The statlingua Package

Introduction

Statistical models are indispensable tools for extracting insights from data, yet their outputs can often be cryptic and laden with technical jargon. Deciphering coefficients, p-values, confidence intervals, and various model fit statistics typically requires a solid statistical background. This can create a barrier when communicating findings to a wider audience or even for those still developing their statistical acumen.

The statlingua R package is here to change that! It masterfully leverages the power of Large Language Models (LLMs) to translate complex statistical model outputs into clear, understandable, and context-aware natural language. By simply feeding your R statistical model objects into statlingua, you can generate human-readable interpretations, making statistical understanding accessible to everyone, regardless of their technical expertise.

It’s important to note that statlingua itself doesn’t directly call LLM APIs. Instead, it serves as a sophisticated prompt engineering toolkit. It meticulously prepares the necessary inputs (your model summary and contextual information) and then passes them to the ellmer package, which handles the actual communication with the LLM. The primary workhorse function you’ll use in statlingua is explain().

This vignette will guide you through understanding and using statlingua effectively.

Prerequisites

Before diving in, please ensure you have the following:

1. The statlingua package installed from GitHub (not yet available on CRAN):

if (!requireNamespace("remotes")) {
  install.packages("remotes")
}
remotes::install_github("bgreenwell/statlingua")

2. The ellmer package installed. statlingua relies on it for LLM communication:

install.packages("ellmer")

3. Access to an LLM provider (e.g., OpenAI, Google Gemini, or Anthropic) and a corresponding API key. You’ll need to configure your API key according to the ellmer package’s documentation. This usually involves setting environment variables like OPENAI_API_KEY, GOOGLE_API_KEY, or ANTHROPIC_API_KEY. Note that while While ellmer supports numerous LLM providers, this vignette will specifically use Google Gemini models via ellmer::chat_google_gemini(); I find Google Gemini to be particularly well-suited for explaining statistical output and they offer a generous free tier. You’ll need to configure your API key according to the ellmer package’s documentation. This typically involves setting the GEMINI_API_KEY environment variable in your R session or .Renviron file (e.g., Sys.setenv(GEMINI_API_KEY = "YOUR_API_KEY_HERE")).
4. For the examples in this vignette, you’ll also need the following packages: ISLR2, MASS, and survival.

install.packages(c("ISLR2", "jsonlite", "lme4", "MASS", "survival"))

How statlingua Works: The explain() Function and ellmer

The primary function you’ll use in ****statlingua**** is explain(). This is an S3 generic function, meaning its behavior adapts to the class of the R statistical object you provide (e.g., an "lm" object, "glm" object, "lmerMod" object, etc.).

The process explain() follows to generate an interpretation involves several key steps:

1. Input & Initial Argument Resolution: You call explain() with your statistical object, an ellmer client, and optionally context, audience, verbosity, and the new style argument. The explain() generic function first resolves audience, verbosity, and style to their specific chosen values (e.g., audience = "novice", style = "markdown") using match.arg(). These resolved values are then passed to the appropriate S3 method for the class of your object.

2. Model Summary Extraction: Internally, explain() (typically via the .explain_core() helper function or directly in explain.default()) uses the summarize() function to capture a text-based summary of your statistical object. This captured text (e.g., similar to what summary(object) would produce) forms the core statistical information that the LLM will interpret.

3. System Prompt Assembly (via .assemble_sys_prompt()): This is where statlingua constructs the detailed instructions for the LLM. The internal .assemble_sys_prompt() function pieces together several components, all read from .md files stored within the package’s inst/prompts/ directory. The final system prompt typically includes the following sections, ordered to guide the LLM effectively:

