Using Latent Trait Modeling to Conceptualize an Alcohol Problems Continuum

Psychological Assessment Copyright 2004 by the American Psychological Association 2004, Vol. 16, No. 2, 107 119 1040-3590/04/$12.00 DOI: 10.1037/1040-3590.16.2.107 Using Latent Trait Modeling to Conceptualize an Alcohol Problems Continuum Robert F. Krueger, Penny E. Nichol, Brian M. Hicks, Kristian E. Markon, Christopher J. Patrick, William G. Iacono, and Matt McGue University of Minnesota, Twin Cities Campus Recent research points toward the viability of conceptualizing alcohol problems as arrayed along a continuum. Nevertheless, modern statistical techniques designed to scale multiple problems along a continuum (latent trait modeling; LTM) have rarely been applied to alcohol problems. This study applies LTM methods to data on 110 problems reported during in-person interviews of 1,348 middle-aged men (mean age 43) from the general population. The results revealed a continuum of severity linking the 110 problems, ranging from heavy and abusive drinking, through tolerance and withdrawal, to serious complications of alcoholism. These results indicate that alcohol problems can be arrayed along a dimension of severity and emphasize the relevance of LTM to informing the conceptualization and assessment of alcohol problems. Historically, much research on alcoholism has conceived of alcohol problems as defining distinct types of alcoholics. Might such problems be better conceived of as arrayed along a dimension of severity? What implications would this perspective have for the clinical assessment of alcohol problems? In the current study, we used a statistical approach called latent trait modeling (LTM) to investigate this perspective. We introduce LTM (an approach also referred to as item response theory or item response modeling; see Heinen, 1996; Krueger & Piasecki, 2002), and we applied the technique to investigate the viability of a dimensional approach to conceptualizing alcohol problems. The latent trait model has mostly been applied to the study of individual differences in intellectual ability and achievement, making the approach less familiar to researchers studying alcoholism and related disorders. Nevertheless, these techniques can also be applied to other individual differences, such as differences in problem alcohol use. We therefore applied LTM to data on an extensive variety of alcohol problems assessed via in-person interviews in a large communitybased sample of middle-aged men. LTM techniques were used to model the ways in which specific alcohol problems index a broad, latent alcohol problems dimension. We begin by reviewing recent research that suggested to us the possibility that alcohol problems might be arrayed along a dimension of severity. Latent Class Analyses of Alcohol Problems Point Toward a Dimension of Severity Typological approaches have a long history in the study of alcohol problems (e.g., Cloninger, 1987; Jellinek, 1960; Schuckit, Robert F. Krueger, Penny E. Nichol, Brian M. Hicks, Kristian E. Markon, Christopher J. Patrick, William G. Iacono, and Matt McGue, Department of Psychology, University of Minnesota, Twin Cities Campus. This work was supported in part by U.S. Public Health Service Grants AA00175, AA09367, DA05147, and MH65137. Correspondence concerning this article should be addressed to Robert F. Krueger, Department of Psychology, University of Minnesota, Twin Cities Campus, N414 Elliott Hall, 75 East River Road, Minneapolis, MN 55455-0344. E-mail: krueg038@umn.edu 1985). The possibility of distinct types of alcoholics has traditionally been explored via cluster analytic methods (e.g., Babor et al., 1992; Morey, Skinner, & Blashfield, 1984; Schulenberg, O Malley, Bachman, Wadsworth, & Johnston, 1996). Shortcomings of traditional cluster analytic methods are well known, including problems with different clustering procedures producing different solutions for the same data and difficulties in determining the number of clusters in a given data set (Blashfield, 1984). Because of these shortcomings, investigators have recently turned to more rigorous exploratory categorical data analytic techniques to explore the possibility of distinct types of alcoholics. Specifically, a number of recent studies have taken an exploratory approach to identifying types of individuals with the same alcohol problem profiles using a statistical approach known as latent class analysis (LCA). As applied to alcohol problems, LCA is used to identify mutually exclusive groups of people who, within groups, are identical in terms of their probability of having specific alcohol problems (Muthén & Muthén, 2000). A number of LCA studies of alcohol problems have been reported in a variety of samples, including adult relatives of alcoholics (Bucholz et al., 1996), male Australian twins (Heath et al., 1994), an epidemiological sample of noninstutionalized U.S. civilians (Nelson, Heath, & Kessler, 1998), adolescent female twins (Bucholz, Heath, & Madden, 2000), Swedish male twins (Kendler, Karkowski, Prescott, & Pedersen, 1998), and adolescents recruited from clinical settings (Chung & Martin, 2001). Each of these studies reported evidence of alcohol classes that were distinguished primarily by the extent of their problems with alcohol. That is, although LCA is designed to identify discrete alcoholic subtypes, the subtypes that emerge from this research are distinguished not by unique profiles of alcohol problems, but rather, by their placement along a continuum of severity linking diverse alcohol problems. As Heath et al. (1994) concluded from their LCA results, It appears that there is a continuum of severity of alcohol-related problems (p. 299). Toward a Dimensional Approach to Alcohol Problems If alcohol problems define a continuum, then statistical or psychometric approaches designed to model continuous latent vari- 107

