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examples in which hypnosis is present, it functions as a remarkably powerful technique for manipulating subjective experience and for intensifying emotional response. It provides a method for influencing people to imagine impossible events such as those that supposedly occurred in their ‘‘past lives,’’ the future, or during visits to other planets. If persons so manipulated misidentify the hypnotically induced fantasies, and classify them as previously unavailable memories, their confidence in the content of a particular ideology can be increased (Bainbridge and Stark 1980).

Hypnosis can also be used to lead people to allow themselves to relive actual traumatic life events (e.g., rape, childhood sexual abuse, neardeath experiences, etc.) or to fantasize the existence of such events and, thereby, stimulate the experience of extreme emotional distress. When imbedded in a reform program, repeatedly leading the person to experience such events can function simply as punishment, useful for coercing compliance.

Accounts of contemporary programs also describe the use of sophisticated techniques intended to strip away psychological defenses, to induce regression to primitive levels of coping, and to flood targets with powerful emotion (Ayalla 1998; Haaken and Adams 1983; Hockman 1984; Temerlin and Temerlin 1982; Singer and Lalich 1996). In some instances stress and fatigue have been used to promote hallucinatory experiences that are defined as therapeutic (Gerstel 1982). Drugs have been used to facilitate disinhibition and heightened suggestibility (Watkins 1980). Thought-re- form subjects have been punished for disobedience by being ordered to self-inflict severe pain, justified by the claim that the result will be therapeutic (Bellack et al. v. Murietta Foundation et al.).

Programs attempting thought reform appear in various forms in contemporary society. They depend on the voluntary initial participation of targets. This is usually accomplished because the target assumes that there is a common goal that unites him or her with the organization or that involvement will confer some benefit (e.g., relief of symptoms, personal growth, spiritual development, etc.). Apparently some programs were developed based on the assumption that they could be used to facilitate desirable changes (e.g., certain

rehabilitation or psychotherapy programs). Some religious organizations and social movements utilize them for recruitment purposes. Some commercial organizations utilize them as methods for promoting sales. In some instances, reform programs appear to have been operated for the sole purpose of gaining a high degree of control over individuals to facilitate their exploitation (Ofshe 1986; McGuire and Norton 1988; Watkins 1980).

Virtually any acknowledged expertise or authority can serve as a power base to develop the social structure necessary to carry out thought reform. In the course of developing a new form of rehabilitation, psychotherapy, religious organization, utopian community, school, or sales organization, it is not difficult to justify the introduction of thought-reform procedures.

Perhaps the most famous example of a thoughtreforming program developed for the ostensible purpose of rehabilitation was Synanon, a drugtreatment program (Sarbin and Adler 1970, Yablonsky 1965; Ofshe et al. 1974). The Synanon environment possessed all of Lifton’s eight themes. It used as its principle coercive procedure a highly aggressive encounter/therapy group interaction. In form it resembled ‘‘struggle groups’’ observed in China (Whyte 1976), but it differed in content. Individuals were vilified and humiliated not for past political behavior but for current conduct as well as far more psychologically intimate subjects, such as early childhood experiences, sexual experiences, degrading experiences as adults, etc. The coercive power of the group experience to affect behavior was substantial as was its ability to induce psychological injury (Lieberman, Yalom, and Miles 1973; Ofshe et al. 1974).

Allegedly started as a drug-rehabilitation program, Synanon failed to accomplish significant long-term rehabilitation. Eventually, Synanon’s leader, Charles Diederich, promoted the idea that any degree of drug abuse was incurable and that persons so afflicted needed to spend their lives in the Synanon community. Synanon’s influence program was successful in convincing many that this was so. Under Diederich’s direction, Synanon evolved from an organization that espoused nonviolence into one that was violent. Its soldiers were dispatched to assault and attempt to murder persons identified by Diederich as Synanon’s enemies (Mitchell, Mitchell, and Ofshe 1981).