   • Role Definition:
     • A base role description is read from inst/prompts/common/role_base.md.
     • If available, model-specific role details are appended from inst/prompts/models/<model_name>/role_specific.md (where <model_name> corresponds to the class of your object, like “lm” or “lmerMod”). If this file doesn’t exist for a specific model, this part is omitted.
   • Intended Audience and Verbosity:
     • Instructions tailored to the specified audience (e.g., "novice", "researcher") are read from inst/prompts/audience/<audience_value>.md (e.g., inst/prompts/audience/novice.md).
     • Instructions defining the verbosity level (e.g., "brief", "detailed") are read from inst/prompts/verbosity/<verbosity_value>.md (e.g., inst/prompts/verbosity/detailed.md).
   • Response Format Specification (Style):
     • This crucial part is determined by the style argument. Instructions for the desired output format (e.g., "markdown", "html", "json", "text", "latex") are read from inst/prompts/style/<style_value>.md (e.g., inst/prompts/style/markdown.md). This tells the LLM how to structure its entire response.
   • Model-Specific Instructions:
     • Detailed instructions on what aspects of the statistical model to explain are read from inst/prompts/models/<model_name>/instructions.md (e.g., for an "lm" object, it would read from inst/prompts/models/lm/instructions.md). If model-specific instructions aren’t found, it defaults to inst/prompts/models/default/instructions.md.
   • Cautionary Notes:
     • A general caution message is appended from inst/prompts/common/caution.md.

   These components are assembled into a single, comprehensive system prompt that guides the LLM’s behavior, tone, content focus, and output format.

4. User Prompt Construction (via .build_usr_prompt()): The “user prompt” (the actual query containing the data to be interpreted) is constructed by combining:

   • A leading phrase indicating the type of model (e.g., “Explain the following linear regression model output:”).
   • The captured model output_summary from step 2.
   • Any additional context string provided by the user via the context argument.

5. LLM Interaction via ellmer: The assembled sys_prompt is set for the ellmer client object. Then, the constructed usr_prompt is sent to the LLM using client$chat(usr_prompt). ellmer handles the actual API communication.

6. Output Post-processing (via .remove_fences()): Before returning the explanation, ****statlingua**** calls an internal utility, .remove_fences(), to clean the LLM’s raw output. This function attempts to remove common “language fence” wrappers (like markdown ... or json ...) that LLMs sometimes add around their responses.

7. Output Packaging: The cleaned explanation string from the LLM is then packaged into a statlingua_explanation object. This object’s text component holds the explanation string in the specified style. It also includes metadata like the model_type, audience, verbosity, and style used. The statlingua_explanation object has a default print method that uses cat() for easy viewing in the console.

This comprehensive and modular approach to prompt engineering allows statlingua to provide tailored and well-formatted explanations for a variety of statistical models and user needs.

The Power of context: Why It Matters

You could just pass your model object to explain() and get a basic interpretation. However, to unlock truly insightful and actionable explanations, providing context is paramount.

LLMs are incredibly powerful, but they don’t inherently know the nuances of your specific research. They don’t know what “VarX” really means in your data set, its units, the specific hypothesis you’re testing, or the population you’re studying unless you tell them. The context argument is your channel to provide this vital background.

What makes for effective context?

• Research Objective: What question(s) are you trying to answer? (e.g., “We are investigating factors affecting Gentoo penguin bill length to understand dietary adaptations.”)
• Data Description:
  • What do your variables represent? Be specific. (e.g., “bill_length_mm is the length of the penguin’s bill in millimeters.”)
  • What are their units? (e.g., “Flipper length is in millimeters, body mass in grams.”)
  • Are there any known data limitations or special characteristics? (e.g., “Data collected from three islands in the Palmer Archipelago.”)
• Study Design: How was the data collected? (e.g., “Observational data from a field study.”)
• Target Audience Nuances (Implicitly): While the audience argument handles the main targeting, mentioning specific interpretation needs in the context can further refine the LLM’s output (e.g., “Explain the practical significance of these findings for wildlife conservation efforts.”).

By supplying such details, you empower the LLM to:

• Interpret coefficients with their true, domain-specific meaning.
• Relate findings directly to your research goals.
• Offer more relevant advice on model assumptions or limitations.
• Generate explanations that are less generic, more targeted, and ultimately far more useful.

Think of context as the difference between asking a generic statistician “What does this mean?” versus asking a statistician who deeply understands your research area, data, and objectives. The latter will always provide a more valuable interpretation.

Some Examples in Action!

Let’s see statlingua shine with some practical examples.

Important Note on API Keys: The following code chunks that call explain() are set to eval = FALSE by default in this vignette. This is because they require an active API key configured for ellmer. To run these examples yourself:

1. Ensure your API key (e.g., GOOGLE_API_KEY, OPENAI_API_KEY, or ANTHROPIC_API_KEY) is set up as an environment variable that ellmer can access.
2. Change the R chunk option eval = FALSE to eval = TRUE for the chunks you wish to run.
3. You may need to adjust the ellmer client initialization (e.g., ellmer::chat_openai()) to match your chosen LLM provider.

