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Tree View   Mplus Discussion Announcements Exploratory Factor Analysis Confirmatory Factor Analysis Structural Equation Modeling Multilevel Data/Complex Sample Latent Variable Mixture Modeling Growth Modeling of Longitudinal Data Timepoints Constraining residual variances in growth models with cat... Meaning of "variance" in LTM when outcome is categorical... Regressions Among Random Coefficients Computing effect sizes of of growth rates Model identification Growth Models with Censored Data? Power Estimation for Intervention Study Growth model with time-varying variable Invariance constraints on factor means Data interpretation Multi-level Growth Curve Modeling Specifying a reg path from inpt to slope Sample size in LGM? Interpretation of quadratic factor Comparing two growth trajectories Latent Growth Curve without the same observations Std and StdYX coefficients GGMM with categorical indicators of c Residual variance and R-Square of slope factor in LGM Interpreting output Growth models with age-specific indicators Confidence Intervals around Growth Curve Trajectories Longitudinal binary data Nonlinear LGM Growth Mixture Survival Analysis Residual output for GGMM with covariates Decomposition of variance in growth curve model Growth modeling with multiple trajectories Latent Class Growth Analysis Interpretation and significance of growth factors Latent growth model with weight variable Using time-varying predictor of latent class variable Multiple Indicator Growth Model Growth modeling with categorical variables Time scores associated with slope growth factors Time-varying covariates Regression paths or correlated residuals between intercep... Piecewise LGM Log odds in growth modeling with categorical data Variances of growth factors INTERPREATION OF LOG ODDS CHANGE WITH NON-LINEAR MODELS Log odds to odds interpretation with LGM Modeling the influence of time-varying covariatews in lat... The RUNALL Utility The Delta Method LGM Power Analysis Contrasts for growth-curve effects Centering Three level LGM with latent variables Meaning of the coefficients in penn8 Complex mixture (multilevel growth mixture model) Missing data Factor scores in Growth Mixture Modeling Initial Status by Treatment Interaction Negative variance Aggregate Data Growth Modeling and Fixed/Random effects m... LGM with two groups Monte Carlo Modeling Moderation and monte carlo modeling Equality constraints in prediction Factor analysis of latent slopes? Modeling error structure in growth model. References Growth modeling of latent repeated measures Invariance in observed variables across time Are slopes hard to predict? Question of interpreting covariate effects on a non-linea... Parallel process for non-time-strucutured data Two group LGM with time invariant covariates Two group LGM with categorical data Multiple cohort Constraint of x Effect Size Piecewise RMSEA Parameterization for Parallel & Sequential Growth process... Shape factors Power calculations in LGM Random Time Experiments, multivlevel data, noncompliance and weights Random times of observations for two variables Two parallel processes growth model Significant Digits for Printed Output BINARY MULTIPLE INDICATORS Effect of correlations between growth parameters Graphing growth curves LGM and within person correlations Reading data from ascii file Two groups analysis in growth models Added Growth LGM The old quadratic issue Piecewise Growth With Individually Varying Times of Meas. Fitting LGMs and MLMs and comparing results Cutpoints in Monte Carlo Simulation About "individually-varying times of observation" No. of decimal places Error structure in multilevel models Cohort-sequential design with missing data Testing the threshold assumption in LGC analysis GEE Dual trajectory model Logistic Growth Trajectories Interaction Model and Fit Indices Interpretation of coefficients in growth model Reciprocal effects between slopes Survival analysis with latent independent variables An identifiability issue in the EM algorithm PLOT3 adjusted by covariates Simple constraints on multigroup mean structure LGM Decision on Growth Mixture Model Using Means in LCGA models Warning messages in GGMM LCGA and Zero-Inflated Poisson Model Can Mplus mimic a HLM growth curve trick - setting scores... Levels of analysis in latent growth modeling Questions on LGC A flat slope issue? Intercept factor loadings Insufficient memory error message Regression to the mean in LGM Multivariate longitudinal analysis Equality constraints on the level-1 residual variances wi... Standardizing the dependent variables - or not! Question about RMSEA Very basic question Slopes as Indicators Constraining growth curves and interpreting quadratic curves Negative error variance LGCM and cross-lagged Mplus 2 vs Mplus 3 MAR