The manipulative techniques of self-styled messiahs, such as People’s Temple leader Jim Jones (Reiterman 1982), and influence programs operated by religious organizations, such as the Unification Church (Taylor 1978) and Scientology (Wallis 1977; Bainbridge and Stark 1980), can be analyzed as thought-reform programs. The most controversial recruitment system operated by a religious organization in recent American history was that of the Northern California branch of the Unification Church (Reverend Moon’s organization). The influence program was built directly from procedures of psychological manipulation that were commonplace in the human-potential movement (Bromley and Shupe 1981). The procedures involved various group-based exercises as well as events designed to elicit from participants information about their emotional needs and vulnerabilities. Blended into this program was content intended to slowly introduce the newcomer to the group’s ideology. Typically, the program’s connection with the Unification Church or any religious mission was denied during the early stages of the reform process. The target was monitored around the clock and prevented from communicating with peers who might reinforce doubt and support a desire to leave. The physical setting was an isolated rural facility far from public transportation.

Initial focus on personal failures, guilt-laden memories, and unfulfilled aspirations shifted to the opportunity to realize infantile desires and idealistic goals, by affiliating with the group and its mission to save the world. The person was encouraged to develop strong affective bonds with current members. They showed unfailing interest, affection, and concern, sometimes to the point of spoon-feeding the person’s meals and accompanying the individual everywhere, including to the toilet. If the unfreezing and change phases of the program succeeded, the individual was told of the group’s affiliation with the Unification Church and assigned to another unit of the organization within which refreezing procedures could be carried forward.

POLICE INTERROGATION AND FALSE

CONFESSIONS

Police interrogation in America was transformed in the twentieth century from a method of gaining

compliance relying largely on physical coercion into one that relies almost exclusively on psychological means (Leo 1992). Psychological methods of interrogation were developed to influence persons who know they are guilty of a crime to change their decision to deny guilt, to admit responsibility for the crime, and to confess fully to their role in the crime (see Hilgendorf and Irving 1981; Ofshe and Leo 1997a,b). Compared to the other extreme influence environments described in this entry, a police interrogation is of relatively short duration and is entirely focused on the single issue of eliciting a confession. It is nevertheless an environment in which a person can be influenced to make a dramatic shift in position—from denial of guilt to confession.

The techniques and tactics that lead a guilty suspect to admit guilt constitute an impressive display of the power of influence to change a person’s decision even when the consequence of the shift is obviously disadvantageous. If the procedures of interrogation are misused, modern interrogation methods can have an even more impressive result. If the influence procedures and techniques of modern interrogation methods are directed at innocent persons, some false confessions will result (Bedau and Radelet 1987; Leo and Ofshe 1998). In most instances when an innocent person is led to give a false confession the cause is coer- cion—the use of a threat of severe punishment if the person maintains that he is innocent and an offer of leniency if he complies with the interrogator’s demand to confess. Most persons who decide to comply and offer a false confession in response to coercion remain certain of their innocence and know that they are falsely confessing in order to avoid the most severe possible punishment.

Under some circumstances, however, interrogation tactics can cause an innocent person to give what is called a persuaded false confession—a false confession that is believed to be true when it is given. Influence procedures now commonly used during modern police interrogation can sometimes inadvertently manipulate innocent persons’ beliefs about their own innocence and, thereby, cause them to falsely confess. Confessions resulting from accomplishing the unfreezing and change phases of thought reform are classified as persuaded false confessions (Kassin and Wrightsman 1985;

Gudjonsson and MacKeith 1988; Ofshe and Leo 1997a). Although they rarely come together simultaneously, the ingredients necessary to elicit a temporarily believed false confession are: erroneous police suspicion, the use of certain commonly employed interrogation procedures, and some degree of psychological vulnerability in the suspect. Philip Zimbardo (1971) has reviewed the coercive factors generally present in modern interrogation settings. Richard Ofshe and Richard Leo (1989, 1997a) have identified those influence procedures that if present in a suspect’s interrogation contribute to causing unfreezing and change.

