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Recall from simple linear regression that the slope coef cient 1 was interpreted as the change in the response variable for every unit increase in the predictor The slope coef cient 1 is interpreted analogously in logistic regression, but through the logit function That is, the slope coef cient 1 may be interpreted as the change in the value of the logit for a unit increase in the value of the predictor In other words, 1 = g(x + 1) g(x) In this section we discuss the interpretation of 1 in simple logistic regression for three cases: (1) a dichotomous predictor, (2) a polychotomous predictor, and (3) a continuous predictor To facilitate our interpretation, we need to consider the concept of odds Odds may be de ned as the probability that an event occurs divided by the probability that the event does not occur.

For example, earlier we found that the estimated probability that a 72-year-old patient has the disease is 61%, and the estimated probability that the 72-year-old patient does not have the disease is 39% Thus, the odds of a 72-year-old patient having the disease is odds = 061/039 = 156 We also found that the estimated probabilities of a 50-year-old patient having or not having the disease are 26% and 74%, respectively, providing odds for the 50-year-old patient to be odds = 026/074 = 035 Note that when the event is more likely than not to occur, odds > 1; when the event is less likely than not to occur, odds < 1; and when the event is just as likely as not to occur, odds = 1.

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Note also that the concept of odds differs from the concept of probability, since probability ranges from zero to 1, and odds can range from zero to in nity Odds indicate how much more likely it is that an event occurred compared to its not occurring.

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In binary logistic regression with a dichotomous predictor, the odds that the response variable occurred (y = 1) for records with x = 1 can be denoted as e 0 + 1 /(1 + e 0 + 1 ) (1) = = e 0 + 1 1 (1) 1/(1 + e 0 + 1 ) Correspondingly, the odds that the response variable occurred for records with x = 0 can be denoted as e 0 /(1 + e 0 ) (0) = = e 0 1 (0) 1/(1 + e 0 ) We also need to discuss the odds ratio (OR), de ned as the odds that the response variable occurred for records with x = 1 divided by the odds that the response variable occurred for records with x = 0.

That is, (1) [1 (1)] OR = (0) [1 (0)] e 0 + 1 = e 0 1 =e (43) The odds ratio has come into widespread use in the research community because of this simply expressed relationship between the odds ratio and the slope coef cient..

Several neo-analytic theories became particularly in uential in the decades following Freud s death. Among the most important of these were Jung s (1933, 1961) analytical psychology, Erikson s (1963, 1968) psychosocial theory, Sullivan s (1947, 1953) interpersonal theory, and the quasidynamic models of Adler (1921, 1923), Fromm (1941, 1947), and Horney (1937, 1945). These theories shared a Freudian emphasis on intrapsychic dynamics, childhood experiences, and unconscious processes as determinants of personality and psychopathology. However, each neo-analytic theorist rejected the classical psychoanalytic emphasis on sexuality as a key component of personality, and each theory sought to supplant sexuality with its own unique elements. Key features of the most prominent neo-analytic models are summarized in Table 5.3. Each neo-analytic model in Table 5.3 attained a loyal following during its heyday, but for the most part these neoanalytic models are no longer in uential in mainstream psychology. To be sure, aspects of these neo-analytic theories continue to be discussed (and on occasion isomorphically rediscovered by other personality theorists). However, with the exceptions of Erikson and Sullivan, the neo-analytic theories summarized in Table 5.3 have comparatively few adherents today, and they do not receive much attention within the clinical and research communities. Erikson s (1963, 1968) psychosocial approach continues to have a strong impact on personality and developmental research (Franz & White, 1985). Sullivan s (1953, 1956) interpersonal theory not only helped lay the groundwork for

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