instead of censored analyses? Fixed effects and sem growth models Significace of non-linear slopes Estimation of saturated model for LRT Growth models with varying time of intervention Multinomial regression with slope as predictor Growth of latent variable construct measured by multiple ... Multiple group parallel process GLM Interactions: cross-product vs. multiple group Sample size for LGM with missing data option Binary case / Growth Curve Analysis Individually varying times Growth modeling about Binary Responses Convergence Growth modeling and latent growth curve analysis Suggestion for Mplus 4 Documentation Non-Positive Definite Psi Matrix Which model would be appropriate to my data? Theta Matrix--Non positive Definite Latent growth factors predicting binary outcomes Simulation and Growth Modeling Admixture model - M+ LGM with different data collection between groups Basic questions concerning LGM GCM - wide range of ages at baseline Growth modeling with parallel processes Basics of model estimation Two-level latent growth modeling (ex 9.12-9.13) Intercept-slope relation Time-varying Covariates .. Comparing growth curves Comparing growth curves Dist Out - Time Vary CV - User Spec Start Values Missing Data Appropriate df in mean-adjusted chi-square calc Estimated means for latent growth factors Diff between LGC and RE models Growth of normed data Can this be estimated using LGC? Growth modeling with factor scores? Time-varying covariates in GMM Latent Growth Curve modeling - some Questions Class membership in LGC mixture modelling? Z-scores in LGM C#1 ON cg#1 command on GMM with known classes LGM: Multiple indicator and regular models Total effects Power to detect group differences in slope Slope as mediator Interpretation Issue of Growth Curve Modeling LGM with non-linear data Correlated Errors in Growth Curve Models Multigroup tests in multiple growth curve model Unbalanced data Graphical display Interaction between two slopes Natural log transformation in growth model Can Mplus 4 estiamte piecewise Gompertz model? Survival Mixture Analysis LGC for 3-group RCT Model fit indices for two-part growth model Mixture growth modeling on sequential processes Convergence for Linear vs. Nonlinear Models Parallel Process Growth Model Smoking cessation trial Poisson distribution for count data? Sibling clustering in LGM Saving intercept and slope scores Count Data in LDA Using the Poisson Distribution Binary Outcome Growth Model Growth model output Multiple group LGM -- some questions Lgm with missing data Multiple mediation analysis Multilevel growth model (three-level model) ... Baseline by Tx Interactions in LGM Interactions in zero-inflated poisson LGCM Simultaneous growth model-Complex survey data Wlsmv estimation How to get predicted values out of a growth model DTSA latent variable as a predictor? Multilevel vs. multivariate approach Limiting the latent classes in a known class Truly Nonlinear Models Growth curves and random slopes Fscoefficients in latent growth models Freely estimated time scores and more Interpreting Covariate Effects under ML estimation Auxillary threshold parameterization binary LCM Dynamic Nonlinear Panel data Binary LCM Significance test in LCM Class enumeration Recognising stabilty and change in a growth model Longitudinal modeling - mplus course Correlated indicator variables Growth curve reliability Power analysis for GGMM with distal outcome Growth factor intercepts vs means Specific case assignment to LCGA/GMM? GMM vs. GGMM Endogenous variables Growth modeling of reactivity Unconditional vs. conditional GMM Unconditional vs. conditional GMM Analysis type in growth modeling Modeling parallel processes Comparing nested GMMs The sign of the trend factor LL difference testing between two models LGM in intervention research Random effects Poisson model Nonpositive definite psi matrix Integration Points Singularity in covariance matrix Problems with Parameter Estimates Multiple group growth modeling Effect of the dependence on the invariance tests GMM vs. LCGA - interpretation of classes Model Test with growth models Two-part model with an ordinal outcome TECH11 and TECH14 GROWTH CURVE MODELING AND BIOMETRICS Latent Growth Curves with Twin Data Generating a new latent variable that represents Model selection, entropy, processing time No variation in growth parameter estimates Growth model for categorical outcome (ALT) Models: How To? Count and continuous variables in PPLGM Plot with individually-varying time Autoregressive model vs autocorrelated disturbance Standardized parameters in growth modeling Very unequal time intervals Two-part growth model with continuous data Is TSB2 implented in MPlus (L)LCA vs GMM Problem with adding a quadratic factor Notation for growth model with ordinal outcome Modeling a quadratic term with three time