General Linear Model — gamlj

General Linear Model. Estimates models using lm() function and provides options to facilitate estimation of interactions, simple slopes, simple effects, post-hoc tests, contrast analysis, effect size indexes and visualization of the results.

gamlj_lm(
  formula = NULL,
  data,
  dep = NULL,
  fixed_intercept = TRUE,
  factors = NULL,
  covs = NULL,
  model_terms = NULL,
  nested_terms = NULL,
  nested_intercept = NULL,
  omnibus = "F",
  estimates_ci = TRUE,
  betas_ci = FALSE,
  ci_width = 95,
  ci_method = "wald",
  boot_r = 1000,
  contrasts = NULL,
  contrast_custom_values = NULL,
  contrast_custom_focus = NULL,
  show_contrastnames = TRUE,
  show_contrastcodes = FALSE,
  vcov = FALSE,
  plot_x = NULL,
  plot_z = NULL,
  plot_by = NULL,
  plot_raw = FALSE,
  plot_yscale = FALSE,
  plot_xoriginal = FALSE,
  plot_black = FALSE,
  plot_around = "ci",
  plot_jn = FALSE,
  emmeans = NULL,
  posthoc = NULL,
  simple_x = NULL,
  simple_mods = NULL,
  simple_interactions = FALSE,
  covs_scale = NULL,
  covs_conditioning = "mean_sd",
  ccm_value = 1,
  ccp_value = 25,
  ccra_steps = 3,
  covs_scale_labels = "labels",
  adjust = list("bonf"),
  posthoc_es = list("dm"),
  d_ci = FALSE,
  es = list("beta", "etap"),
  homo_test = FALSE,
  colli_test = FALSE,
  qq_plot = FALSE,
  norm_test = FALSE,
  norm_plot = FALSE,
  resid_plot = FALSE,
  intercept_info = FALSE,
  es_info = FALSE,
  dep_scale = "none",
  se_method = "standard"
)