For this examples in this vignette

data(Carseats, package = "ISLR2")  # load the Carseats data

# Fit a linear model to the Carseats data set
fm_carseats <- lm(Sales ~ . + Price:Age + Income:Advertising, data = Carseats)
summary(fm_carseats)  # print model summary
#> 
#> Call:
#> lm(formula = Sales ~ . + Price:Age + Income:Advertising, data = Carseats)
#> 
#> Residuals:
#>     Min      1Q  Median      3Q     Max 
#> -2.9208 -0.7503  0.0177  0.6754  3.3413 
#> 
#> Coefficients:
#>                      Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)         6.5755654  1.0087470   6.519 2.22e-10 ***
#> CompPrice           0.0929371  0.0041183  22.567  < 2e-16 ***
#> Income              0.0108940  0.0026044   4.183 3.57e-05 ***
#> Advertising         0.0702462  0.0226091   3.107 0.002030 ** 
#> Population          0.0001592  0.0003679   0.433 0.665330    
#> Price              -0.1008064  0.0074399 -13.549  < 2e-16 ***
#> ShelveLocGood       4.8486762  0.1528378  31.724  < 2e-16 ***
#> ShelveLocMedium     1.9532620  0.1257682  15.531  < 2e-16 ***
#> Age                -0.0579466  0.0159506  -3.633 0.000318 ***
#> Education          -0.0208525  0.0196131  -1.063 0.288361    
#> UrbanYes            0.1401597  0.1124019   1.247 0.213171    
#> USYes              -0.1575571  0.1489234  -1.058 0.290729    
#> Price:Age           0.0001068  0.0001333   0.801 0.423812    
#> Income:Advertising  0.0007510  0.0002784   2.698 0.007290 ** 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 1.011 on 386 degrees of freedom
#> Multiple R-squared:  0.8761, Adjusted R-squared:  0.8719 
#> F-statistic:   210 on 13 and 386 DF,  p-value: < 2.2e-16

library(statlingua)

# Establish client connection
client <- ellmer::chat_google_gemini(echo = "none")
#> Using model = "gemini-2.0-flash".

# Additional context for the LLM to consider
carseats_context <- "
The model uses a data set on child car seat sales (in thousands of units) at 400 different stores.
The goal is to identify factors associated with sales.
The variables are:
  * Sales: Unit sales (in thousands) at each location (the response variable).
  * CompPrice: Price charged by competitor at each location.
  * Income: Community income level (in thousands of dollars).
  * Advertising: Local advertising budget for the company at each location (in thousands of dollars).
  * Population: Population size in the region (in thousands).
  * Price: Price the company charges for car seats at each site.
  * ShelveLoc: A factor with levels 'Bad', 'Good', and 'Medium' indicating the quality of the shelving location for the car seats. ('Bad' is the reference level).
  * Age: Average age of the local population.
  * Education: Education level at each location.
  * Urban: A factor ('No', 'Yes') indicating if the store is in an urban or rural location. ('No' is the reference level).
  * US: A factor ('No', 'Yes') indicating if the store is in the US or not. ('No' is the reference level).
Interaction terms `Income:Advertising` and `Price:Age` are also included.
The data set is simulated. We want to understand key drivers of sales and how to interpret the interaction terms.
"

explain(fm_carseats, client = client, context = carseats_context,
        audience = "novice", verbosity = "detailed")

Interpretation of Linear Regression Model Output

This output details a linear regression model analyzing car seat sales based on various factors. The model aims to understand how competitor price, income, advertising, population, car seat price, shelving location, age, education, urban/rural location, US location, and interactions between price & age and income & advertising relate to car seat sales. Given that the response variable (Sales) is continuous, a linear regression model is potentially appropriate, assuming the relationships are approximately linear and other assumptions are met.

lm(formula = Sales ~ . + Price:Age + Income:Advertising, data = Carseats)

    Min      1Q  Median      3Q     Max 
-2.9208 -0.7503  0.0177  0.6754  3.3413

Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.011 on 386 degrees of freedom