Techniques that contribute to unfreezing include falsely telling a suspect that the police have evidence proving the person’s guilt (e.g., fingerprints, eyewitness testimony, etc.). Suspects may be given a polygraph examination and then falsely told (due either to error or design) that they failed and the test reveals their unconscious knowledge of guilt. Suspects may be told that their lack of memory of the crime was caused by an alcoholor drug-induced blackout, was repressed, or is explained because the individual is a multiple personality.

The techniques listed above regularly appear in modern American police interrogations. They are used to lead persons who know that they have committed the crime at issue to decide that the police have sufficient evidence to convict them or to counter typical objections to admitting guilt (e.g., ‘‘I can’t remember having done that.’’). In conjunction with the other disorienting and distressing elements of a modern accusatory interrogation, these tactics can sometimes lead innocent suspects to doubt themselves and question their lack of knowledge of the crime. If innocent persons subjected to these sorts of influence techniques do not reject the false evidence and realize that the interrogators are lying to them, they have no choice but to doubt their memories. If the interrogator supplies an explanation for why the suspect’s memory is untrustworthy, the person may reason that ‘‘I must have committed this crime.’’

Tactics used to change the suspect’s position and elicit a confession include maneuvers designed to intensify feelings of guilt and emotional distress following from the suspect’s assumption of guilt.

Suspects may be offered an escape from the emotional distress through confession. It may also be suggested that confession will provide evidence of remorse that will benefit the suspect in court.

RECOVERED MEMORY PSYCHOTHERAPY

The shifts in belief and conduct promoted during political reeducation concern an intellectual analysis of society and one’s role it; in the context of high control groups the beliefs are about theology and one’s role in a community; and in police interrogation the newly created beliefs concern a crime the suspect has no knowledge of having committed. The progression in these illustrations is from influence efforts directed at an intellectual or philosophical assumption to that of an influence effort directed at changing beliefs about a single fact—Did the suspect commit a crime and not know of it due to a memory defect? The final example of extreme influence and belief change is arguably the most dramatic example of the power of interpersonal influence and particular influence techniques to change a person’s beliefs about the historical truth relating to a major dimension of his or her life history, such as whether or not he or she had been viciously raped and horribly brutalized by a parent (or parents, or siblings, or teachers, or neighbors, etc.) for periods of as long as two decades.

Psychotherapy directed at causing a patient to retrieve allegedly repressed and therefore supposedly unavailable memories (e.g., of sexual abuse, and/or having spent one’s life suffering from an unrecognized multiple personality disorder, and/or having spent one’s childhood and teenage years as a member of a murderous satanic cult) is one of the most stunning examples of psychological/ psychiatric quackery of the twentieth century. It is also perhaps the most potent example of the power of social influence to predictably create beliefs (in this case beliefs that are utterly false) and thereby alter a person’s choices and conduct (Loftus 1994; Perdergrast 1995; Ofshe and Watters 1994; Spanos 1996).

The elements of a thought-reforming process are visible in the steps through which a patient undergoing recovered memory therapy is manipulated. The patient’s identity is destabilized by the therapist’s insistence that the reason for the patient’s distress or mental illness is that she or he

suffered a series of sexual traumas in childhood that he or she don’t know about because he or she has repressed them. Recovered memory therapists organize their treatment programs on the presumption that repression exists despite the fact that the notion of repression was never more than a fanciful, unsubstantiated speculation that was long ago rejected as useless by the scientific community that studies human memory (Loftus 1994; Crews 1998; Watters and Ofshe 1999). Recovered memory therapists rely on assertions of authority, claims of expertise, and outright trickery (e.g., inducing the patient to experience hypnotic fantasies of sexual abuse that they lead patients to misclassify as memories and interpreting the patient’s dreams as proof that they suffer from repressed memories) to convince the patient of the existence of repression. Recovered memory therapists rely on the alleged ‘‘repression mechanism’’ to undermine patients’ confidence in their normal memories of their lives. If patients can be successfully convinced that repression exists and that the hypnotic fantasies that the therapist suggests to them are memories of events that happened during their lives, they can no longer trust that they know even the broad outlines of their life histories.