Arguments

formula: (optional) the formula of the model, see the examples. If not passed model terms should be defined as a list in model_terms option.
data: the data as a data frame
dep: a string naming the dependent variable from data; the variable must be numeric. Not needed if formula is used.
fixed_intercept: TRUE (default) or FALSE, estimates fixed intercept. Overridden if formula is used and contains ~1 or ~0.
factors: a vector of strings naming the fixed factors from data. Not needed if formula is used.
covs: a vector of strings naming the covariates from data. Not needed if formula is used.
model_terms: a list of character vectors describing fixed effects terms. Not needed if formula is used.
nested_terms: A right-hand formula for the nested model. It can be passed as a list of character vectors describing effects terms for the nested model.
nested_intercept: TRUE (default) or FALSE, estimates fixed intercept. Overridden if model_ters is a formula and contains ~1 or ~0..
omnibus: Omnibus tests are based on F-test F (default) or loglikelihood ration test LRT.
estimates_ci: TRUE (default) or FALSE , parameters CI in table
betas_ci: TRUE (default) or FALSE , parameters CI in table
ci_width: a number between 50 and 99.9 (default: 95) specifying the confidence interval width for the plots.
ci_method: the method to compute the confidence intervals. It can be `wald` (default) for large samples confidence intervals, `quantile` for percentile bootstrap method, or `bcai` for bias corrected accelarated method.
boot_r: a number bootstrap repetitions.
contrasts: a named vector of the form c(var1="type", var2="type2") specifying the type of contrast to use, one of 'deviation', 'simple', 'dummy', 'difference', 'helmert', 'repeated', 'polynomial' 'custom'. If NULL, simple is used. Can also be passed as a list of list of the form list(list(var="var1",type="type1")). If any factor contrast is defined as 'custom', a named list of the form list(factorname=numeric vector), for instance list(factorname=c(1,1,-2)) should be passed to the option contrast_custom_values.
contrast_custom_values: a named list with the custom contrast weights, of the form list(factorname=numeric vector), for instance list(factorname=c(1,1,-2)). only one constrast per variable is allowed.
contrast_custom_focus: if any factor is coded with 'custom', when TRUE or NULL (default) the coefficients, simple effects and simple interactions are focused on the custom contrast. If FALSE , variables are coded accordingly to the passed contrast, but no special table or test is devoted to the contrast.
show_contrastnames: TRUE or FALSE (default), shows raw names of the contrasts variables in tables
show_contrastcodes: TRUE or FALSE (default), shows contrast coefficients tables
vcov: TRUE or FALSE (default), shows coefficients covariances
plot_x: a string naming the variable placed on the horizontal axis of the plot
plot_z: a string naming the variable represented as separate lines in the plot
plot_by: a list of variables defining the levels at which a separate plot should be produced.
plot_raw: TRUE or FALSE (default), plot raw data along the predicted values
plot_yscale: TRUE or FALSE (default), set the Y-axis range equal to the range of the observed values.
plot_xoriginal: TRUE or FALSE (default), use original scale for covariates.
plot_black: TRUE or FALSE (default), use different linetypes per levels.
plot_around: 'none' (default), 'ci', or 'se'. Use no error bars, use confidence intervals, or use standard errors on the plots, respectively.
plot_jn: 'FALSE' (default), 'TRUE'. produces Johnson-Neyman plots for the variables specified in the main plot.
emmeans: a rhs formula with the terms specifying the marginal means to estimate (of the form '~x+x:z')
posthoc: a rhs formula with the terms specifying the table to apply the comparisons (of the form '~x+x:z'). The formula is not expanded, so 'x*z' becomes 'x+z' and not 'x+z+x:z'. It can be passed also as a list of the form list("x","z",c("x","z")
simple_x: The variable for which the simple effects (slopes) are computed
simple_mods: a character vector with the variable(s) providing the levels at which the simple effects are computed
simple_interactions: should simple Interactions be computed
covs_scale: a named vector of the form c(var1='type', var2='type2') specifying the transformation to apply to covariates, one of 'centered' to the mean, 'standardized' or 'none'. 'none' leaves the variable as it is.
covs_conditioning: 'mean_sd' (default), or 'percent'. How to condition covariates in simple effects and plots. 'mean_sd' for mean +/- 'ccp_value' * sd. 'percent' for median +/-'ccp_value' for percentiles. range conditions to min and max divided in ccra_steps steps (aproximately).
ccm_value: how many st.deviations around the means used to condition simple effects and plots. Used if covs_conditioning='mean_sd'
ccp_value: offsett (number of percentiles) around the median used to condition simple effects and plots. Used if simpleScale='percent'
ccra_steps: Covariate condition steps from min to max: At how many values between min and max should the covariate be conditioned simpleScale='range'
covs_scale_labels: how the levels of a continuous moderator should appear in tables and plots: labels, values and values_labels, ovalues, `ovalues_labels. The latter two refer to the variable orginal levels, before scaling.
adjust: adjustment method for postho tests. One or more of 'none', 'bonf','tukey' 'holm'; provide no, Bonferroni, Tukey and Holm Post Hoc corrections respectively.
posthoc_es: effect size indices for mean comparisons. One or more of 'dm', 'ds','g' for Cohen's d (dm=model SD,ds=sample SD ) or Hedge's g
d_ci: TRUE or FALSE (default), d confidence intervals
es: a list of effect sizes to print out. They can be: "eta" for eta-squared, 'etap' for partial eta-squared, 'omega' for omega-squared, 'omegap' for partial omega-squared, 'epsilon' for epsilon-squared, 'epsilonp' for partial epsilon-squared and 'beta' for standardized coefficients (betas). Default is "beta" and "parEta".
homo_test: TRUE or FALSE (default), performs homogeneity tests
colli_test: TRUE or FALSE (default), computes VIF and Tollerance for the terms in the model
qq_plot: TRUE or FALSE (default), provide a Q-Q plot of residuals
norm_test: TRUE or FALSE (default), provide a test for normality of residuals
norm_plot: TRUE or FALSE (default), provide a histogram of residuals superimposed by a normal distribution
resid_plot: TRUE or FALSE (default), provide a scatterplot of the residuals against predicted
intercept_info: TRUE or FALSE (default), provide ìnformation about the intercept (F test, effect size indexes)
es_info: TRUE or FALSE (default), provide ìnformation about the effect size indexes
dep_scale: Re-scale the dependent variable.
se_method: Method to compute the standard error. Classical standard errors is the default standard. Four methods for heteroschedasticy-consistent standard errors are available: HC0, HC1,HC2,HC3, from package sandwich . See vcovHC for details.

