{
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  "Title": "Simulation of Correlated Data with Multiple Variable Types\nIncluding Continuous and Count Mixture Distributions",
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  "Author": "Allison Cynthia Fialkowski",
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  "Description": "Generate continuous (normal, non-normal, or mixture\ndistributions), binary, ordinal, and count (regular or\nzero-inflated, Poisson or Negative Binomial) variables with a\nspecified correlation matrix, or one continuous variable with a\nmixture distribution.  This package can be used to simulate\ndata sets that mimic real-world clinical or genetic data sets\n(i.e., plasmodes, as in Vaughan et al., 2009\n<DOI:10.1016/j.csda.2008.02.032>).  The methods extend those\nfound in the 'SimMultiCorrData' R package.  Standard normal\nvariables with an imposed intermediate correlation matrix are\ntransformed to generate the desired distributions. Continuous\nvariables are simulated using either Fleishman (1978)'s third\norder <DOI:10.1007/BF02293811> or Headrick (2002)'s fifth order\n<DOI:10.1016/S0167-9473(02)00072-5> polynomial transformation\nmethod (the power method transformation, PMT).  Non-mixture\ndistributions require the user to specify mean, variance,\nskewness, standardized kurtosis, and standardized fifth and\nsixth cumulants.  Mixture distributions require these inputs\nfor the component distributions plus the mixing probabilities.\nSimulation occurs at the component level for continuous mixture\ndistributions.  The target correlation matrix is specified in\nterms of correlations with components of continuous mixture\nvariables.  These components are transformed into the desired\nmixture variables using random multinomial variables based on\nthe mixing probabilities.  However, the package provides\nfunctions to approximate expected correlations with continuous\nmixture variables given target correlations with the\ncomponents. Binary and ordinal variables are simulated using a\nmodification of ordsample() in package 'GenOrd'. Count\nvariables are simulated using the inverse CDF method.  There\nare two simulation pathways which calculate intermediate\ncorrelations involving count variables differently. Correlation\nMethod 1 adapts Yahav and Shmueli's 2012 method\n<DOI:10.1002/asmb.901> and performs best with large count\nvariable means and positive correlations or small means and\nnegative correlations.  Correlation Method 2 adapts Barbiero\nand Ferrari's 2015 modification of the 'GenOrd' package\n<DOI:10.1002/asmb.2072> and performs best under the opposite\nscenarios.  The optional error loop may be used to improve the\naccuracy of the final correlation matrix.  The package also\ncontains functions to calculate the standardized cumulants of\ncontinuous mixture distributions, check parameter inputs,\ncalculate feasible correlation boundaries, and summarize and\nplot simulated variables.",
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  "Date/Publication": "2018-07-01 12:46:01 UTC",
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    "corr_error",
    "corrvar",
    "corrvar2",
    "intercorr",
    "intercorr_cat_nb",
    "intercorr_cat_pois",
    "intercorr_cont",
    "intercorr_cont_nb",
    "intercorr_cont_nb2",
    "intercorr_cont_pois",
    "intercorr_cont_pois2",
    "intercorr_nb",
    "intercorr_pois",
    "intercorr_pois_nb",
    "intercorr2",
    "maxcount_support",
    "norm_ord",
    "ord_norm",
    "plot_simpdf_theory",
    "plot_simtheory",
    "rho_M1M2",
    "rho_M1Y",
    "summary_var",
    "validcorr",
    "validcorr2",
    "validpar"
  ],
  "_help": [
    {
      "page": "calc_mixmoments",
      "title": "Find Standardized Cumulants of a Continuous Mixture Distribution by Method of Moments",
      "topics": [
        "calc_mixmoments"
      ]
    },
    {
      "page": "contmixvar1",
      "title": "Generation of One Continuous Variable with a Mixture Distribution Using the Power Method Transformation",
      "topics": [
        "contmixvar1"
      ]
    },
    {
      "page": "corr_error",
      "title": "Error Loop to Correct Final Correlation of Simulated Variables",
      "topics": [
        "corr_error"
      ]
    },
    {
      "page": "corrvar",
      "title": "Generation of Correlated Ordinal, Continuous (mixture and non-mixture), and/or Count (Poisson and Negative Binomial, regular and zero-inflated) Variables: Correlation Method 1",
      "topics": [
        "corrvar"
      ]
    },
    {
      "page": "corrvar2",
      "title": "Generation of Correlated Ordinal, Continuous (mixture and non-mixture), and/or Count (Poisson and Negative Binomial, regular and zero-inflated) Variables: Correlation Method 2",
      "topics": [
        "corrvar2"
      ]
    },
    {
      "page": "intercorr",
      "title": "Calculate Intermediate MVN Correlation for Ordinal, Continuous, Poisson, or Negative Binomial Variables: Correlation Method 1",
      "topics": [
        "intercorr"
      ]
    },
    {
      "page": "intercorr_cat_nb",
      "title": "Calculate Intermediate MVN Correlation for Ordinal - Negative Binomial Variables: Correlation Method 1",
      "topics": [
        "intercorr_cat_nb"
      ]
    },
    {
      "page": "intercorr_cat_pois",
      "title": "Calculate Intermediate MVN Correlation for Ordinal - Poisson Variables: Correlation Method 1",
      "topics": [
        "intercorr_cat_pois"
      ]
    },
    {
      "page": "intercorr_cont",
      "title": "Calculate Intermediate MVN Correlation for Continuous Variables Generated by Polynomial Transformation Method",
      "topics": [
        "intercorr_cont"
      ]
    },
    {
      "page": "intercorr_cont_nb",
      "title": "Calculate Intermediate MVN Correlation for Continuous - Negative Binomial Variables: Correlation Method 1",
      "topics": [
        "intercorr_cont_nb"
      ]
    },
    {
      "page": "intercorr_cont_nb2",
      "title": "Calculate Intermediate MVN Correlation for Continuous - Negative Binomial Variables: Correlation Method 2",
      "topics": [
        "intercorr_cont_nb2"
      ]
    },
    {
      "page": "intercorr_cont_pois",