108 KRUEGER ET AL. ables such as abilities could also be informative in modeling alcohol problems. Little research has focused on the application of more modern psychometric techniques to the study of alcohol problems or on the use of such modern techniques to inform the conceptualization, and therefore the assessment, of problem drinking. This may be due in part to the categorical nature of many current conceptualizations of alcohol problems, such as the Diagnostic and Statistical Manual of Mental Disorders (4th ed.) conceptualization involving two categories of alcohol abuse and dependence (American Psychiatric Association, 1994). Nevertheless, as described above, the search for discrete types of alcoholics with distinct profiles of alcohol problems yields evidence for a continuum of severity. This points toward the potential utility of modern dimensional psychometric models in informing the conceptualization of alcohol problems (cf. Kahler, Strong, Hayaki, Ramsey, & Brown, 2003; Muthén, 1996). If such problems define a continuum, rather than discrete groups of alcoholics, this would have fundamental implications for how researchers think about alcohol problems, and hence, for the assessment of alcohol problems. For example, rather than focusing assessment on determining category membership, researchers might frame assessment in terms of determining the extent or severity of problems. Applying LTM to Alcohol Problems: The Current Study If a broad dimension of severity links multiple alcohol problems, then it is important to understand how specific alcohol problems map onto this dimension. Which problems are empirically more and less severe? Which problems are most informative and discriminate best among persons at nearby levels of severity? Taken as a group, how well does a specific set of alcohol problems capture the alcohol problems continuum? What implications do the answers to these questions have for the clinical assessment of alcohol problems? These issues can be addressed by using statistical models grouped under the rubric of LTM. Specifically, we used a twoparameter logistic latent trait model to determine empirically which alcohol problems were more and less severe (the first parameter of a specific symptom), and which problems were more and less discriminating (the second parameter of a specific symptom). In other words, the model we used is characterized by two parameters that index the probability of a certain symptom being present in persons at each level of the latent alcohol problems continuum. These indices can be explained graphically through the use of symptom response functions (SRFs; see Figure 1). An SRF is a plot of the model-derived probability of a symptom being present as a function of standing on a latent continuum. The first index is severity, which conveys the symptom s location along the latent continuum. The severity is the point on the latent continuum where there is a 50% chance of a symptom being present; this is the point where the slope of the SRF is at its maximum value. In Figure 1, Symptom B is more severe than Symptom A because the midpoint of the SRF for Symptom B occurs at a higher value of the continuum (located on the horizontal axis and scaled in a z-score standardized metric with M 0, SD 1) than the midpoint of the SRF for Symptom A. The second index is discrimination, which refers to how well a symptom can distinguish between those who are higher on the continuum and those who are lower on the continuum. Discrimination is indicated by how steep the slope of the SRF is at its steepest point (i.e., at the point identified by the severity parame- Figure 1. Sample symptom response functions.

ALCOHOL PROBLEMS CONTINUUM 109 ter). Although Symptom B in Figure 1 is more severe than Symptom A, it is less discriminating because the slope of Symptom B is less steep than the slope of Symptom A. A SRF can also be mathematically transformed into a symptom information function (SIF). To transform an SRF in this way, the slope of the SRF is squared and divided by the symptom s variance, conditional on the latent continuum level. The location of the information function is related to the symptom s severity parameter the peak of the SIF coincides with the location of the symptom s severity. The height of the SIF is a function of the symptom s discrimination parameter the higher the discrimination value, the higher the peak of the SIF. Conceptually, information refers to the symptom s discriminating power at a specific location on the latent continuum. Thus, better symptoms those that are more discriminating have more peaked SIFs. Figure 2 shows the SIFs that correspond to the SRFs given in Figure 1. Note how the peaks of the two SIFs correspond to the points along the continuum where the severities are located in Figure 1 (i.e., the peaks on Figure 2 correspond to the points on Figure 1 where the SRFs intersect the dotted line representing 50% probability of the symptom being present). Note also the considerably larger amount of information conveyed by Symptom A, relative to Symptom B, as is also indicated by the differences in the discriminations of the two symptoms (i.e., the slopes of the SRF lines shown on Figure 1). Thus, in the current research, we fit a two-parameter latent trait model to data on 110 alcohol problems reported during in-person interviews of a large sample of middle-aged men (mean age 43) from the general population. The two parameters of our model correspond to the severity and discrimination of each problem (i.e., where the problem is located along the alcohol problems continuum and how well the problem is able to discriminate among men at nearby levels on the continuum). The 110 problems we studied provide broad coverage of a variety of different problems with alcohol, including criteria for Feighner alcoholism (Feighner et al., 1972), research diagnostic criteria (RDC) alcoholism (Spitzer, Endicott, & Robins, 1978), Diagnostic and Statistical Manual of Mental Disorders (3rd ed.; DSM III) alcohol abuse and dependence (American Psychiatric Association, 1980), and Diagnostic and Statistical Manual of Mental Disorders (3rd ed., rev.; DSM III R) alcohol abuse and dependence (American Psychiatric Association, 1987) as well as additional coverage of quantity and frequency of drinking. We sought to model these problems in a sample of middle-aged men because they are beyond the age of maximal risk for the development of alcoholism (i.e., late adolescence to young adulthood; Helzer, Burnam, & McEvoy, 1991). To our knowledge, the LTM approach has not been applied to data on a wide range of interview-assessed alcohol problems in a large general-population sample of adults. We used the empirically estimated severity and discrimination values to answer a number of specific questions regarding alcohol problems. First, we examined how the group of problems, taken as a whole, indexes the alcohol problems continuum. Summing the individual SIFs across a group of symptoms, conditional on latent continuum level, creates an aggregate SIF. This SIF function gives a picture of the information value of the symptoms as a collective. Thus, we were able to determine where along the alcohol problems continuum the 110 problems were conveying the most information. Correspondingly, the procedure also identifies gaps in coverage areas of the continuum where additional information could be obtained to optimize coverage of the entire continuum. Figure 2. Sample symptom information functions.