Multiple R-squared:  0.8761,    Adjusted R-squared:  0.8719

F-statistic:   210 on 13 and 386 DF,  p-value: < 2.2e-16

query <- paste("Could you explain the R-squared values (Multiple R-squared and",
               "Adjusted R-squared) in simpler terms for this car seat sales",
               "model? What does it practically mean for predicting sales?")
client$chat(query)
#> [1] "## Simplified Explanation of R-squared Values\n\nLet's break down what R-squared and Adjusted R-squared mean in the context of predicting car seat sales:\n\n**Multiple R-squared: 0.8761 (or 87.61%)**\n\nThink of it like this: Imagine you're trying to guess the car seat sales at a store.\n\n*   **Without any information:** If you had absolutely no information about the store (competitor prices, income levels, advertising budgets, etc.), your guesses would likely be pretty far off. There'd be a lot of variation (or \"variance\") in your prediction errors.\n\n*   **With the model:** Now, using our linear regression model (which includes all the predictors like competitor price, income, etc.), we can make much better predictions.\n\nR-squared tells us how much *better* our predictions are with the model compared to just guessing randomly. An R-squared of 0.8761 means that *our model explains 87.61% of the total variation (or variance) in car seat sales across all the stores in our data*. In other words, 87.61% of the differences in sales figures we see between stores can be attributed to the factors included in our model (competitor price, income, advertising, etc.). The remaining 12.39% (100% - 87.61%) is due to other factors *not* included in the model (e.g., random chance, unmeasured variables, store manager skill, local events, etc.).\n\n**In simpler terms:** The model captures a large proportion of the reasons why sales vary from store to store.\n\n**Adjusted R-squared: 0.8719 (or 87.19%)**\n\nAdjusted R-squared is a slightly more refined version of R-squared. The regular R-squared *always* increases when you add more variables to your model, even if those variables don't really help predict sales. It's like saying, \"I can explain sales even better if I add the color of the store's walls to the model!\" (Even though wall color is probably irrelevant).\n\nAdjusted R-squared *penalizes* you for adding useless variables. It only increases if the new variable actually improves the model's predictive power *more than you'd expect by chance*.\n\nIn this case, the Adjusted R-squared (0.8719) is very close to the regular R-squared (0.8761). This suggests that the variables included in our model are, on the whole, useful for predicting sales. The penalty for including 13 variables was very small.\n\n**Practical Meaning for Predicting Sales:**\n\n*   **Good predictive power:** An Adjusted R-squared of 0.8719 indicates that the model has relatively strong predictive power. We can use the model to estimate car seat sales at new stores, and these estimates are likely to be fairly accurate. However, it is essential to remember that there is still 12.81% of the variation that the model *doesn't* explain.\n\n*   **Identifying key factors:** The model helps us identify which factors are most strongly associated with car seat sales (e.g., competitor price, the company's own price, shelf location). This knowledge can be used to make strategic decisions about pricing, advertising, and product placement to improve sales.\n\n*   **Not perfect prediction:** Even with a high R-squared, the model doesn't predict sales *perfectly*. There will still be some error in our predictions. Other factors not included in the model also influence sales.\n\n*   **Useful for comparisons:** The R-squared values are especially useful for comparing this model to other models you might build to predict car seat sales. The model with the higher Adjusted R-squared (assuming both models meet the regression assumptions) is generally considered the better model.\n"

data(Pima.tr, package = "MASS")  # load the Pima.tr data set

# Fit a logistic regression model
fm_pima <- glm(type ~ npreg + glu + bp + skin + bmi + ped + age,
               data = Pima.tr, family = binomial(link = "logit"))
summary(fm_pima)  # print model summary
#> 
#> Call:
#> glm(formula = type ~ npreg + glu + bp + skin + bmi + ped + age, 
#>     family = binomial(link = "logit"), data = Pima.tr)
#> 
#> Deviance Residuals: 
#>     Min       1Q   Median       3Q      Max  
#> -1.9830  -0.6773  -0.3681   0.6439   2.3154  
#> 
#> Coefficients:
#>              Estimate Std. Error z value Pr(>|z|)    
#> (Intercept) -9.773062   1.770386  -5.520 3.38e-08 ***
#> npreg        0.103183   0.064694   1.595  0.11073    
#> glu          0.032117   0.006787   4.732 2.22e-06 ***
#> bp          -0.004768   0.018541  -0.257  0.79707    
#> skin        -0.001917   0.022500  -0.085  0.93211    
#> bmi          0.083624   0.042827   1.953  0.05087 .  
#> ped          1.820410   0.665514   2.735  0.00623 ** 
#> age          0.041184   0.022091   1.864  0.06228 .  
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> (Dispersion parameter for binomial family taken to be 1)
#> 
#>     Null deviance: 256.41  on 199  degrees of freedom
#> Residual deviance: 178.39  on 192  degrees of freedom
#> AIC: 194.39
#> 
#> Number of Fisher Scoring iterations: 5

