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Lazarsfeld’s Numerous Contributions to Theory and History of Sociological Measurement: An Enduring Impact of Combined Professional Roles Inna F. Deviatko, Moscow

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How can we fully comprehend the relevance of Lazarsfeld’s ideas for the continuously evolving field of measurement and quantification in social sciences? Impediments to a catalog-oriented approach: new developments in the field bring up to date the initially underestimated, contentious or half-forgotten ideas. Examples of changing perceptions and evaluations: -(Supposed) benefits of panel designs for substantiating a causal inference in non-experimental social sciences (recent advances in panel data modeling − compare, e.g., Lazarsfeld, 1948 and Halaby, 2004); -(Unexpected)possible uses of indirect indicators and unobtrusive measures for Internet-based communication research (Deviatko, 2010); -(Impressive) recent refinements in deployment of categorical effect indicators for latent categorical variables and estimating the accuracy of data-driven classifications based on such indicators (Lazarsfeld and Henry, 1968; Bollen, 2002).

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By focusing on some salient and persistent themes in Lazarsfeld’s works on measurement and quantification in sociology; By trying to rely on texts written by Lazarsfeld in most important among his multiple professional roles, in a case considered now - one of them being the role of a methodologist and another – of a historian of social sciences. This strategy may be helpful for revealing the Lazarsfeld’s contributions into persistent attempts to solve the most daunting and long- dated problems of sociological measurement.

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Conditions of possibility for a “combined professional roles” approach: 1) Lazarsfeld “had a longstanding interest in the history of empirical social research which dated back to his Vienna years” (Obershall, 1978, p.199). 2) Some of his well-known papers on the history of sociological measurement (e.g., Lazarsfeld, 1957; Lazarsfeld, 1961 ) may shed some additional light on views Lazarsfeld held on the important topics: interchangeability of indicators, potential scope and limits of applying indirect and non-reactive measures in sociological research, possible benefits of using multiple manifest variables for improvement of latent variables measurement quality, probabilistic nature of interrelations between latent variables and their indicators.

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An Example. The Lazarsfelf’s idea of intrinsically probabilistic nature of interconnections between latent variables and manifest indicators Lazarsfeld, P.F. (1955). Recent Developments in Latent Structure Analysis (Sociometry, Vol. 18, No. 4): “It is taken for granted that between the latent property and the manifest indicator there exists a probability relationship”. Why? (This idea directly contradicts to basically deterministic view on linear relationships between unobservable human qualities and their effect indicators measured with error - e.g. in works by C. Spearman and H.M. Blalock). Lazarsfeld, P.F. (1961). Notes on the History of Quantification in Sociology − Trends, Sources and Problems (Isis, Vol. 52, No. 2) “Quetelet assumes a deterministic relation between the hypothetical construct and its manifestations. This obviously derives from his training as a natural scientist. In the natural sciences, for example, the acceleration of an object is related to a force in a deterministic way. But in the social sciences, indicators or symptoms have a probabilistic relation to the underlying propensity ”.

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Why did Lazarsfeld chose to think about latent propensity – manifest indicators relationship in probabilistic terms - 1? I.Probabilistic causality – an important idea that can be reconstructed from both his methodological and historical-sociological works. A probabilistic causal theory: causes change the probabilities of their effects (contrary to regularity theories of causation) Lazarsfeld was obsessed with causal analysis and, particularly, considered his ‘elaboration scheme” to be one of his four most important contributions (Cole, 2004).

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Why did Lazarsfeld choose to think about latent propensity – manifest indicators relationship in probabilistic terms – 1, cont’d? Related approach aimed at reduction of causation to probability without boiling it down to observed “regularities” – H.Reichenbach (1925; 1956). Lazarsfeld’s interpretation of probability: “Probability” = “Propensity” = disposition/tendency of a latent variable to cause an observed indicator value, or to determine a relative frequency of some observed values. Propensity here is a theoretical construct lying beyond a finite sample of relevant empirical observations and understood as a hidden cause of the former manifesting itself depending on a context.

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Why did Lazarsfeld chose to think about latent propensity – manifest indicators relationship in probabilistic terms - 2? II.Centrality of the “local independence” as a definition of latent variables (see Bollen, 2002 for a discussion and comparisons with other approaches toward conceptualization of latent variables): P[Y 1, Y 2, …, Y K ] = P[Y 1 │ η]P[Y 2 │ η]…[Y k │ η], where Y1, Y2, …, Y K are random observed variables, η is a vector of latent variables, P[Y1, Y2, …, Y K ] is the joint probability of the observed variables, and P[Y1 │ η]P[Y2 │ η]…[Yk │ η] are the conditional probabilities. Propensity ≠ Observed regularity in relationships between indicators. The correlations between indicators are ‘explained away” via latent variables.