110 KRUEGER ET AL. Second, we divided the problems by their correspondence with the six criteria sets (i.e., Feighner alcoholism, RDC alcoholism, DSM III alcohol abuse, DSM III alcohol dependence, DSM III R alcohol abuse, and DSM III R dependence). Each of these criteria sets identifies a construct that has been a focus of alcoholism research, and considered historically, they highlight the continually evolving nature of clinical conceptions of alcohol problems. Nevertheless, to our knowledge, these six constructs have not been directly compared on the basis of the information provided by their criteria. Using LTM, we were able to directly compare the six alcohol disorder constructs in terms of the information they provided with reference to the underlying alcohol problems continuum. This procedure offers new perspectives on similarities and differences among the six constructs. For example, we predicted that the syndromes defined by putatively less severe criteria (e.g., DSM III R abuse, including criteria such as drinking in dangerous situations) provide information about a lower part of the alcohol continuum than do syndromes defined by putatively more severe criteria (e.g., DSM III R dependence, including criteria such as often drinking to alleviate withdrawal symptoms). From this perspective, the abuse and dependence constructs might be better understood and assessed as collections of symptoms with distinct locations on the same underlying continuum rather than as distinct categories of disorder. Along these same lines, a third goal was to use the information about the severity and discrimination of the 110 problems to identify a subset of problems that conveyed the most information along the entire breadth of the continuum. This endeavor is important because the nature of these unusually informative symptoms helps to inform our understanding of the alcohol problems continuum across its entire range. By examining the most informative symptoms, one learns about how alcohol problems are manifested at different levels of overall severity (e.g., in heavy drinking vs. withdrawal vs. tolerance). In addition, we predicted that problems that were more normative and common in our sample (e.g., intoxication on at least one occasion) would be located at lower levels of the continuum than would problems that were more rarely observed and serious (e.g., needing alcohol to function) yet all the problems would be located on the same underlying continuum. This finding would indicate that more normal and more abnormal alcohol problems differ primarily in degree, rather than in kind. Research Participants Method The sample was composed of fathers (n 1,348; mean age 43 years, SD 6 years) who participated in the Minnesota Twin Family Study (MTFS). The MTFS is a longitudinal study designed to identify factors that contribute to substance abuse and related psychopathology in a large epidemiological sample of adolescent twins and their parents (Iacono, Carlson, Taylor, Elkins, & McGue, 1999). Families were recruited and included in the study using a population-based ascertainment method in which all twins born in Minnesota were identified using public birth records. For any given year, the study was able to locate more than 90% of all twin pairs in which both members were still living. Families were excluded from participation if they lived further than a day s drive from the University of Minnesota, Twin Cities campus or if either twin had a cognitive or physical handicap that would preclude their completing our day-long, in-person assessment. Of the eligible families, 17% declined participation and 78% ultimately completed the intake assessment. To investigate potential sampling biases, we conducted a brief telephone interview or mail survey that was completed by 82.6% of the nonparticipating families. In terms of socioeconomic status, nonparticipating biological fathers had slightly, albeit significantly, less education [13.8 vs. 14.0 years; t(2346) 2.44, p.02] than participating biological fathers. They did not, however, differ in occupational status as coded using the Hollingshead system (Hollingshead & Redlich, 1958). Also, participating and nonparticipating biological fathers did not differ on a brief mental health assessment that included self-reported rates of alcoholism or treatment for alcoholism: 11.8% for participating vs. 13.5% for nonparticipating, 2 (1) 1.45, p.20. Consistent with the demographics of Minnesota for individuals whose children were born in Minnesota during the 1970s and 1980s, more than 98% of participating fathers were Caucasian. In addition, 94% were employed full time. Regarding drinking behavior, 1% of the sample reported never having used alcohol. In the past year, the average frequency of drinking in the sample was 2 3 times a month, the average number of drinks on one of those occasions was 2 3 drinks, and the average proportion of times the participant drank to intoxication was between once in a while and never, on a scale ranging from every time to never. Regarding use of other drugs within the sample, 9.8% reported using marijuana in the last year, and 3.6% reported using an illicit substance other than marijuana. Alcohol Problems Assessment Participants were assessed in person in our university laboratories by trained lay interviewers. Lifetime substance use disorders were assessed using an expanded version of the Substance Abuse Module (SAM; Robins, Babor, & Cottler, 1987), which was developed to supplement the World Health Organization s Composite International Diagnostic Interview (Robins et al., 1988). The SAM was designed to provide a comprehensive assessment of alcohol use, abuse, and dependence, incorporating multiple diagnostic systems representing