pima_context <- "
This logistic regression model attempts to predict the likelihood of a Pima
Indian woman testing positive for diabetes. The data is from a study on women of
Pima Indian heritage, aged 21 years or older, living near Phoenix, Arizona. The
response variable 'type' is binary: 'Yes' (tests positive for diabetes) or 'No'.

Predictor variables include:
  - npreg: Number of pregnancies.
  - glu: Plasma glucose concentration in an oral glucose tolerance test.
  - bp: Diastolic blood pressure (mm Hg).
  - skin: Triceps skin fold thickness (mm).
  - bmi: Body mass index (weight in kg / (height in m)^2).
  - ped: Diabetes pedigree function (a measure of genetic predisposition).
  - age: Age in years.

The goal is to understand which of these factors are significantly associated
with an increased or decreased odds of having diabetes. We are particularly
interested in interpreting coefficients as odds ratios.
"

# Establish fresh client connection
client <- ellmer::chat_google_gemini(echo = "none")
#> Using model = "gemini-2.0-flash".

explain(fm_pima, client = client, context = pima_context,
        audience = "researcher", verbosity = "moderate")

Explanation of the Binomial GLM with Logit Link Output

This output represents a logistic regression model, a type of Generalized Linear Model (GLM), used to predict the probability of a binary outcome (in this case, diabetes status). The model uses a binomial family with a logit link function.

Core Concepts:

• Binomial Family with Logit Link: This combination is appropriate for binary (0/1 or Yes/No) outcome variables. The logit link transforms the probability of the event (diabetes) into the log-odds of the event. The model then predicts the log-odds as a linear combination of the predictor variables.

Key Assumptions:

• Independence: The diabetes status of each woman is independent of the others.
• Linearity in Log-Odds: The relationship between the predictors and the log-odds of diabetes is linear.
• Correctly Specified Variance: The variance of the binary outcome is determined by the binomial distribution.
• No Overdispersion: The variance is assumed to be as predicted by the binomial distribution; there isn’t more variance than expected.

Assessing Model Appropriateness:

Given that the outcome variable ‘type’ is binary, the binomial family with a logit link is generally appropriate. We rely on the correctness of the above assumptions given the context. Overdispersion is a possible issue, which we can check based on the deviance relative to the degrees of freedom.

Interpretation of the glm() Output:

• Call: glm(formula = type ~ npreg + glu + bp + skin + bmi + ped + age, family = binomial(link = "logit"), data = Pima.tr) This is the R command used to fit the model.

• Deviance Residuals: Min 1Q Median 3Q Max -1.9830 -0.6773 -0.3681 0.6439 2.3154 Deviance residuals measure the difference between the observed and predicted values. They are analogous to residuals in a linear regression. Ideally, they should be symmetrically distributed around zero. Here, the distribution appears reasonably symmetric.

• Coefficients Table:

  Each row in this table provides information about the effect of a predictor on the log-odds of testing positive for diabetes.

