6) based on our program were not as significant as the ones based on Mplus.

• Demographic Variables

We performed the latent class model with demographic variables to explore the relation between the latent class and demographic variables. In Table 8, the summary based on the resulting from our program was demonstrated, whereas the summary resulting from Mplus was shown in Table 9. The symptoms of each latent class were similar to the latent class without covariates. There were also five classes labeled: mixed, negative, disorganized thought, delusion and positive/a little mixed.

According to the result based on our program, the parameter estimate of gender in the negative class versus the positive class was significantly different from 0. The parameter estimate was the log odds ratio of having negative symptoms when comparing men with women. The odds ratio for association between gender and having negative symptoms was e^0.9 = 2.47. The men were 2.47 times more likely to develop negative symptoms than women. In addition, the older patients would be having serious symptoms, because the log odds ratio of age in the mixed class versus the positive class was significantly different from 0. The patients with fewer years of education were more likely to be in the mixed class or the disorganized thought class because the log odds ratio of years of education in the mixed/disorganized thought class versus the positive class was negative. On the other hand, the odds ratio of years of education in the delusion class versus the positive class was e^0.17= 1.19, thus the patients with high years of education were more likely to develop delusion symptoms. The log odds ratio of occupation in the delusion class versus the positive class was significantly different from 0. The result expressed that the patients

with occupation had high probability to belong to the delusion class. In addition, the patients with the older age at onset would belong to the delusion class, because the odds ratio of age of onset of psychotic symptom in the mixed class versus the positive class was e^0.15= 1.17.

According to the conclusion based on Mplus, there was only one significant parameter estimate of gender in the delusion class versus the a little mixed class. The parameter estimate was the log odds ratio of having delusion symptom comparing men with women.

The odds ratio for association between gender and having delusion symptoms was e^−1.31 = 0.27. The women were 3.71 (=1/0.27) times more likely to develop delusion symptom than men.

• Environmental Factors

We performed the latent class model with environmental factors after adjusting sig-nificant demographic variables to explore the relation between the latent class and envi-ronmental factors. The conclusion resulting from our program was shown in Table 10, and the result based on Mplus was shown in Table 11. The symptoms of each latent class were similar to the latent class without covariates. There were also the five classes labeled: mixed, negative, disorganized thought, delusion and positive/a little mixed.

Based on the conclusion resulting from our program, after the adjustment of signifi-cant demographic variables, i.e., gender, age, years of education, occupation and age of onset of psychotic symptom, the parameter estimate of the slight environmental factor 2 in the negative class versus the positive class was significantly different from 0. The result indicated that patients who had unstable mood or abnormal behavior to interfere with adapting to the daily life had higher tendency to be listed in the negative class than the patients without unstable mood or abnormal behavior, as compared with the positive class. In addition, patients who had no unstable mood or abnormal behavior to interfere with adapting to life had higher trend to be assigned to the mixed class than patients who had these characteristics, as compared with the positive class, because the

parame-ter estimate of the obvious environmental factor 2 in the mixed class versus the positive class was significant negative. Patients who had obvious psychological problems in their infancy were also more likely to belong to the delusion class than the patients without psychological problems, as compared with the positive class, because the parameter esti-mate of the obvious environmental factor 3 in the delusion class versus the positive class was significantly different from 0. However, according to the result based on Mplus, after the adjustment of significant demographic variable, i.e., gender, there were no significant parameter estimates of the environmental factors, as shown in Table 10.

• Neuropsychological Variables

In the acute phase, the neuropsychological variables only contained the sensitivity index (d’) of the CPT performance to reflect the subject’s sustained attention. According to both conclusions based on our program and Mplus, the symptoms of each latent class were similar to the latent class without covariates. According to the result based on the program (Table 12), the undegraded d’ was significant in the negative class versus the positive class. The result elucidated that the patients who had low sustained attention were more likely to be in the negative class than the patients who had high sustained attention, as compared with the positive class. However, the parameter estimates of the undegraded d’ by the latent class model using Mplus were non-significant, as shown in Table 13. In addition, Table 14 and 15 also shows the fact that the parameter estimates of degraded d’ in the resulting from our program or Mplus were non-significant.