varying conceptualizations of alcohol use disorder. The SAM provides coverage of the criteria for Feighner alcoholism, RDC alcoholism, DSM III alcohol abuse and dependence, and DSM III R alcohol abuse and dependence. (DSM III R was the current diagnostic system when the MTFS study began.) Each of these entities is diagnosed reliably by the SAM in our study, with kappa values greater than.90. Other studies also support the test retest reliability of the symptoms assessed by the SAM (Cottler, Robins, & Helzer, 1989), the reliability of SAM-derived diagnoses within distinct demographic groups (Horton, Compton, & Cottler, 2000), and the congruence of SAM data with data obtained by less structured interviews (Compton, Cottler, Dorsey, & Spitznagel, 1996). We also augmented the SAM to include noncriterion questions (e.g., questions assessing the quantity and frequency of alcohol use; see Table 1). The SAM symptoms we used in our analysis were assessed on a lifetime basis. Data Analysis Unidimensionality assessment. The two parameters of the logistic latent trait model are most interpretable when the symptoms primarily reflect a single dimension. In other words, one primary latent continuum accounts for correlations among the symptoms. Unidimensionality can be assessed via exploratory factor analysis (EFA) of tetrachoric correlations among the symptoms (cf. Lord, 1980; Reise & Waller, 1990). In EFA, the extraction of additional factors beyond the first results in increased model fit, by definition. For example, the best fitting exploratory model will contain as many factors as there are variables being factored because this model simply reexpresses the observed data without imposing any structure on those data. However, this kind of model is clearly lacking in parsimony; little is learned from a model that simply reexpresses the observed data. Hence, evaluation of unidimensionality via EFA consists of integrating the

ALCOHOL PROBLEMS CONTINUUM 111 Table 1 Symptom Parameter Estimates for All Alcohol Problems in Order of Severity Severity rank Diagnostic system Description Discrimination Severity Est. SE Est. SE 1 Ever used alcohol 2.502 3.814 3.026 0.382 2 Ever been intoxicated 2.082 0.235 2.070 0.071 3 5 drinks on 1 occasion 2.695 0.359 1.984 0.064 4 Calm and relaxed a 0.209 0.027 1.951 0.302 5 7 drinks on 1 occasion 1.435 0.108 1.376 0.057 6 III Ra Drank in dangerous situations (e.g., driving a car) 1.435 0.080 1.239 0.059 7 III Ra DSM III R problems persisted > 1 month 2.836 0.322 1.140 0.040 8 IIIa DSM III problems persisted > 1 month 2.092 0.105 0.000 0.034 9 Seven drinks 1 time/week 1.190 0.070 0.212 0.037 10 R RDC problems persisted > 1 month 1.958 0.108 0.235 0.030 11 III Ra Drank in dangerous situations or rode with someone who was high 2 times 0.351 0.036 0.399 0.098 12 Tolerance 1 month 1.304 0.085 0.417 0.036 13 20 drinks at one time 0.988 0.064 0.417 0.042 14 IIId, III Rd Able to drink more before drunk 1.161 0.078 0.549 0.038 15 F, R Thought you were an excessive drinker 1.368 0.084 0.576 0.034 16 III Ra Drank after realized had problems 1.463 0.098 0.586 0.032 17 III Rd Drinking more than intended 1.612 0.106 0.620 0.031 18 IIIa, F Blackouts 1.255 0.087 0.635 0.037 19 F, R Family objected to drinking 1.323 0.084 0.695 0.036 20 Passed out 0.675 0.048 0.704 0.062 21 F Felt guilty about drinking 0.783 0.054 0.726 0.053 22 Stopped drinking entirely for 3 months 1.250 0.082 0.810 0.040 23 IIId, III Rd Needed more to get an effect 1.188 0.088 0.852 0.040 24 Stayed drunk throughout an entire day 1.504 0.096 0.858 0.035 25 III Ra Rode with someone who was high 0.392 0.039 0.864 0.107 26 IIIa 20 drinks at one time 3 times 1.398 0.100 0.897 0.039 27 III Rd Repeatedly wanted to quit or control drinking 1.526 0.109 1.096 0.039 28 IIIa, F, R Trouble driving because of drinking (e.g., accident or arrest for drunk driving) 1.014 0.074 1.105 0.051 29 Drank again after stopping for 3 months 0.953 0.072 1.160 0.055 30 IIIa, F, R Arrested because of drinking 1.005 0.078 1.194 0.056 31 F Drank before breakfast 1.124 0.087 1.247 0.056 32 Drank when decided not to 1.555 0.121 1.280 0.045 33 Needed/depended on alcohol 1.797 0.139 1.292 0.041 34 IIIa Went on benders 1.834 0.146 1.324 0.041 35 IIId, III Rd Sad or irritable b 2.559 0.214 1.335 0.033 36 IIIa, F, R Fights or physically violent while drinking 1 1.172 0.098 1.366 0.057 37 R Frequent blackouts 1.406 0.114 1.371 0.050 38 F, R Professional said you were drinking too much 1.754 0.137 1.457 0.045 39 III Rd Little time for anything but drinking 2.375 0.227 1.466 0.040 40 Difficult to get along with a 1.052 0.079 1.472 0.069 41 IIIa, R Difficulties with friends and family 1.682 0.143 1.473 0.050 42 7 drinks every day for 2 weeks 1.637 0.139 1.479 0.051 43 IIId, III Rd Nervous or uptight b 2.692 0.254 1.482 0.035 44 IIIa, III Rd Little time for family 2.238 0.216 1.499 0.040 45 IIId, III Rd Weak or tired b 1.897 0.163 1.512 0.045 46 IIIa, F, R, III Rd Wanted to stop drinking but couldn t 2.086 0.192 1.579 0.048 47 Little time for anything but drinking 1 month 2.271 0.229 1.592 0.045 48 Accidentally injured self while drinking 0.982 0.082 1.598 0.081 49 R During binges, consumed at least a fifth of liquor, 24 beers, or 3 bottles of wine each day 1.900 0.189 1.601 0.048 (table continues)