  	Estimate	Std. Error	z value	Pr(>|z|)	Interpretation	Odds Ratio (exp(Estimate))	Interpretation as Odds Ratio
  (Intercept)	-9.773062	1.770386	-5.520	3.38e-08	The estimated log-odds of testing positive for diabetes when all predictors are zero. This is often not practically interpretable.	0.000056	Not directly interpretable; serves as the baseline when all other predictors are zero.
  npreg	0.103183	0.064694	1.595	0.11073	For each additional pregnancy, the log-odds of testing positive for diabetes are expected to increase by 0.103, holding all other variables constant.	1.1087	For each additional pregnancy, the odds of testing positive for diabetes are estimated to increase by a factor of 1.109, holding all other variables constant.
  glu	0.032117	0.006787	4.732	2.22e-06	For each one-unit increase in plasma glucose concentration, the log-odds of testing positive for diabetes are expected to increase by 0.032, holding all other variables constant.	1.0326	For each one-unit increase in plasma glucose concentration, the odds of testing positive for diabetes are estimated to increase by a factor of 1.033, holding all other variables constant.
  bp	-0.004768	0.018541	-0.257	0.79707	For each one-unit increase in diastolic blood pressure, the log-odds of testing positive for diabetes are expected to decrease by 0.0048, holding all other variables constant.	0.9952	For each one-unit increase in diastolic blood pressure, the odds of testing positive for diabetes are estimated to decrease by a factor of 0.995, holding all other variables constant.
  skin	-0.001917	0.022500	-0.085	0.93211	For each one-unit increase in triceps skin fold thickness, the log-odds of testing positive for diabetes are expected to decrease by 0.0019, holding all other variables constant.	0.9981	For each one-unit increase in triceps skin fold thickness, the odds of testing positive for diabetes are estimated to decrease by a factor of 0.998, holding all other variables constant.
  bmi	0.083624	0.042827	1.953	0.05087	For each one-unit increase in body mass index, the log-odds of testing positive for diabetes are expected to increase by 0.084, holding all other variables constant.	1.0873	For each one-unit increase in body mass index, the odds of testing positive for diabetes are estimated to increase by a factor of 1.087, holding all other variables constant.
  ped	1.820410	0.665514	2.735	0.00623	For each one-unit increase in the diabetes pedigree function, the log-odds of testing positive for diabetes are expected to increase by 1.820, holding all other variables constant.	6.1743	For each one-unit increase in the diabetes pedigree function, the odds of testing positive for diabetes are estimated to increase by a factor of 6.174, holding all other variables constant. This is a substantial effect.
  age	0.041184	0.022091	1.864	0.06228	For each additional year of age, the log-odds of testing positive for diabetes are expected to increase by 0.041, holding all other variables constant.	1.0420	For each additional year of age, the odds of testing positive for diabetes are estimated to increase by a factor of 1.042, holding all other variables constant.

  • Estimate: The estimated coefficient on the log-odds scale.
  • Std. Error: The standard error of the estimated coefficient.
  • z value: The test statistic (Estimate / Std. Error).
  • Pr(>|z|): The p-value associated with the z-test. It represents the probability of observing a z-value as extreme or more extreme than the one calculated, assuming the null hypothesis (that the coefficient is zero) is true.
  • Odds Ratio: The exponentiated estimate (exp(Estimate)). This is the multiplicative change in the odds of diabetes for a one-unit increase in the predictor, holding all other variables constant. An odds ratio greater than 1 indicates a positive association with the odds of diabetes, while an odds ratio less than 1 indicates a negative association.

• Signif. codes: As in linear regression, these indicate the level of statistical significance of the coefficients.

• (Dispersion parameter for binomial family taken to be 1): For the binomial family, the dispersion parameter is fixed at 1. If there were overdispersion (more variance than expected), this value would be greater than 1, and one might consider using a quasibinomial family.

• Null deviance: Null deviance: 256.41 on 199 degrees of freedom This represents the deviance of a model with only an intercept (i.e., no predictors). It indicates the total variability in the response variable. The degrees of freedom are n - 1, where n is the number of observations.

• Residual deviance: Residual deviance: 178.39 on 192 degrees of freedom This represents the deviance of the fitted model. It indicates the amount of variability not explained by the model. The degrees of freedom are n - p, where n is the number of observations and p is the number of parameters in the model (including the intercept).

• AIC: AIC: 194.39 The Akaike Information Criterion (AIC) is a measure of model fit that penalizes model complexity. Lower AIC values indicate a better trade-off between fit and complexity. It’s useful for comparing different models.

• Number of Fisher Scoring iterations: Number of Fisher Scoring iterations: 5 This indicates that the iterative algorithm used to fit the model converged in 5 iterations.

Suggestions for Checking Assumptions:

• Deviance/Pearson Residuals vs. Fitted Values Plot: Plotting the deviance or Pearson residuals against the fitted values (predicted log-odds) can help assess whether the variance is constant and whether the link function is appropriate. Look for patterns or trends in the residuals.
• Influential Observations: Check for observations that have a disproportionate influence on the model’s results.
• Overdispersion: The residual deviance (178.39) is less than the residual degrees of freedom (192), suggesting that overdispersion is not a major concern in this case. A rough rule of thumb is that substantial overdispersion is possible if the residual deviance is substantially larger than the residual degrees of freedom (e.g., residual deviance more than twice the residual df).