Results of the Chronic Phase

In Table 16, the summary of the results of the chronic phase with the latent four-class model without covariates which was run by our program was demonstrated. The result based on our program indicated that the first class was labeled as the a little mixed class because of high conditional probabilities on three positive (P1-P3), two negative (N4-N5), and two general psychopathological (G9, G12) symptoms. The second class could

be labeled as a pure negative one, because there were only significant negative symptoms.

In the third class, there were only two significant symptoms, delusions (P1) and lack of judgment and insight (G12). We thus labeled the third class as the delusion class. In the fourth class, the patients were diagnosed as being without any symptoms, thus the no-symptoms class was labeled to the fourth class. In addition, the latent class probabilities were equal to or greater than twenty-three percent. In Table 17, the conclusion based on Mplus showed that the symptoms of each latent class were similar to the conclusion resulting from our program. There were also four classes labeled: a little mixed, negative, delusion and no-symptoms.

• Demographic Variables

The symptoms of each latent class of adding the demographic variables were in com-mon with the results without covariates, as shown in Table 18 and Table 19. The age variables in the a little mixed class versus the no-symptoms class were significant when our program and Mplus were applied. The result indicated that the older patients would have more serious symptoms. In addition, patients with higher years of education would have no symptoms because the log odds ratio of years of education of the conclusion based on our program in the a little mixed/negative/delusion class versus the no-symptoms class was negative. According to the conclusion based on Mplus, the odd ratio of years of edu-cation in the a little mixed/negative class versus the no-symptoms class was also negative, thus patients with high years of education were more likely to have no symptoms. In both conclusions based on our program and Mplus, the log odds ratio of occupation in the a little mixed/negative class versus the no-symptoms class was significantly different from 0, representing that the patients without occupation had high probability to belong to the a little mixed/negative class. In addition, the result based on our program also indicated that the single patients would belong to the a little mixed class, because the odds ratio of marital status in the a little mixed class versus the no-symptoms class was e^1.39= 4.03.

• Environmental Factors

The symptoms of each latent class of adding the significant demographic variables and the environmental factors were similar to the latent class without covariates. Table 20 demonstrates the result based on the program. After adjusting significant demographic variables, i.e., age, years of education, occupation and marital status, the parameter estimates of the two dummy variables of the environmental factor 2 in the a little mixed class versus the no-symptoms class were significantly different from 0. As displayed in the result, patients with unstable mood or abnormal behavior to interfere with adapting to the daily life had higher probability to be assigned to the a little mixed class than the patients without unstable mood or abnormal behavior, as compared with the no-symptoms class. Furthermore, the parameter estimate of the slight environmental factor 2 in the negative class versus the no-symptoms class was significantly different from 0. Based on the result, it was apparent that patients who had unstable mood or abnormal behavior to interfere with adapting to the daily life would have higher probability to be located in the negative class than the patients without unstable mood or abnormal behavior, as compared with the no-symptoms class. Patients without psychological problems in their infancy also had higher probability to be located in the negative class than patients with slight psychological problems, as compared with no-symptoms class, because the parameter estimate of the slight environmental factor 3 in the negative class versus the no-symptoms class was significant negative.

Table 21 shows the result based on Mplus after adjusting significant demographic variables, i.e., age, years of education, and occupation. According to the result, there were only the significant parameter estimates of the environmental factor 2. When com-paring with patients without unstable mood or abnormal behavior, patients with these characteristics were more likely to be diagnosed as having symptoms.

• Neuropsychological Variables

In the chronic phase, the neuropsychological variables were mainly consisted of the sensitivity index (d⁰) of the CPT performance, the perseverative error score and the

num-ber of categories completed of the WCST, the Full Scale IQ of the WAIS-R, the sum of WMS-R Logical Memory I and Logical Memory II, and TMT-A and TMT-B. The re-sulting from Mplus by performing the RLCA with the sensitivity index (d⁰) of the CPT performance or the number of categories completed of the WCST after adjusting signifi-cant demographic variables, which were age, years of education and occupation, had too low latent class probability in the first class. Therefore, we didn’t show the results of the sensitivity index (d⁰) of the CPT performance and the number of categories completed of the WCST using Mplus. On the other hand, our program could not be utilized to perform the RLCA with the sum of WMS-R Logical Memory I and Logical Memory II after adjusting significant demographic variables, i.e. age, years of education, occupation and martial status, because there were too less number of subjects of the sum of WMS-R Logical Memory I and Logical Memory II. However, it was able to perform the RLCA with the sum of WMS-R Logical Memory I and Logical Memory II after adjusting significant demographic variables, i.e. age, years of education and occupation, by utilizing Mplus.