points Modeling a quadratic term with three time points GCM with Truncated Endogenous Variable Failure to achieve measurement invariance Correlation between intercept and slope Error decomposition 2-part piecewise models Outliers/influential case in Single Class Growth Monte Carlo setup for Growth Model Power Analysis Multigroup tests of indirect effects MG Growth Mixture Model (Syntax Issue) Warning flag for non+ def 1-order deriv matrix Individual Growth Parameters Missing data across Class LCGA Output for Class Membership GMM, Cont distal outcome, time varying covariate GGMM equations for ordered & continuous Lcgm and binary outcome Number of observations Modeling a proportion Time-lagged discontinuous growth curves Non-parametric GMM Zero-class in GMM: Model specifications A lot of questions... ...part two... ...part three... ...part 4... ...part 5... ...part 6... ...part 7... ...part 8... ...part 9... ...part 10... LTA and distal outcomes Growth model using zero-inflated poisson model GMM and Plotting Both Sample and Estimated Means Comparison of LGC and LCGA GMM warning Joint survival and logit model, selectivity Beta coefficient into effect size Model fit Latent growth curve code COVARIANCE MATRIX NOT POSITIVE DEFINITE GMM with two growth structures Individual growth curves Centering Age differences in parallel growth processes MIMIC growth model GMM with missing/truncated data Chi-square in discrete-time survival model Group-based GMM Zero cells in the bivariate table Higher Order Latent Growth Two-class growth and single-class growth Do growth factors have "standard deviations" Mplus crash Power for added growth Multilevel Latent Growth w/ Unstructured Time Growth modeling with Count data Growth model with no intercept Covariates & Constrained (0) Random Variances Conditional Mean (Intercept & Slope) Discrepancies in Estimated Cox PH Coefficients Using longtowide Mixture model for parallel growth Question about factor means Type=RANDOM and standardization Testing for intervention effects in LGMs Two-part modeling Random Starts Non linear parametric growth curves Residual variance/covariance Two-part growth model Cells with zero covariance coverage Syntax for basic growth model with ordinal outcome Question for chi-square test model fit Modeling 3 waves of data as quadratic trajectory When to run conditional models LGM to GMM Plotting probabilties for categorical outcome Slope Growth Factor Interpreting Linear and Quadratic Slope Intercept of outcome variable LCGA/GMM with time-varying covariates Estimated survival probabilities Interpreting thresholds (in version 5) Ecological Momentary Assessment Types of treatment in trajectory classes Quadratic Effects and Multilevel Growth Modeling Plot commands about individual growth curves Path diagram for lgc model with binary outcome Rank Longitudinal Data Growth model with interval and binary variables Modeling of parallel process Interaction between slope and a covariate Cross-domain versus parallel processes models Longitudinal Growth Mixture Models Syntax for curvilinear effects GMM and multiple indicators Semi-Continuous GMM Comparing slopes in piecewise models RESIDUAL COVARIANCE MATRIX NOT POSITIVE DEFINITE Starting Values in GMM Associations between slopes and intercepts Factor Scores as Predictors Effect of Covariate Categorical covariates OBSERVED INDIVIDUAL growth CURVE Test the parallel regression assumption LGCA and warnings Savedata for growth factors Mplus Short Courses August 21-22 at Johns Hopkins Odds ratio output for LGMM Negative Covariate on Negative Slope Effects of covariates Longitudinal Data Analysis Excercises Modeling with Time-Varying Covariates Missing Data Analysis Exercise: Pattern-Mixture Missing Data Excercise Cont'd: References Estimating Power and required Sample in GMM Models Time Points Varying Across Students Prelim analysis with ANOVA? Missingness in semicontinuous model Practice or retesting effects Graphing growth cuves for different groups Growth modeling with many time points Small sample size Parallel processes with multiple outcomes Multiple indicator linear growth models Missing at random and covariates Individual estimates of growth factors in LGM Growth Mixture Modeling with Unbalanced Data Non-convergence with centered data Correlated Residuals with Categorical Dependents Modeling intecept by T0 measure Cohort sequential designs Constraining correlations instead of covariances Covariates at second time point Confirmatory GGMM? Knownclass LGMM with nested data Plotting estimated factors Entropy and interpretation Control variables in longitudinal model Fit ARMA model in latent growth model in Mplus LGM with ZIP Number of observations Time score estimation and GMM Modeling intraindividual variability Effect size of predictor? Input question based on LSAY example