      "title": "Calculate Intermediate MVN Correlation for Continuous - Poisson Variables: Correlation Method 1",
      "topics": [
        "intercorr_cont_pois"
      ]
    },
    {
      "page": "intercorr_cont_pois2",
      "title": "Calculate Intermediate MVN Correlation for Continuous - Poisson Variables: Correlation Method 2",
      "topics": [
        "intercorr_cont_pois2"
      ]
    },
    {
      "page": "intercorr_nb",
      "title": "Calculate Intermediate MVN Correlation for Negative Binomial Variables: Correlation Method 1",
      "topics": [
        "intercorr_nb"
      ]
    },
    {
      "page": "intercorr_pois",
      "title": "Calculate Intermediate MVN Correlation for Poisson Variables: Correlation Method 1",
      "topics": [
        "intercorr_pois"
      ]
    },
    {
      "page": "intercorr_pois_nb",
      "title": "Calculate Intermediate MVN Correlation for Poisson - Negative Binomial Variables: Correlation Method 1",
      "topics": [
        "intercorr_pois_nb"
      ]
    },
    {
      "page": "intercorr2",
      "title": "Calculate Intermediate MVN Correlation for Ordinal, Continuous, Poisson, or Negative Binomial Variables: Correlation Method 2",
      "topics": [
        "intercorr2"
      ]
    },
    {
      "page": "maxcount_support",
      "title": "Calculate Maximum Support Value for Count Variables: Correlation Method 2",
      "topics": [
        "maxcount_support"
      ]
    },
    {
      "page": "norm_ord",
      "title": "Calculate Correlations of Ordinal Variables Obtained from Discretizing Normal Variables",
      "topics": [
        "norm_ord"
      ]
    },
    {
      "page": "ord_norm",
      "title": "Calculate Intermediate MVN Correlation to Generate Variables Treated as Ordinal",
      "topics": [
        "ord_norm"
      ]
    },
    {
      "page": "plot_simpdf_theory",
      "title": "Plot Simulated Probability Density Function and Target PDF by Distribution Name or Function for Continuous or Count Variables",
      "topics": [
        "plot_simpdf_theory"
      ]
    },
    {
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      "title": "Plot Simulated Data and Target Distribution Data by Name or Function for Continuous or Count Variables",
      "topics": [
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    },
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      "title": "Approximate Correlation between Two Continuous Mixture Variables M1 and M2",
      "topics": [
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    },
    {
      "page": "rho_M1Y",
      "title": "Approximate Correlation between Continuous Mixture Variable M1 and Random Variable Y",
      "topics": [
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      ]
    },
    {
      "page": "SimCorrMix",
      "title": "Simulation of Correlated Data with Multiple Variable Types Including Continuous and Count Mixture Distributions",
      "topics": [
        "SimCorrMix-package",
        "SimCorrMix"
      ]
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      "topics": [
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      "title": "Determine Correlation Bounds for Ordinal, Continuous, Poisson, and/or Negative Binomial Variables: Correlation Method 1",
      "topics": [
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    },
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      "title": "Determine Correlation Bounds for Ordinal, Continuous, Poisson, and/or Negative Binomial Variables: Correlation Method 2",
      "topics": [
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      "title": "Parameter Check for Simulation or Correlation Validation Functions",
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      "title": "Comparison of Correlation Methods 1 and 2",
      "author": "Allison C Fialkowski",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Methods Used in Both Pathways:",
        "Ordinal Variables:",
        "Continuous Variables:",
        "Continuous-Ordinal Pairs:",
        "Overview of Correlation Method 1:",
        "Simulation Process:",
        "Overview of Correlation Method 2:",
        "References"
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      "title": "Continuous Mixture Distributions",
      "author": "Allison C Fialkowski",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Example: Mixture of 2 Normal Distributions",
        "Step 1: Obtain the standardized cumulants",
        "Step 2: Simulate the variable",
        "Step 3: Determine if the constants generate a valid PDF",
        "Step 4: Select a critical value",
        "Step 5: Calculate the cumulative probability for the simulated variable up to $1 - \\alpha$",
        "Step 6: Plot graphs",
        "References"
      ],
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      "engine": "knitr::rmarkdown",
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        "Extension to more than two component distributions:",
        "Approximate Correlations for Continuous Mixture Variables:",
        "Correlation between continuous mixture variables M1 and M2:",
        "Correlation between continuous mixture variable M1 or M2 and other random variable Y:",
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      ],
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      "author": "Allison C Fialkowski",
      "engine": "knitr::rmarkdown",
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        "Examples",
        "Step 1: Obtain the distributional parameters",
        "Step 2: Check the parameter inputs",
        "Step 3: Calculate the lower skurtosis bounds for the continuous variables",
        "Simulation using Correlation Method 1:",
        "Step 4: Verify the target correlation matrix falls within the feasible correlation bounds",
        "Step 5: Generate the variables",
        "Step 6: Summarize the results numerically and Step 7: Summarize the results graphically",
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        "The Frechet-Hoeffding Correlation Bounds:",
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        "Correlation Method 2:",
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