112 KRUEGER ET AL. Table 1 (continued) Severity rank Diagnostic system Description Discrimination Severity Est. SE Est. SE 50 Had emotional or psychological problems due to drinking 2.419 0.253 1.603 0.047 51 IIIa, III Rd Trouble getting work done 2.301 0.236 1.617 0.050 52 Try to control drinking by making rules (e.g., never drinking alone) 0.904 0.076 1.631 0.088 53 III Ra Continued to drink despite emotional problems 2.419 0.257 1.634 0.048 54 Couldn t keep from drinking even though wanted to 2.247 0.234 1.660 0.047 55 IIIa, F Neglected responsibilities 2.453 0.254 1.670 0.047 56 IIId, III Rd Sweating b 1.951 0.190 1.671 0.049 57 IIIa, III Rd Reduced important activities in order to drink 2.573 0.264 1.680 0.046 58 Depressed a 0.758 0.059 1.732 0.105 59 IIId, F, R, III Rd Shakes after stopping or cutting down 1.620 0.155 1.736 0.065 60 IIIa, F, R Job or school trouble 1.556 0.146 1.737 0.069 61 Trouble driving several times 1.246 0.120 1.741 0.079 62 IIIa Stopped drinking for 3 months then started again 1 time 0.982 0.093 1.742 0.091 63 Violent a 0.989 0.084 1.747 0.092 64 Reduced activities in order to drink > 1 month 2.647 0.289 1.753 0.048 65 R Frequently drink before breakfast 1.477 0.139 1.763 0.072 66 Grandiose a 0.269 0.034 1.775 0.240 67 IIId, III Rd Trouble sleeping b 1.864 0.200 1.783 0.062 68 IIId Drink to avoid hangover or shakes 1.263 0.117 1.810 0.082 69 Taken drink to alleviate withdrawal symptoms 1.799 0.166 1.834 0.067 70 Try to follow rules about drinking 1 month or made rules several times 1.347 0.130 1.836 0.082 71 Emotional problems due to drinking lasted for 1 month 2.183 0.226 1.865 0.058 72 IIIa, F Rules for drinking because had trouble limiting drinking 1.472 0.153 1.883 0.081 73 III Rd Drank all day, every day 1.925 0.203 1.887 0.069 74 III Rd Cared for children while drinking 0.878 0.089 1.901 0.118 75 R 3 binges lasting 3 days 1.855 0.212 1.912 0.071 76 IIIa, R, III Rd Couldn t work when intended to 1.512 0.166 1.965 0.091 77 IIIa, F Lost friends because of drinking 2.086 0.260 1.965 0.069 78 III Rd Drinking while working 1.210 0.120 1.968 0.100 79 Strong desire couldn t think of anything else 2.050 0.215 1.971 0.073 80 IIIa Needed alcohol to function, e.g., couldn t do work without a drink 2.531 0.338 1.974 0.062 81 III Rd Often taken a drink to alleviate withdrawal symptoms 2.056 0.231 1.986 0.073 82 Tense and anxious a 0.795 0.071 2.008 0.127 83 IIIa, III Ra Continued to drink when knew drinking caused a medical condition 1.787 0.236 2.038 0.095 84 Injured self when drinking several times 1.671 0.205 2.041 0.096 85 IIId, III Rd Throwing up b 1.618 0.206 2.067 0.093 86 IIId, III Rd Heart racing b 1.991 0.259 2.068 0.083 87 IIId, III Rd Headaches b 1.633 0.227 2.147 0.108 88 IIIa, R Separated or divorced 1.384 0.177 2.150 0.113 89 After going back to drinking, began to have problems with alcohol within 1 month 1.041 0.118 2.186 0.137 90 First drink before age 15 0.363 0.038 2.220 0.230 91 After going back to drinking, was drinking as much as before within 1 month 0.917 0.106 2.224 0.156 92 F, R Stomach disease 1.402 0.195 2.319 0.151 93 IIIa, R Lost a job or kicked out of school because of drinking 1.315 0.163 2.415 0.153

ALCOHOL PROBLEMS CONTINUUM 113 Table 1 (continued) Severity rank Diagnostic system Description Discrimination Severity Est. SE Est. SE 94 IIIa, III Ra Continued to drink when knew had a physical illness made worse by drinking 1.299 0.192 2.435 0.173 95 F, R Memory problems even when not drinking 1.977 0.359 2.452 0.155 96 Saw or heard things after cutting down, i.e., hallucinations > 1 2.806 1.186 2.482 0.199 97 IIId, F, R, III Rd Saw or heard things after cutting down, i.e., hallucinations 2.335 0.634 2.546 0.201 98 F Tingling or numbness in feet 1.857 0.439 2.611 0.230 99 Withdrawn a 0.550 0.055 2.650 0.227 100 IIId, III Rd Visual distortions b 2.072 0.574 2.670 0.242 101 IIId, F, R, III Rd Delirium tremens after quitting drinking 1.601 0.398 2.796 0.285 102 Stopped drinking for a few weeks, gone back to drinking 0.524 0.079 2.835 0.336 103 IIIa, F Drank nonbeverage forms of alcohol 1.163 0.197 2.963 0.302 104 Memory problems cleared up 1.583 0.320 3.054 0.307 105 F, R Liver disease or jaundice 1.347 0.426 3.059 0.465 106 Accidentally injured someone while drinking 0.837 0.155 3.153 0.399 107 IIIa Stopped drinking for a few weeks, gone back to drinking 1 time 0.545 0.098 3.162 0.444 108 IIId, F, R, III Rd Fits after cutting down 1.249 0.507 3.527 0.787 109 F, R Pancreatitis 1.189 0.355 3.530 0.624 110 F, R Neurological problems 1.033 0.525 4.879 1.819 Note. Boldface indicates symptoms with highest information within consecutive segments of the continuum. Est. estimate. III Ra Diagnostic and Statistical Manual of Mental Disorders (DSM III R) criteria for alcohol abuse; IIIa Diagnostic and Statistical Manual of Mental Disorders (DSM III) criteria for alcohol abuse; R research diagnostic criteria for alcoholism; III Rd DSM III R criteria for alcohol dependence; F Feighner criteria for alcoholism; IIId DSM III criteria for alcohol dependence. a Feelings and behaviors associated with alcohol use during period of most extensive use. b Withdrawal symptoms associated with quitting or cutting down on drinking. concepts of fit and parsimony. Specifically, unidimensionality is established by demonstrating that a one-factor model provides a parsimonious fit to the data. That is, if an acceptable model fit can be achieved with one factor, then one primary dimension can be said to parsimoniously account for the observed data. We used the computer program MicroFACT 2.0 (Waller, 2000) to assess dimensionality in this manner. Model fit was assessed using the goodnessof-fit index (GFI) provided by MicroFACT. This index is computed as 1 (mean squared residual/mean squared correlation). Hence, a GFI of 1.0 indicates a perfect fit of the model to the data (i.e., in this situation, the mean squared residual is zero). A principal factor analysis was performed on the tetrachoric correlations among the 110 symptoms. The GFI for a one-factor solution was nearly perfect (.96), and we therefore concluded that the 110 alcohol problems could be conceptualized as indicators of one dominant dimension, as one dimension was sufficient to provide a nearly perfect fit. Symptom parameter estimation. The discrimination and severity parameters for each symptom were estimated using marginal maximum likelihood (MML; Bock & Aitkin, 1981) by the computer program BILOG 3.11 (Mislevy & Bock, 1990). MML is a commonly used iterative estimation procedure that provides maximum likelihood estimates of severity and discrimination parameters from the data by use of the patterns of symptoms present in the individuals in the sample. 