Value

A results object containing:

`results$model`					a property
`results$info`					a table
`results$main$r2`					a table of R
`results$main$intercept`					a table of information for the model intercept
`results$main$anova`					a table of ANOVA results
`results$main$effectsizes`					a table of effect size indeces
`results$main$coefficients`					a table
`results$main$vcov`					a table
`results$main$contrastCodeTables`					an array of contrast coefficients tables
`results$posthoc`					an array of post-hoc tables
`results$posthocEffectSize`					an array of post-hoc effect size
`results$simpleEffects$anova`					a table of ANOVA for simple effects
`results$simpleEffects$coefficients`					a table
`results$simpleInteractions`					an array of simple interactions tables
`results$emmeans`					an array of predicted means tables
`results$mainPlots`					an array of results plots
`results$plotnotes`					a html
`results$assumptions$homotest`					a table of homogeneity tests
`results$assumptions$normtest`					a table of normality tests
`results$assumptions$qqplot`					a q-q plot
`results$assumptions$normPlot`					Residual histogram
`results$assumptions$residPlot`					Residual Predicted plot
`results$predicted`					an output
`results$residuals`					an output

Tables can be converted to data frames with asDF or as.data.frame. For example:

results$info$asDF

as.data.frame(results$info)

Examples

data('ToothGrowth')
GAMLj3::gamlj_lm(formula = len ~ supp,  data = ToothGrowth)
#> 
#>  GENERAL LINEAR MODEL
#> 
#>  Model Info                                                            
#>  ───────────────────────────────────────────────────────────────────── 
#>    Info                                                                
#>  ───────────────────────────────────────────────────────────────────── 
#>    Model Type       Linear Model    OLS Model for continuous y         
#>    Model            lm              len ~ 1 + supp                     
#>    Distribution     Gaussian        Normal distribution of residuals   
#>    Omnibus Tests    F                                                  
#>    Sample size                60                                       
#>    Converged        yes                                                
#>    Y transform      none                                               
#>    C.I. method      Wald                                               
#>  ───────────────────────────────────────────────────────────────────── 
#> 
#> 
#>  MODEL RESULTS
#> 
#>  Model Fit                                                             
#>  ───────────────────────────────────────────────────────────────────── 
#>    R²           Adj. R²      df    df (res)    F           p           
#>  ───────────────────────────────────────────────────────────────────── 
#>    0.0594836    0.0432678     1          58    3.668253    0.0603934   
#>  ───────────────────────────────────────────────────────────────────── 
#> 
#> 
#>  ANOVA Omnibus tests                                                        
#>  ────────────────────────────────────────────────────────────────────────── 
#>                 SS              df    F            p            η²p         
#>  ────────────────────────────────────────────────────────────────────────── 
#>    Model         205.3500000     1    3.6682525    0.0603934    0.0594836   
#>    supp          205.3500000     1    3.6682525    0.0603934    0.0594836   
#>    Residuals    3246.8593333    58                                          
#>    Total        3452.2093333    59                                          
#>  ────────────────────────────────────────────────────────────────────────── 
#> 
#> 
#>  Parameter Estimates (Coefficients)                                                                                                    
#>  ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── 
#>    Names          Effect         Estimate      SE           Lower         Upper         β             df    t             p            
#>  ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── 
#>    (Intercept)    (Intercept)    18.8133333    0.9659221    16.8798301    20.7468365    -0.0000000    58    19.4770705    < .0000001   
#>    supp1          VC - OJ        -3.7000000    1.9318443    -7.5670064     0.1670064    -0.4837034    58    -1.9152683     0.0603934   
#>  ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── 
#>