Therefore, we could merely show the results about the sum of WMS-R Logical Memory I and Logical Memory II by applying Mplus. In both results based on our program and Mplus, the structures of the PANSS under RLCA with each neuropsychological variable, excluded from the sum of WMS-R Logical Memory I and Logical Memory II, were similar to the structures of the PANSS under RLCA without covariates.

In Table 22, the result based on our program demonstrated that the undegraded d⁰ of the CPT was significant in the a little mixed class versus the no-symptoms class. Under the comparison of the no-symptom class, patients with lower sustained attention would have higher probability to be allocated to the a little class than patients with higher sustained attention. However, as shown in Table 23, there was no significant parameter estimates of the degraded d⁰ of the CPT.

In Table 24, the results based on WCST showed the fact that the parameter estimate of the number of categories completed in the a little mixed class versus the no-symptoms class

under the appliance of our program was significant. The result displayed that patients who completed less the number of categories were easier to be assigned to the a little mixed class than patients who completed more the number of categories, as compared with the no-symptoms class. As shown in Table 25 and Table 26, the parameter estimates of the perseverative errors under the utilization of our program and Mplus were non-significant.

Table 27 and Table 28 describe the results of the WAIS-R under the appliance of our program and Mplus. According to the result, the parameter estimate of the full scale IQ in the a little mixed/negative class versus the no-symptoms class was significant. Patients with lower IQ were more likely to belong to the a little mixed/negative class than patients with higher IQ, as compared with the no-symptoms class. However, it is suspected that the result might be unstable because the number of free parameters was more than the number of subjects.

The result of the sum of WMS-R Logical Memory I and Logical Memory II using Mplus was demonstrated in Table 29. The structure of the PANSS was not similar to the structures of the PANSS using RLCA without covariates. The negative and no-symptoms classes were still retained in the first and fourth classes, but the symptoms of the second or third classes had been changed. In the second class, there were only two significant symptoms that had equal or higher conditional probabilities, difficulty in abstract thinking (N5), and unusual thought content (G9). In the third class, there were three significant symptoms, i.e., delusions (P1), difficulty in abstract thinking (N5) and lack of judgment and insight (G12). The parameter estimate in the negative class versus the no-symptoms class was significant. The result indicated that patients with worse memory were more likely to belong to the negative class than the patients with better memory, as compared with the no-symptoms class. However, the result could be unstable due to that the number of free parameters was more than the number of subjects.

After adjusting significant demographic variables, the structures of the PANSS under the appliance of RLCA with covariates of the Trail Making Test (TMT) were similar to

the structures of the PANSS under the appliance of RLCA without covariates. Based on the results relating to the A, patients who spent long time to complete the TMT-A had higher tendency to be listed on the negative class than patients who spent less time to complete it, as compared with the no-symptoms class, which was mainly due to that the parameter estimate in the negative class versus the symptoms class by using our program was significant (Table 30). However, in the results relating to the TMT-A under the utilization of Mplus, there were no significant parameter estimates as shown in Table 31. On the other hand, according to the results relation to the TMT-B, the parameter estimate in the a little mixed class versus the no-symptoms class under the appliance of our program or Mplus was significant. As demonstrated in the result, patients who spent

the structures of the PANSS under the appliance of RLCA without covariates. Based on the results relating to the A, patients who spent long time to complete the TMT-A had higher tendency to be listed on the negative class than patients who spent less time to complete it, as compared with the no-symptoms class, which was mainly due to that the parameter estimate in the negative class versus the symptoms class by using our program was significant (Table 30). However, in the results relating to the TMT-A under the utilization of Mplus, there were no significant parameter estimates as shown in Table 31. On the other hand, according to the results relation to the TMT-B, the parameter estimate in the a little mixed class versus the no-symptoms class under the appliance of our program or Mplus was significant. As demonstrated in the result, patients who spent