Once the patient’s identity has been destabilized, the therapist guides the patients to build a new identity centered on his or her status as victim of sexual abuse. This victim role may include requiring the patient to learn to act as if she or he suffers from multiple personality disorder, or suggesting that the patient publicly denounce, sue, or file criminal charges against the persons who supposedly abused them.

CONCLUSION

Extreme influence environments are not easy to study. The history of research on extreme influence has been one in which most of the basic descriptive work has been conducted through posthoc interviewing of persons exposed to the influence procedures. The second-most frequently employed method has been that of participant observation. In connection with work being done on police interrogation methods, it has been possible to analyze contemporaneous recordings of interrogation sessions in which targets’ beliefs are actually made to undergo radical change. All this work

has contributed to the development of an understanding in several ways.

Studying these environments demonstrates that the extremes of influence are no more or less difficult to understand than any other complex social event. The characteristics that distinguish extreme influence environments from other examples of social settings are influence in the order in which the influence procedures are assembled and the degree to which the target’s environment is manipulated in the service of social control. These are at most unusual arrangements of commonplace bits and pieces.

As it is with all complex, real-world social phenomena that cannot be studied experimentally, understanding information about the thoughtreform process proceeds through the application of theories that have been independently developed. Explaining data that describe the type and organization of the influence procedures that constitute an extreme influence environment depends on applying established social-psychological theories about the manipulation of behavior and attitude change. Assessing reports about the impact of the experiences on the persons subjected to intense influence procedures depends on the application of current theories of personality formation and change. Understanding instances in which the thought-reform experience appears related to psychiatric injury requires proceeding as one would ordinarily in evaluating any case history of a stressrelated or other type of psychological injury.

(SEE ALSO: Attitudes; Persuasion; Social Control)

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RICHARD J. OFSHE

FACTOR ANALYSIS

Factor analysis is a mathematical and statistical technique for analyzing differences among units of analysis and the structure of relationships among variables assessing those units. The units of analysis may be persons, groups, organizations, ecological units, or any other justifiable basis of aggregation although persons are most often the focus of analysis. The chief purpose of the method is the attainment of scientific parsimony, which is achieved by positing a set of latent common factors that underlie the data. The factor model was developed by Charles Spearman (1904a, 1927) to be used to describe economically the correlations among mental test scores observed for persons. Spearman’s famous bi-factor model of intelligence held that measures of mental abilities had two major sources: a factor common to all measures of ability, which he called the g-factor (factor of general ability), and a specific component of variation (an s-factor) unique to the test. For example, a test of numerical ability may be affected in part by a general factor of intelligence as well as a factor specific to numerical aptitude. This model, although never the predominant psychological theory of mental tests, has persisted in the culture in the sense that people often believe there is a general factor of intelligence underlying performance across different domains (see Gould 1981 for a critique of this view).

Although Spearman’s work did not go very far beyond such a simple model, his approach to model construction and theory testing using tetrad

differences has provided the basis for much further work (see, e.g., Glymour et al. 1987). Many contemporaries of Spearman—Cyril Burt, Karl Pearson, Godfrey Thomson, J. C. Maxwell Garnett, and others—working in the fields of human abilities and statistics also contributed to the development of factor analysis. Several worked to modify Spearman’s bi-factor model to include multiple factors of intelligence. But the most radical departure from the g-factor view of human intelligence came with Thurstone’s (1938) publication of Primary Mental Abilities, in which he demonstrated empirically through the application of multiple factor analysis that several common factors were necessary to explain correlations among measures of human abilities. While Thurstone (1947) is usually credited with the popularization of this more general technique, the concept of multiple factor analysis first arose in the work of Garnett (1919–1920; see Harmon 1976).

