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• Response to Dr Adamiak
  Ana V. Diez Roux
  Published on: 13 September 2002
• Population average and logistic models
  Grazyna T Adamiak
  Published on: 14 August 2002

• Published on: 13 September 2002

  Response to Dr Adamiak

  • Ana V. Diez Roux, Epidemiologist

  Dear Editor

  I thank Dr Adamiak for her careful reading of the glossary. I believe the confusion may be motivated by the fact that the sentence she refers to is not as clearly stated as it could have been. By "in the case of continuous dependent variables" I meant more precisely "when the response variable is normally distributed and the link function is identity (ie models usually referred to as linear models)". By "i...

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  Dear Editor

  I thank Dr Adamiak for her careful reading of the glossary. I believe the confusion may be motivated by the fact that the sentence she refers to is not as clearly stated as it could have been. By "in the case of continuous dependent variables" I meant more precisely "when the response variable is normally distributed and the link function is identity (ie models usually referred to as linear models)". By "in the case of non-normally distributed variables (for example, logistic models)" I meant more precisely "in the case of other models such as logistic models (where the response variable is the log odds of a binary outcome)". Of course, as Dr Adamiak notes, linear regression could be performed using dichotomous variables, and continuous variables can be dichotomized and modelled using a logistic model. The essence of the statement however is correct: In the linear model (as defined above), regression coefficients derived from random effects and population-average models are equivalent but in the logistic model they are not (see references 46 and 47 in the glossary for more details). I apologize for the confusion and thank Dr Adamiak for the opportunity to clarify this.

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  Conflict of Interest:
  None declared.

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• Published on: 14 August 2002

  Population average and logistic models

  • Grazyna T Adamiak, PhD Student

  Dear Editor

  I have found that under the heading Population-average models (page 592), when comparing the multilevel models to population-average models, the Author is stating that in the case of continuous dependent variables the coefficients are mathematically equivalent in the marginal models. In the next phrase the Author suggest "...but in the case of non-normally distributed variables (for example, logistic...

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  Dear Editor

  I have found that under the heading Population-average models (page 592), when comparing the multilevel models to population-average models, the Author is stating that in the case of continuous dependent variables the coefficients are mathematically equivalent in the marginal models. In the next phrase the Author suggest "...but in the case of non-normally distributed variables (for example, logistic models) etc.".

  Linear regression might be performed using dichotomous variables as well as dependent variables. The issue of mathematical equivalence is some what tricky, the value of dichotomous variables, if 1, might be also regarded as continuous whether mathematically there is infinity and we can continue to count 0.999999999 etc.

  There is no contradiction between the first statement and the second, after "but". Continuous variables might also be non-normally distributed, which is quite common in the context of measurements in health care, for example age distribution among inpatients is usually strongly skewed. Logistic regression might be performed on normally distributed variables as well.

  The logistic regression is based on the assumption of binomial distribution, which means that it does not matter if the variables are normally distributed or not. Both in the multiple linear and the logistic regressions there is an assumption about the variance of the outcome variable. In the linear model there is an expectation that the variance of the outcome variable is equal around the mean whether in the logistic regression the variance depends only on the mean. The linear models model the mean value of the outcome whether the logistic the logarithm of the odds of the outcome (referred to as logit). The relationship of multiple independent variables to outcome in the linear regression is such that the mean value of outcome changes with linearly with multiple independent variables. In the logistic model, the logit of outcome changes linearly with multiple independent variables. Thus, both are based on the assumption of linearity and averages appear to play a role in both.

  Grazyna Adamiak

  Reference

  (1) Katz MH. Multivariable analysis. A practical guide for Clinicians. Cambridge: Cambridge University Press.

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  Conflict of Interest:
  None declared.

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