Error variance. Effects of trends on levels Degrees of freedom in example 6.14 CFA & EFA in Multiple indicator growth model Comparing Type=Mean Structure and Type=Random MGA in parallel process model SAVEDATA command Latent distal regressed onto GGMM Error intercorrelations TSCORES without "|"? Latent distal/ggmm regression with knownclass Longtowide Multiple indicator LGM Regressing covariates on slope Chi-sq diff testing Estimation steps and samples How to Obtain Asymptotic Covariance Matrices Too much data? Extreme skew in longitudinal model Split plot question Survival analysis of two time to event outcomes Partial measurement invariance Error message about untrustworthy standard error Seasonal effects Longitudindal invariance analysis Parallel process regress on covariates PPM Question about plots Linear growth model with binary outcome Covariates and their interaction terms. Cohort effects GMM and missings Linear Hypothesis Test? Test for autocorrelation Positive linear slope, negative quadratic slope Class specific constraints in LCGA Multiple Groups on a Single Graph Intercept loadings DTSA - output interpretation Obtaning and comparing predicted values Constraints in a GMM Error trying to plot Sample and estimated means Correlated slopes Fit indices and stand residus with nonnormal data XWITH w/ multi indicator quadratic growth model ALT with explicit residual AR & ALT for Count data Count as DV Local solution problem?? Cubic spline model Intercept/slope correlations Regression of slope on intercept GMM with standardized variables Predicting Dummy Covariate from LGM Model Individually-varying times of observations? Bootstrap LGC Integration dimension DTSA Power Analysis Growth Model with Latent Predictors Effect size Confidence interval for distal outcome regression Growth curve modeling with multiple imputation Coupling-Effect - Interpretation Small sample for LGA? Problem with variable / Tech4 A question about TSCORES Coupling Effects < 0.000 Interpretation of results with covariates GMM with type=complex Parameter as a "function of change" Reordering classes Cross loadings in measurement instrument Hierachical effects of covariates in parallel GMM Sample selection and missing data Model Fit Statistics Contradicting results in GGMM Longitudinal proportion data First order autoregressive error covariance Power analysis on Latent Growth Mixture Model Model warning in LCGA Linear Spline Model GMM Residuals FIi Indices Handling missingness and zeros Latent growth modeling of binary outcome in Mplus Multiple group analysis within GGMM Intraclass Correlation in unconditional means LGCM regression slope on intercept vs. correlation Inequality constraints in a growth model Multicollinearity in LGM Understanding Implications of setting variance When do I use linear growth model? Error when correlating residuals Mplus versions Correlation of covariances Receiving estimates to more decimal places Interpretating LGC results for argument Interpretation of Y-axis in parallel GGMM Equivalent models in sequential LGCM Monte Carlo Simulation of Survival Data Individually varying occasions with nested models Multiple group growth curve-complete missing data Status change model Multigroup comparison Calculating Probabilities in growth model Ceiling effect in growth curve analyses Monte Carlo data generation for DTSA power Dynamic #discrete# choice models in MPlus Scaling in semi-continuous model Parallel growth model and zero cases Survival analysis without time-censoring LGCA with (unused) predictors in the dataset Growth factor covariances with quadratic growth Multivariate LGM, growth factor corrs >1.0 Modeling trajectory for latent variables GMM with type=complex GMM with different growth parameters Quadratic growth model with ZIP variables GMM with distal outcome SINGULARITY OF THE INFORMATION MATRIX Growth: multi-group pretest/postest & clustered GCM with chronological age on x-axis Specifying a second order curve model Incorrect Covariance Coverage Incremental Fit Indices Parallel growth and survival modeling Latent curve modeling with Couple data Interaction term with growth trajectory GMM and multi-level data Growth model with Version 6.0 and Version 5.2 Question about data import and ouputs export Warnings about starts value Autocorrelation in a Monte Carlo Post-Hoc - Differences at Each Time Point GMM/LCGA -- non-linear with few time points Categorial predictor of Latent Growth model Estimated means and variance for LGC models SEM with Cross Sectional-Time Series Data Measurement distance problem Multiple indicator LGM - Slope variance Class-specific time scores Time unstructured data with two slopes Plotting piecewise models Fit indices in complex survey data (TSCORE) Planned comparisons of slopes Analysis of change without latent variables Mediate effect