Multiple factor analysis proved to be a major advance over the Spearman model, which was later to be seen as a special case (the one-factor case). Multiple factor analysis permitted a general solution to the possibility of positing multiple factors (k) in a set of variables (p). Within this framework, two competing research strategies emerged, each resting on distinct principles. One was based on Pearson’s principle of principal axes, which was later developed by Hotelling (1933) as the method of principal components. This approach emphasized the objective of ‘‘extracting’’ a maximum of variance from the set of p variables so that the k factors explained as much of the variance in

the variables as they could. This tradition still exists in approaches to factor analysis that rely on principal components analysis, and, although many researchers use the technique, they are likely to be unaware of the objectives underlying the approach (see Harman 1976).

In contrast to the strategy of maximizing the variance explained in the variables, the other basic strategy—more squarely in the tradition of Spearman—emphasized the objective of reproducing the observed correlations among the variables. These two objectives—one emphasizing the extraction of maximum variance in the variables and the other emphasizing the fit to the correlations among the variables—eventually became the object of serious debate. However, with time there has emerged a consensus that the ‘‘debate’’ between these approaches rested on a misconception. The method of principal axes, which is the basis of principal components analysis—involving the analysis of a correlation matrix with unities in the diagonal—is now better understood as a computational method and not a model, as the factor analysis approach is now considered (see Maxwell 1977).

The early developments in the field of factor analysis and related techniques were carried out primarily by psychometricians. These early developments were followed by many important contributions to estimation, computation, and model construction during the post–World War II period. Some of the most important contributions to the method during the 1950s were made by a sociologist, Louis Guttman. Guttman made important contributions to the resolution of the issue of deciding upon the best number of latent factors (Guttman 1954), the problem of ‘‘factor indeterminacy’’ (Guttman 1955), and the problem of estimating communalities (Guttman 1956), among many others. Guttman (1960) also invented yet a third model, called image analysis, which has a certain elegance but is rarely used (see Harris 1964; Kaiser 1963).

Research workers in many fields made contributions to the problem of deciding how best to represent a particular factor model in a theoretical/geometrical space, via the transformation or rotation of factors. Methods of rotation included the quartimax (Neuhaus and Wrigley 1954), varimax (Kaiser 1958), and oblimax (Harman 1976), among

others. Several contributions were made during the early development of factor analysis with respect to the most useful strategies for estimating factor scores (see reviews by Harris 1967 and McDonald and Burr 1967) and for dealing with the problem of assessing factorial invariance (e.g., Meredith 1964a, 1964b; Mulaik 1972). Beginning in the mid-1960s the advances in the field of factor analysis have focused on the development of maxi- mum-likelihood estimation techniques (Lawley and Maxwell 1971; Jöreskog 1967; Jöreskog and Lawley 1968); alternative distribution-free techniques (Bentler 1983, 1989; Bentler and Weeks 1980; Browne 1974, 1984; Browne and Shapiro 1988); the development of confirmatory factor analysis, which permits the setting of specific model constraints on the data to be analyzed (Bentler 1989; Jöreskog 1966, 1967, 1970, 1971a, 1973; Jöreskog and Sörbom 1986); and the development of factor analysis strategies for categoric variables (Christofferson 1975; Jöreskog and Sörbom 1988; Muthén 1983, 1988).

Factor analysis is used extensively by sociologists as a research tool. It is used in at least four related ways. First, it is frequently used as a data reduction or item analysis technique in index construction. Second, it is used as an exploratory device for examining the dimensional structure of content within a well-specified domain. Third, it is used as a confirmatory, hypothesis-testing tool aimed at testing prior hypotheses about the dimensional structure of a set of variables. And fourth, it is used to conceptualize the relationships of multiple indicators of latent variables in a causal modeling framework in which a factor model is assumed for the relationships between latent variables and their indicators. After a brief introduction to each of these four ways in which factor analytic tools are used in sociological research, this discussion covers the basic factor model and issues that arise in its application, either in the exploratory or confirmatory frameworks of analysis.