1 Very little data were missing on specific symptoms: The maximum percentage of missing data on any specific symptom was 3%. Missing data were handled by treating missing observations as omitted from the assessment; this procedure results in LTM parameter estimates based on all available data. Results Symptom Parameter Estimation How do the symptoms perform as indicators of the alcohol problems continuum? To answer this question, we fit the twoparameter logistic model to the 110 symptoms. The estimated symptom discrimination parameters, severity parameters, and associated standard errors of these parameter estimates are presented in Table 1. The mean of the discrimination parameters was 1.543, with a standard deviation of 0.612. The severity parameters mean was 1.494, with a standard deviation of 1.173. The severity parameter is scaled on a standard (z-score) metric and therefore can be directly referenced to the underlying continuum. Zero indicates 1 Our estimates were made using the 1.7 scaling factor that causes the logistic response function to approximate the normal ogive (a functional form in which probability of response is modeled by the cumulative proportion of observations in the normal distribution). This adjustment is commonly made in LTM because, whereas the logistic model is more computationally tractable, the normal ogive could be regarded as more theoretically elegant. However, when the logistic model is adjusted using the 1.7 scaling factor, the two models predict nearly identical probabilities of symptom presence. Hence, one essentially combines the computational tractability of the logistic and the theoretical elegance of the ogive by using the approach we used here.

114 KRUEGER ET AL. the average level of alcohol problems in the sample on the underlying continuum. Discrimination parameters can also be interpreted by converting them to a correlation metric. For instance, a discrimination of 1.543 (the mean for these symptoms) corresponds to a correlation of.84 between a symptom and the underlying continuum. Thus, in general, these symptoms had very good discrimination values and are measuring the higher end of the alcohol problems continuum. To assess the robustness of the symptom parameter estimates, we randomly divided the sample into two subsamples (each with n 674). Parameters were estimated separately in each subsample, and these estimates were correlated using Spearman s r s correlation. Spearman s r s was used because the consistency of the rank ordering of the symptom parameters is most useful for comparisons between samples, not the magnitudes of the estimates. The high value of the correlations for the discrimination parameters (r s.83) and the severity parameters (r s.95) indicate that the parameter estimates were robust. Overall Aggregate Information Function How is the alcohol problem continuum indexed by this set of symptoms? The aggregate information function and a corresponding function termed the aggregate standard error of measurement function for the 110 symptoms combined are presented in Figure 3. The horizontal axis represents the alcohol problems continuum, scaled to a standard or z-score metric (M 0, SD 1). To ease interpretation of measurement precision and imprecision, we use the standard error of measurement (SEM) because it is in the units of the continuum (i.e., z-score units). The smaller the SEM, the better the symptoms are at assessing the continuum at a specific level. For example, in Figure 3, the continuum is assessed better at the continuum level of 1 than at 1 because the SEM value is lower at the continuum level of 1 (or, alternatively, the information value is higher at 1 than at 1). Therefore, the set of symptoms discriminates better among participants around a continuum level one standard deviation above average than among participants around a continuum level of one standard deviation below average. The peak of the information function (or, conversely, the nadir of the SEM curve) is at an alcohol problem level almost two standard deviations above the average (zero) alcohol problem level. Hence, this collection of symptoms is assessing the higher end of the continuum better than the lower end. Aggregate Information Functions for Specific Criteria Sets Aggregate information functions for symptoms corresponding to the Feighner system (25 symptoms corresponded to Feighner criteria), RDC (26 symptoms), DSM III abuse (25 symptoms), DSM III dependence (16 symptoms), DSM III R abuse (8 symptoms), and DSM III R dependence (27 symptoms) are displayed in Figure 4. Examining Figure 4, one can see how subsets of symptoms corresponding to each system related to the alcohol problems continuum. For example, Figure 4 illustrates how the concept of information provides useful data beyond number of symptoms in assessing the capacity of a set of symptoms to capture specific ranges of the alcohol problems continuum. Although the Feighner, RDC, DSM III abuse, and DSM III R dependence constructs have similar numbers of corresponding symptoms (25, 26, 25, and 27, respectively), they are contributing different amounts of information, and all are contributing information primarily Figure 3. Aggregate information function and standard error of measurement.