Starting value Multivariate survival analysis Association between a stable slope and an outcome Plotting growth curves with varying time scores Thresholds Negative binomial growth model Latent Curve Modeling Categorical indep var in cross-lagged panel Software for plotting growth curves Measuring over time growth, but not on individuals Optimal decision of LRT Process Mixture T-Score question Modelling change in 2 repeated meausres Adjusted estimated means plot High Correlation Between S and Q Syntax for modeling "holiday effects" Negative Variance in Growth Factor Recommend and article? Covariances vs Correlations Default in GMM Mixed ANOVA using sampling weights? LONGTOWIDE Plots when modeling categorical data Covariates with LCGA Increase model fit Two level continuous time survival analysis Fit data to Zero-inflated Poisson Parallel Process and Multi-level Modeling Interaction covariates (intercept & slope) Standard disturbances reporting Latent growth modeling with three time points data Getting Mplus to properly read data Why a WITH statement affects the model fit Simulation of overdispersion in LGM Covariances among growth parameters in LGCM Effect size & slope var for multiple indicator LGM LGM with binary outcomes Continuous time and unbalanced measurement Modeling interaction effects in LGCA Multicollinearity bivariate autoregressive model Growth model for three parallel processes Interpret the growth factor means (binary obs var) Freed loading growth Simulating LGM models Input Plots Ploting trajectories of multiple subscales Multilevel piecewise latent growth model CPROB output Growth Model Questions Weighted Analyses The number of characters in input line TSCORE: time variation only available in wave 3 Minimum time points needed for LCGA RMESA CI Fixing outcome intercepts for parametrization? Latent Interactions in Growth Curve Modeling Mediation Growth Curve Modeling Conditional effects model Chi-Square Test for the Baseline Model Parallel growth curve process: error message Question on Muthén et al. (2011) Effect size Latent Class Growth Anlaysis Quadratic Issue MIMIC LGM Model Olsen and Schafer(20010 method and TSCORES option Psi matrix troubles Covariance matrix - toplix or homogeneous? ML-GMM with different within-level variables? Significant slope with WLSMV but not MLR estimator How to interpret the mean of stvc? Growth model and covariate adjustment J-shaped Likert items/scales No growth Plausible values with varying times of observation Coefficient changes when introducing MGA to PPM Set Bayesian Priors in LGM How to interpret continuous-time survival analysis Number of INTEGRATION Interpreting GGMM error messages (various) Significant effect on insignificant slope? Nested model GMM Introduction & Sample Size Add latent covariate to Level and Shape Model Growth process in meal composition study Model fits linear latent growth model Moderation in a Growth model for two processes Growth modeling with data missing by design Predictors of decline Univariate ALT model Growth curve multilevel modeling Multilevel growth modeling GMM: Fixing Common Intercepts with Random Slopes LGM interpretation Bootstrapped standard errors Correlations > 1 Monte carlo study with GMM LGM with "underdispered" count data Mod index of an indicator ON itself Equality constraints in cohort sequential design Second order growth model Getting SRMR in a cohort sequential model Missing outcome and classification quality Finding breakpoint in a piecewise model Multiple group multiple cohort growth model query Intercepts in orderered logit Multiple Indicator Linear Growth Model SEM with latent growth Multiple group analysis for count outcome LGC Randomized Clinical Trial Why slope variance changes in growth models Time varying covariates Parallel process model with interations Pre post data with pre post mediator LCGM with covariates Correlations with covariates Simultaneaous MODEL TEST statements vs one Zero-class in LCGA with categorical outcomes Zero-inflated model w/ categorical covariate Parallel process count and continuous outcomes Reporting negative binomial LGM results A negative variance/residual variance for i? Conditional Model Higher-order Multivariate growth curve models Individually time-varying measurements Multilevel LGC with unequal time intervals Measurement invariance bi-factor growth model Matched case-control analysis. Observed by latent variable interaction Time points for Cubic GMM Mid-point intercept in growth curve analysis Meaning of WITH on %BETWEEN% level? Dummy-Coded Predictors Reading CSV into Mplus Getting posterior class probabilities for cases? Large variances Non significant VLMR concerns Non-Linear Constraint in Survival Analysis Fixing residual variance to zero Individual varying times of observation Possible incorrect assignment to