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Mixtures of Acids03:27

Mixtures of Acids

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The pH of a solution containing an acid can be determined using its acid dissociation constant and its initial concentration. If a solution contains two different acids, then its pH can be determined using one of several methods depending upon the relative strength of the acids and their dissociation constants.
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The pH of a solution containing an acid can be determined using its acid dissociation constant and initial concentration. If a solution contains two different acids, then its pH can be determined using one of several methods depending on the relative strength of the acids and their dissociation constants.
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In the case of systematic errors, the sources can be identified, and the errors can be subsequently minimized by addressing these sources. According to the source, systematic errors can be divided into sampling, instrumental, methodological, and personal errors.
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Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
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The margin of error is also called the maximum error of an estimate. The margin of error is the maximum possible or expected difference between the observed sample parameter value and the actual population parameter value. For proportion, it is the maximum difference between the value of sample proportion obtained from the data and the true value of population proportion. As the true value of the population parameter is not known, the margin of error is calculated using the sample statistic.
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Extracting Spurious Latent Classes in Growth Mixture Modeling With Nonnormal Errors.

Kiero Guerra-Peña1, Douglas Steinley2

  • 1Pontificia Universidad Católica Madre y Maestra, Santiago, Dominican Republic.

Educational and Psychological Measurement
|May 26, 2018
PubMed
Summary
This summary is machine-generated.

Growth mixture modeling can incorrectly identify extra latent classes when data is not normally distributed. This occurs even when nonnormality is only in covariates, affecting model fit statistics and likelihood ratio tests.

Keywords:
fit indexgrowth mixture modelinglatent classeslikelihood ratio testsimulation studyspurious classes

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Area of Science:

  • Statistics
  • Psychometrics
  • Data Analysis

Background:

  • Growth mixture modeling (GMM) is used for subgroup identification and distribution approximation.
  • Current GMM application often indiscriminately uses fit statistics and likelihood ratio tests for both purposes.
  • This can lead to overextraction of latent classes and misinterpretation of spurious classes.

Purpose of the Study:

  • To evaluate Bayesian Information Criterion (BIC), sample-adjusted BIC, and bootstrap likelihood ratio test performance in GMM with nonnormal outcomes.
  • To assess the impact of nonnormal time-invariant covariates on latent class estimation with normal outcomes.

Main Methods:

  • Two simulation studies were conducted.
  • Examined GMM performance under various nonnormal conditions, including nonnormal time-invariant covariates.
  • Evaluated model fit indices and class enumeration accuracy.

Main Results:

  • Spurious latent classes can be selected when the population deviates from normality.
  • Optimal solutions may be identified even with nonnormal data, particularly when nonnormality resides in time-invariant covariates.
  • Model fit statistics and tests may not reliably distinguish correct from incorrect class solutions under nonnormality.

Conclusions:

  • Researchers must be cautious when interpreting latent classes from GMM with nonnormal data.
  • Nonnormality in time-invariant covariates can inflate the perceived number of latent classes.
  • Standard GMM fit indices may be misleading when distributional assumptions are violated.