DATA REDUCTION APPROACHES

When a researcher wishes to build a composite score from a set of empirical variables, factor analysis and related techniques are often useful. Indeed, it is perhaps in this area of ‘‘index construction’’ that factor analysis is most often used by sociologists. There are various related data

reduction approaches that fall under the heading of ‘‘dimensional analysis’’ or ‘‘cluster analysis,’’ but the basic goal of all these techniques is to perform some decomposition of the data into sets of variables, each of which is relatively independent and homogeneous in content. When factor analysis is used in this way the researcher is essentially interested in determining the sets of linear dependence among a set of variables that are intended to measure the same general domain of content. The factor analysis of such variables may proceed in a number of different ways, but the basic goal is to determine the number of clusters of homogeneous content and the extent of relationship among various clusters or factors. Relationships among factors may be conceptualized either in terms of uncorrelated (or orthogonal) sets of factors or in terms of correlated (or oblique) factors. Such analyses are often supplemented with information on how to build ‘‘factor scores,’’ with item-analysis information, such as item-to-total score correlations, and with information estimating the ‘‘internal consistency’’ or ‘‘reliability’’ of such composite scores (see Greene and Carmines 1979; Maxwell 1971).

When using factor analysis and related techniques as a basis for index construction, one of two situations is typically the case. Either the investigator has some a priori basis for expecting that items in a set have a common factor (or common factors) underlying them, and therefore the investigator has certain well-founded expectations that the items can be combined into a scale, or the investigator has no a priori set of hypotheses for what clusters will be found and is willing to let the inherent properties of the data themselves determine the set of clusters. In the first case confirmatory factor models are appropriate, whereas in the second case exploratory methods are mandated. In either case the use of factor analysis as a data reduction tool is aimed at the development and construction of a set of ‘‘scores,’’ based on factor analysis, that can then be introduced as variables in research.

Exploratory Factor Analysis. As noted above, in situations where the researcher has no a priori expectations of the number of factors or the nature of the pattern of loadings of variables on factors, we normally refer to applications of factor analysis as exploratory. In the case of exploratory factor analysis the goal is to find a set of k latent

dimensions that will best reproduce the correlations among the set of p observed variables. It is usually desirable that k be considerably less than p and as small as possible. In exploratory factor analysis one typically does not have a clear idea of the number of factors but instead begins with uncertainty about what the data will reveal. The most common practice is to find k orthogonal (uncorrelated) dimensions that will best reproduce the correlations among the variables, but there is nothing intrinsic to the factor analytic model that restricts the conceptual domain to several orthogonal dimensions.

Confirmatory Factor Analysis. Confirmatory factor analysis, in contrast, refers to situations in which the investigator wishes to test some hypotheses regarding the structure of relationships in the presence of a strong set of assumptions about the number of factors, the values of the factor pattern coefficients, the presence or absence of correlations of factors, or other aspects of the model. In confirmatory factor analysis it is essential that one begin with a theory that contains enough detailed specification regarding constraints that should be imposed on the data in order to provide such a test, whereas in exploratory factor analysis there is no requirement that one specify the number of factors and expected relationships to be predicted in the data. Confirmatory approaches are thus more theory-driven, whereas exploratory approaches are more data-driven (see Alwin 1990). However, much of the so-called confirmatory factor analysis that is carried out in modern social and behavioral science is in fact exploratory, and much current research would be more realistically appraised if such confusion did not exist. Often, there is considerable tinkering with ‘‘confirmatory’’ models in order to improve their fit to the data, either by removing variables or by loosening up (or ‘‘freeing’’) certain parameters. It is also often the case that the ‘‘confirmatory’’ factor analyses are actually preceded by an exploratory analysis, and then a confirmatory model based on these results is fit to the same data. Although very common, this approach ‘‘capitalizes’’ on chance and gives an illusory sense that one has confirmed (or verified) a particular model. Placed in the proper perspective, there is nothing in principal wrong with the approach, as long as the ‘‘test’’ of the model is cross-validated in other data.