ALCOHOL PROBLEMS CONTINUUM 115 Figure 4. Aggregate information functions for the six diagnostic groupings of symptoms and the most informative symptoms. DSM III Diagnostic and Statistical Manual of Mental Disorders (3rd ed.); RDC research diagnostic criteria for alcoholism; DSM III R Diagnostic and Statistical Manual of Mental Disorders (3rd ed., rev.). within the same range of the continuum (i.e., the high range). In contrast, DSM III R abuse (8 symptoms) is more spread out than any other criterion set and is unique in providing information about the lower range of alcohol problems. Finally, DSM III dependence (16 symptoms) is roughly as informative as Feighner (25 symptoms), in spite of having 9 less symptoms. Identifying the Most Informative Alcohol Problems Across the Entire Range of Alcohol Problems Is there a way to identify a subset of symptoms that provide the most information across the alcohol problems continuum? With the symptom parameter estimates, we were able to identify a subset of symptoms in our data that assessed alcohol problems well across the entire range of the continuum. Specifically, we sought symptoms providing the most information across the continuum at 0.25 intervals from 3 to 3. That is, we sought symptoms with the best discrimination in 24 windows (e.g., 3 to 2.75, 2.75 to 2.5), ranging from the lowest to the highest levels of the continuum. 2 Using this approach, we found 12 symptoms to provide the most information across the continuum of alcohol problems. 3 The corresponding symptom response functions for these symptoms are presented in Figure 5, with the symptom parameter estimates for these specific symptoms in boldface in Table 1. At the lower end of the continuum are symptoms such as ever been intoxicated and 5 or more drinks on 1 occasion ; in the middle are symptoms such as drinking more than intended ; and at the higher end are saw or heard things more than once and visual distortions. Given the placement of these symptoms along the alcohol problems continuum, a pattern is seen the continuum ranges from milder problems to those that are fundamentally incapacitating (e.g., being unable to function without a drink). The aggregate information function corresponding to these highly informative items is plotted in Figure 4. This function demonstrates how the identification of informative items results in an aggregate that has more consistent information across the entire range of the continuum, relative to symptoms chosen on the basis of their correspondence with diagnostic systems. 2 One symptom (the first symptom in Table 1, ever used alcohol ) had a high information value (high discrimination) at the very lowest part of the continuum (very low severity) but was not included in our list of most informative symptoms because the standard error for the discrimination estimate was larger than the point estimate of the discrimination parameter (see Table 1). This concern about the precision of the discrimination estimate led us to the conservative decision to leave this symptom out of our list of most informative symptoms. 3 The number of highly informative symptoms was less than the number of windows because the same symptom was sometimes identified as the most informative symptom in adjacent windows. That is, a specific symptom was sometimes more informative than any other specific symptom across multiple, adjacent windows, even if other symptoms happened to have their own (lower) points of maximal information in these same windows.

116 KRUEGER ET AL. Figure 5. Symptom response functions for the 12 symptoms providing the most information across the alcohol problems continuum. DSM III R Diagnostic and Statistical Manual of Mental Disorders (3rd ed., rev.); DSM III Diagnostic and Statistical Manual of Mental Disorders (3rd ed.). Discussion Existing quantitative research on alcohol problems, conducted from both categorical and dimensional perspectives, converges on the idea that alcohol problems define a continuum of severity. Nevertheless, formal statistical techniques for modeling the severity and discrimination of specific problems along a continuum have seen little application in the study of alcohol problems. In the current research, we attempted to fill this gap in the literature by applying a two-parameter latent trait model to data on alcohol problems collected via in-person interviews from a communitybased sample of 1,348 middle-aged men. Specifically, we estimated the severity and discrimination of 110 problems, most of which were derived from psychiatric nosological systems, including Feighner alcoholism, RDC alcoholism, DSM III alcohol abuse and dependence, and DSM III R alcohol abuse and dependence. The problems we studied formed a continuum (see Table 1) that ranged from intoxication and heavier use (multiple drinks on one occasion), through abuse (e.g., drank in dangerous situations), through persistence of problems for longer periods of time (e.g., 1 month), through dependence and emotional sequela of withdrawal (e.g., sadness and irritability), to very serious medical and psychological complications of alcoholism (e.g., hallucinations and liver disease). A number of limitations need to be kept in mind when interpreting these results. First, our results are limited to middle-aged men who were primarily White. We pursued this research in men because, relative to women, men are disproportionately affected by alcohol problems (e.g., Helzer et al., 1991; Kessler et al., 1994). In future research, we intend to explore the applicability of this approach to women. Future research could also profitably explore the applicability of our approach in samples with greater demographic diversity (e.g., in ethnicity or age). In addition, given that our research was limited to lifetime symptoms assessed via interview, future research building on our efforts could examine how data from other modalities (e.g., collateral and biological data) link to the alcohol problems continuum as well as how variability in symptomatology over time might be reflected in, for example, movement along the alcohol problems continuum (cf. Carroll, 1995). Although there are limitations to the current research, our findings do contribute to clarifying the optimal conceptualization of alcohol problems and therefore have implications for clinical assessment of alcohol problems. Specifically, our results complement existing quantitative research on alcohol problems by showing that these problems are well conceived of as arrayed along a continuum of severity. In addition, our work extends existing research by formally modeling the severity and discrimination of a wide range of specific problems and by demonstrating the applicability of modern psychometric methods to the study of alcohol problems. We turn now to comment on the implications of these findings for the clinical assessment of alcohol problems. Using the Latent Trait Model to Understand the Nature of Alcohol Problems Our findings show how alcohol problems are arrayed along a continuum, and they demonstrate how latent trait methods can