Additional Considerations:

• Overdispersion: If overdispersion were present, the standard errors would be underestimated, potentially leading to incorrect inferences. If suspected, you could use a quasibinomial model or investigate potential sources of extra variation.
• Zero-Inflation: This is not relevant for this specific model, as the outcome is a binary variable and not count data.

Caution: This explanation was generated by a Large Language Model. Critically review the output and consult additional statistical resources or experts to ensure correctness and a full understanding.

The above (rendered Markdown) explains the logistic regression coefficients (e.g., for glu or bmi) in terms of log-odds and odds ratios, discusses their statistical significance, and interprets overall model fit statistics like AIC and deviance. For a researcher, the explanation might also touch upon the implications of these findings for diabetes risk assessment.

Thank you for catching that error! It’s crucial to have accurate and reliable examples. The Pima.tr data set is a much more suitable choice for this GLM example.

library(survival)

# Load the lung cancer data set (from package survival)
data(cancer)

# Fit a time transform Cox PH model using current age
fm_lung <- coxph(Surv(time, status) ~ ph.ecog + tt(age), data = lung,
     tt = function(x, t, ...) pspline(x + t/365.25))
summary(fm_lung)  # print model summary
#> Call:
#> coxph(formula = Surv(time, status) ~ ph.ecog + tt(age), data = lung, 
#>     tt = function(x, t, ...) pspline(x + t/365.25))
#> 
#>   n= 227, number of events= 164 
#>    (1 observation deleted due to missingness)
#> 
#>                 coef    se(coef) se2      Chisq DF   p      
#> ph.ecog         0.45284 0.117827 0.117362 14.77 1.00 0.00012
#> tt(age), linear 0.01116 0.009296 0.009296  1.44 1.00 0.23000
#> tt(age), nonlin                            2.70 3.08 0.45000
#> 
#>                    exp(coef) exp(-coef) lower .95 upper .95
#> ph.ecog                1.573     0.6358    1.2484     1.981
#> ps(x + t/365.25)3      1.275     0.7845    0.2777     5.850
#> ps(x + t/365.25)4      1.628     0.6141    0.1342    19.761
#> ps(x + t/365.25)5      2.181     0.4585    0.1160    41.015
#> ps(x + t/365.25)6      2.762     0.3620    0.1389    54.929
#> ps(x + t/365.25)7      2.935     0.3408    0.1571    54.812
#> ps(x + t/365.25)8      2.843     0.3517    0.1571    51.472
#> ps(x + t/365.25)9      2.502     0.3997    0.1382    45.310
#> ps(x + t/365.25)10     2.529     0.3955    0.1390    45.998
#> ps(x + t/365.25)11     3.111     0.3214    0.1699    56.961
#> ps(x + t/365.25)12     3.610     0.2770    0.1930    67.545
#> ps(x + t/365.25)13     5.487     0.1822    0.2503   120.280
#> ps(x + t/365.25)14     8.903     0.1123    0.2364   335.341
#> 
#> Iterations: 4 outer, 10 Newton-Raphson
#>      Theta= 0.7960256 
#> Degrees of freedom for terms= 1.0 4.1 
#> Concordance= 0.612  (se = 0.027 )
#> Likelihood ratio test= 22.46  on 5.07 df,   p=5e-04

lung_context <- "
This Cox proportional hazards model analyzes survival data for patients with
advanced lung cancer. The objective is to identify factors associated with
patient survival time (in days). The variables include:
  - time: Survival time in days.
  - status: Censoring status (1=censored, 2=dead).
  - age: Age in years.
  - sex: Patient's sex (1=male, 2=female). Note: In the model, 'sex' is treated as numeric; interpretations should consider this. It's common to factor this, but here it's numeric.
  - ph.ecog: ECOG performance score (0=good, higher values mean worse performance).
We want to understand how age, sex, and ECOG score relate to the hazard of death.
Interpretations should focus on hazard ratios. For example, how does a one-unit increase in ph.ecog affect the hazard of death?
"

# Establish fresh client connection
client <- ellmer::chat_google_gemini(echo = "none")
#> Using model = "gemini-2.0-flash".

explain(fm_lung, client = client, context = lung_context,
        audience = "manager", verbosity = "brief")

Explanation of Cox Proportional Hazards Model Output

This output presents the results of a Cox proportional hazards model examining the survival times of lung cancer patients. The model explores the relationship between survival time and ph.ecog (ECOG performance score) and age while accounting for possible non-linear effects of age via a time-transforming spline (tt(age)).