FACTOR ANALYSIS AND MULTIPLE INDICATOR CAUSAL MODELS

In the 1960s and 1970s, with the introduction of causal modeling strategies in social science (see Blalock 1964; Duncan 1966, 1975; Heise 1968), a fundamental shift occurred in the nature and uses of the common factor models by sociologists. Methods and the logic of causal modeling with nonexperimental statistical designs had been around for a long time. Due largely to the influence of Lazarsfeld (1968), causal inference strategies had been prevalent especially among analysts of sample survey data since the 1940s, but the research strategies were based on tabular presentation of data and the calculation of percentage differences. In the early 1960s there was a general infusion of techniques of causal modeling in sociology and other social science disciplines. Path analysis, principal of these newly adopted techniques, of course, was invented before 1920 by the great geneticist Sewall Wright, but his contributions were not appreciated by social and behavioral scientists, including the psychometricians responsible for the development of factor analysis. Wright (1921) developed path models as deductive systems for deriving correlations of genetic traits among relatives of stated degree. He also used the method inductively to model complex economic and social processes using correlational data (Wright 1925).

Psychometricians, like Spearman, had been dealing with models that could be thought of as ‘‘causal models,’’ which could be understood in Wright’s path analysis framework—common factors were viewed as the causes underlying the observed variables—but Spearman and others who developed common factor models were unfamiliar with Wright’s work. None of the early psychometricians apparently recognized the possibility of causal relationships among the latent variables of their models, or for that matter among their indicators. However, with the publication of work by Jöreskog (1970) and others working in the ‘‘new’’ field of structural equation models (see Goldberger 1971, 1972; Goldberger and Duncan 1973; Hauser and Goldberger 1971); the convergence and integration of linear models in the path analysis tradition and those in the factor analysis tradition provided a basic ‘‘breakthrough’’ in one of the major analytic paradigms most prevalent in social science. These developments were assisted by the interest in conceptualizing measurement

errors within a causal analysis framework. A number of researchers began to incorporate conceptions of measurement error into their causal analyses (Alwin 1973a, 1974; Blalock 1965, 1969, 1970; Costner 1969; Duncan 1972; Heise 1969; Siegel and Hodge 1968), ushering in a new approach that essentially combined factor models and path models.

At about this same time, Karl Jöreskog and his colleagues were developing efficient procedures for estimating the parameters of such models— called LISREL models, named after Jöreskog and his colleagues’ computer program, LISREL—and this provided a major impetus for the widespread use of confirmatory approaches to the estimation of structural equation models. Jöreskog’s (1967) early contributions to maximum-likelihood factor analysis became readily applied by even the most novice of analysts. Unfortunately, the widespread availability of these techniques to researchers who do not understand them has led to serious risks of abuse. This can be true of any technique, including the techniques of exploratory factor analysis. In any event, the proper use and interpretation of the results of LISREL-type model estimation is a significant challenge to the present generation of data analysts.

THE COMMON FACTOR MODEL

The formal mathematical properties of the common factor model are well known and can be found in many of the accompanying references. It is useful for purposes of exposition briefly to review its salient features. Although the model can be most compactly represented using vector and matrix notation, it is normally best to begin with a scalar representation for the data, such as in equation 1.

z1 = a11ƒ1 + a12ƒ2 + ... + a1kƒk + u1 z2 = a21ƒ1 + a22ƒ2 + ... + a2kƒk + u2

Here the z variables are empirical quantities observed in a sample of units of observation (e.g., persons, groups, ecological units), and for present purposes the variables are standardized to have a mean of zero and standard deviation of unity. This