ALCOHOL PROBLEMS CONTINUUM 117 provide an empirical way to conceptualize the alcohol problems continuum. Our results suggest a conceptualization that stems directly from the two parameters of the latent trait model we used, and how these parameters map alcohol problems along a continuum of variation. Consider first the severity parameter. Distinct problems have distinct locations; different problems are not of equal value in determining the extent of an individual s problems with alcohol. Problems that are empirically higher on the continuum indicate greater problems overall, and hence, can be understood to be more severe. As hypothesized, milder symptoms (e.g., those associated with DSM III R abuse) and more severe symptoms (e.g., those associated with dependence) are differentially relevant to determining the overall extent of a person s alcoholrelated problems. Consider also how these ideas relate to the second parameter, discrimination. Distinct problems have distinct discriminatory value some problems were more discriminating than others and hence deserve greater weight in determining the extent of a person s problems with alcohol. Discrimination and severity are integrated within the concept of information (cf. Muthén, 1996). We therefore used the concept of information to pare down our overall problem set to 12 problems that were most informative in specific windows, moving along the entire range of the continuum, from the lowest to progressively higher levels. Hence, the ordering of these 12 problems (see Figure 5) is helpful in clarifying the nature of the alcohol problems continuum. Specifically, the continuum spans a wide range and is anchored on one end by intoxication and heavy use and on the other end by serious withdrawal symptoms (hallucinations and visual distortions) and the need to have alcohol to be able to function. In addition, persistence of problems constitutes a bridge between heavy use and psychological complications of withdrawal (sadness, irritability, nervousness), which in turn constitute the bridge to more serious withdrawal symptoms and needing alcohol to function. This conception dovetails well with previous factor analytic research, which also supports the idea of a broad, higher order dimension of severity (sometimes composed of highly correlated subdimensions; Harford & Muthén, 2001; Muthén, 1995, 1996; Muthén, Grant, & Hasin, 1993; Nelson, Rehm, Ustun, Grant, & Chatterji, 1999; O Neill, Sher, Jackson, & Wood, 2003; Smith, McCarthy, & Goldman, 1995). In sum, less severe problems can be meaningfully located along the same continuum as more severe problems, and these problems define a continuum that makes clinical and psychological sense. LTM also provides an empirical means of identifying problems that are especially useful to know about when assessing the level of severity of alcohol problems for a specific person. For example, the 12 most informative problems formed an aggregate that provided more consistent information across the entire continuum when compared with lists of problems formed on the basis of correspondence with specific diagnostic systems (see Figure 4). This brief set of problems could provide inspiration for a list of problems that would be well suited to creating a brief screen for overall alcohol problem level in samples in which a wide range of alcohol problems are observed, such as community-based samples. In a clinical sample, however, the goals of assessment would be more focused on discrimination at the higher end of the continuum. The 12 most informative problems across the entire continuum might not be well suited to making fine distinctions between individuals at the higher end of the continuum. Nevertheless, the approach implemented here could also be used to identify symptoms that are well suited to making these kinds of distinctions; one would focus on identifying informative symptoms within more narrow windows at the higher end of the continuum. Such psychometrically informative problems might even be viewed as the sorts of problems that would be most relevant for inclusion in official nosological systems, such as the DSM and the International Classification of Diseases (World Health Organization, 1992). Modern classification systems endeavor to be empirically based nosologies, not wedded to a specific theoretical orientation. LTM provides an empirical means to identify those problems that are most indicative of alcohol problems across various ranges that are relevant for various purposes, such as screening for severe cases in the community versus making fine distinctions between levels of severity among clinical cases to be assigned to interventions of varying levels of intensity. In addition, future research could endeavor to identify additional problems that might be located at lower levels of the alcohol problems continuum. Specifically, we found that the problems we studied were disproportionately informative about higher levels of the continuum (see the aggregate information function portrayed in Figure 3). This is not particularly surprising, as the vast majority of the problems we studied define clinical conceptualizations of alcohol use disorder, and we modeled these problems in a community-based sample. It is, however, intriguing in light of the fact that certain problems we modeled clearly anchored the low end of the continuum, with difficulty values well below zero (the average level of problems within the sample). Indeed, one might even question the extent to which these very low-range but informative behaviors, such as intoxication and having more than five drinks on one occasion, are problems. This, however, emphasizes the continuous nature of variation within the alcohol problems realm, in the sense that more normal behaviors such as intoxication are located along the same continuum as more abnormal behaviors such as continuing to drink even when it resulted in medical complications. Yet this finding also points to the intriguing question of what other kinds of problems bridge these more low-range behaviors and the next level of problems that are just above the typical level for the sample. For example, the area just above zero (around.5) is indicated by the development of tolerance; what else bridges more normative problems and increased tolerance? Latent trait research that builds on the findings reported here could address this question. In addition, such research could be important in augmenting the highly informative 1-month duration indicators (see Table 1 and Figure 5) with more specific behavioral indicators of this intermediate range of alcohol problems. Clinical Assessment Issues Inherent in Moving Toward a Dimensional Conceptualization of Alcohol Problems The findings reported here dovetail well with other quantitative research on alcohol problems in showing how such problems define a continuum of variation. Thus, the data encourage a move toward a dimensional and psychometrically informed approach to conceptualizing, classifying, and assessing alcohol problems and related syndromes. Yet there are many important issues that still need to be tackled if the field is to move in this direction (see also Clark, Watson & Reynolds, 1995; Doucette, 2002; Widiger & Clark, 2000). The logic of much contemporary clinical assessment flows from categorical conceptualizations of psychopathology, and