class Structure of data for LGC modeling Relating three sets of classes in Mplus Predicting Future Observations Attrition analysis LGM with time varying covariates Intercept with slope is not significant Competing Risk Model Use Growth Curves for Imbalanced Crossover Design? Person fit? Relative vs. absolute differences Modeling Outcomes of Change Plots for Growth Curves Mplus 7.1 Individual vs multigroup model fit Interpret coefficients for regression w/intercept Zero-inflated data in LCGA Interaction in Growth Modeling Item intercepts in bi-factor model Conditional LCGA/GMM with missing data Plot: estimated mean and estimed individual values Multiple group analysis Plots Hierarchical IRT model Bracketed Factor? Significance Testing of Variance Components Indirect effect of parallel process of LGM Moderators in LGM Negative residual variance Parallel process GMM - Z scores? GMM - including covariates or not? Interpretations of interactions in LGCM Fixing non-significant slopes - or not? Bivariate latent growth with latent moderation Constrain TSCORES in a Monte Carlo Growth Model Effect size for within subject longitudinal change GMM - variance of slope is fixed to be 0 Procedure for parallel process GMM Constraining slopes to equality Loglikelihood for H0 in VLMR and BLRT tests New 3-step approach for GMM with covariates Problems using a continuos covariate in GMM Differing number of response categories Zero inflated variables in a GMM Zero class in a Two-part GMM Joinpoint analysis? Piecewise Time points in mean trajectory curves Modeling longitudinal biomarker profiles LGM with large data set Centering of Factor Loadings; Effect on Chi-Square Factor scores with repeated measures Significance of growth factors Different output Mac vs. Windows Mover Stayer Single Variable Model Covariances with multiple time varying covariates Sample size for latent class growth analysis Correlation analysis for longitudinal variables Discontinuous Modeling GMM with mothers and children Constraints for Correlated Uniquenessess Cross-lagged models 2 Part LGM Correlation between 2 latent variables Exporting class membership in GMM Dyadic LGM GMM with Multiple Continuous Outcomes Adjusted estimated means for parallel processes How can LCA predict the future? Growth Curve&Pattern Mixture Model: Interpretation Missing p-value in conditional growth model Parallel piecewise growth w/ estimated time scores Model constraint and MLR Growth model combined with formative indicators Can I reference your online course material? Lagged effects Dichotomized variables in the latent growth model Model Fit Bootstrap P-Value Latent class linear mixed model? Unconditional LGM un- versus standardized variable 3-step manual calculation Chi-square difference testing Exploratory Latent Growth Models Testing slope variance LCGM OR GMM Sequential GMM Allowing correlations with residuals Control variables - 3 years follow-up study Searching for the right modeling approach Joint latent class analysis ZIP GMM with 1 zero class GMM with predictor covariates and distal outcomes Mediated effects of slope TECH11 and TECH14 in Bayes Growth Mixture Model Latent class mixture fitting for longitudinal data Effectivity intervention:comparison between groups Latent growth model with moderation Binary growth model: crashing w/no diagnostics Identifying members of classes in GMM Longitudinal polytomous IRT growth curves Logit values for GMM models in V7.2 Two-part latent growth modeling with two groups Outputting posterior probabilities Growth for a repeated latent class measure Effect sizes of linear trends GMM for skewed positive dependent variable The role of coding time in growth curve models Computing Variance Using Model Constraint Error intercorrelation Mediation analysis in latent growth curve model Different results from different versions Trajectory modeling of nominal data in MPlus Observed or latent covariates MILM with dropouts and WLSMV estimation Significance of covariates What analysis to use with 2 timepoints 1 variable? Comparing means at each timepoint within an LGM Standardized output for Latent Growth Model Model not running after updating version Different output using parameter labels Number of latent classes Mediation with LGCM Limitation to Latent Transition Analysis LTA with continuous indicators Plotting trajectories continuous data Conditional Multivariate Change Ssd Chemical for cleaning black Dollars, euros, Coding of slope coefficients in conditional LGCM Binary Growth Model GGMM with synthetic cohort data Two data points Parallel Process LGM GMM with combined cluster and knownclass commands Individually varying time points of measurements Importing data Error in covariate Missing Data Modeling Categorical Data Modeling Test topic

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