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Lazarsfeld’s perception of causality: necessary clarification-1 How Lazarsfeld’s perception of causality could go together with his ideas of multifinality of a cause (common cause) and equifinality of independent causes in different contexts (closed causal fork and/or interchangeability of indices)? His views on propensities as causes of human action can be neatly described along the lines of probabilistic theories of causality.

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Important note: Lazarsfeld’s conception of causality is a singular one, referring to singular causal relations between particular attitudes, properties, actions and events in different contexts (no general causal claims). [ Singular causal claims refer to particular individuals, places, and times. General causal claims – to event-types and abstract properties ] This approach can be juxtaposed, e.g., with H. Blalock’s ‘determinist’ approach to causal relations between latent variables and their indicators. Blalock considered causal analysis in social sciences as aiming at formulation of general causal claims and considered latent variable-indicator relations as deterministic ones (yet measured with error).

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Lazarsfeld’s perception of causality: necessary clarification-2 Why Lazasfeld treatment of the role of causal claims in social sciences is mostly about singular actions, attitudes, etc. (i.e. singular causal claims)? Abbot (1998) considers this treatment as “part of Lazarsfeld’s gentling of the harshly scientistic paradigm The Language of Social Research (1955) established the modern concept of methodology and made the investigation of causes central to that methodological process…” BUT : “Explanation here means discovering general regularities, whereas causal assessment means "applying available knowledge to the understanding of a specific case, be it a person or a collective." (1955, p.387) (ibid)

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Lazarsfeld’s probabilistic definition of the nature of causal relations Lazarsfeld, Paul F., 1946. "Interpretation of statistical relations as a research operation.'' Address given at the Cleveland meeting of the American Socilogical Society (Reprinted in P. F. Lazarsfeld and M. Rosenberg, The language of social research. Glencoe, 111: Free Press, 1955). “We can suggest a clear-cut definition of the causal relationship between two attributes. If we have a relationship between "x" and "y"; and if for any antecedent test factor the partial relationships between x and y do not disappear, then the original relationship should be called a causal one. It makes no difference whether the necessary operations are actually carried through or made plausible by general reasoning”.

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Summing up Lazarsfeld probabilistic-causal approach to sociological measurement – in his own words -1: A. Measurement algorithm: 1) “make a list of all the indicators which have been proposed, often dividing them into subsets; these are called dimensions because they seem to represent various major aspects of the original image”; 2) “select a smaller number of this "universe of items" and combine them into a manageable "test“; 3) “collect statistical data in terms of the various indicators” and “compute covariations between observations (units) – individuals, groups, etc.” (Philosophy of Science and Empirical Social Research, 1962, p.467).

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Summing up Lazarsfeld probabilistic-causal approach to sociological measurement – in his own words-2: A. Measurement algorithm, cont’d: 4) “Finally, submit these matrices to mathematical analysis. This can follow a variety of models, but each is explicitly or implicitly guided by the following considerations. The investigator wants to end up with an ordering which does not exist in advance, but is an intended classification. It is to be derived from the statistical behavior of the indicators, but, at the same time, it permits us to establish the diagnostic value of each of them. Whatever the empirical outcome, we know that there is only a probabilistic relation between the intended classification and the indicators.” (ibid, p. 468).

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Summing up Lazarsfeld’s probabilistic-causal approach to sociological measurement – in his own words-3: B. Probabilistic causal relation between a position on a latent variable and observed values of indicators (and supposed interchangeability of the latter): “… we must find a way of combining the indicators, since by their nature the indicators are many, and their relations to outside variables are usually both weaker and more unstable than the underlying characteristic which we would like to measure.” (Evidence and Inference in Social Research, p. 104). “In the formation of indices we typically select a relatively small number of items from a large number of possible ones suggested by the concept and its attendant imagery. It is one of the notable features of such indices that their correlation with outside variables will usually be about the same, regardless of the specific "sampling" of items which goes into them from the broader group associated with the concept. This rather startling phenomenon has been labeled "the interchangeability of indices.” (ibid, p.105)

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Lazarsfeld’s perception of causality and his model of the formation of indices: unresolved questions-1 Questions remaining: Dealing with general causal claims (e.g., “more frustration – more aggression”) how could we use the probabilistic-causality approach to measurement relating singular observed actions, processes and events to latent individual dispositions/beliefs, group properties etc.? Seemingly, we need both kinds of causal claims and an integrated model of sociological measurement.

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Lazarsfeld’s perception of causality and his model of the formation of indices: unresolved questions-2 Questions remaining: Sampling indicators from the multidimensional "universe of items”: if pre-conceptualized dimensions are independent do they belong to the same latent theoretical construct? If no, why it’s a construct? If yes, what about local independence assumptions (uncorrelated measurement errors, no effect of indicators on each other)? How causal (formative) indicators can be incorporated into this model of measurement?

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