Call:

The model was fit using the formula Surv(time, status) ~ ph.ecog + tt(age), where tt(age) represents a time-transforming function using a spline for age.

Data Summary:

• n = 227 patients included in the analysis (one observation was removed due to missing data).
• number of events = 164 deaths were observed.

Coefficients Table:

• ph.ecog (ECOG Performance Score):
  • coef: 0.45284. This is the estimated coefficient on the log-hazard scale. A positive coefficient suggests that a higher ECOG score is associated with an increased hazard of death.
  • exp(coef) (Hazard Ratio - HR): 1.573. For a one-unit increase in ECOG performance score (indicating poorer performance), the hazard of death is estimated to be 1.573 times higher, holding age constant. This translates to a 57.3% higher risk of death.
  • se(coef): 0.117827. Standard error of the coefficient.
  • z: 14.77. Wald test statistic.
  • Pr(>|z|) or p: 0.00012. The p-value is highly significant, indicating strong evidence that ECOG score is associated with survival time.
  • lower .95: 1.2484, upper .95: 1.981. The 95% confidence interval for the hazard ratio is (1.2484, 1.981). Because this interval does not include 1, the effect of ph.ecog is statistically significant at the 0.05 level.
• tt(age) - Time-Transforming Spline for Age: The model uses a time-transforming spline for age, pspline(x + t/365.25). The tt() construct creates a time-dependent effect for age.
  • The output presents a linear and a non-linear component of the spline. The linear component is not statistically significant (p = 0.23000).
  • The non-linear component Chisq value is 2.70 with 3.08 degrees of freedom and a p-value of 0.45, suggesting the non-linear component is also not statistically significant.
  • The hazard ratios and confidence intervals for ps(x + t/365.25)3 through ps(x + t/365.25)14 represent the effect of the spline basis functions. Since age is included with tt(), it’s allowed to have a time-varying effect. The individual hazard ratios for the spline terms are difficult to interpret in isolation; the overall significance of the spline is more informative. Given the non-significance of the non-linear component, a simpler model without the spline might be sufficient.

Model Convergence:

The model converged after 4 outer and 10 Newton-Raphson iterations. Theta= 0.7960256 refers to a parameter in the penalized spline fitting process.

Model Fit and Significance:

• Degrees of freedom for terms: Reports degrees of freedom for each term.
• Concordance= 0.612 (se = 0.027 ): The concordance is 0.612, with a standard error of 0.027. This indicates that in approximately 61.2% of pairs of patients, the model correctly predicts which patient will experience the event (death) sooner. While better than chance (0.5), it suggests moderate discriminative ability.
• Likelihood ratio test= 22.46 on 5.07 df, p=5e-04: The likelihood ratio test compares the fitted model to a null model (without predictors). The small p-value (0.0005) suggests that the model with ph.ecog and the spline for age is significantly better than a model with no predictors.

Recommendations and Cautions:

1. Proportional Hazards Assumption: Given the time-transforming spline for age, the proportional hazards assumption for age is not assumed. However, it is crucial to assess the proportional hazards assumption for ph.ecog. This can be done using Schoenfeld residuals via cox.zph(). Violations of this assumption would suggest that the effect of ph.ecog changes over time.

2. Spline Interpretation: While the overall likelihood ratio test is significant, the individual components of the age spline are not. Consider visualizing the effect of the spline using plots to understand how age might be affecting the hazard over time. Given the non-significance of the non-linear component of the age spline, consider refitting the model without the spline (i.e., a standard linear effect for age).

3. Model Simplicity: If the time-varying effect of age is not critical, simplifying the model by removing the spline and modeling age as a linear term may improve interpretability without sacrificing much predictive power.

4. Review and Validate: Critically review this interpretation and consult statistical resources or experts to ensure correctness and a full understanding of the model, particularly given the use of splines.

The rendered Markdown output above provides a concise, high-level summary suitable for a manager, focusing on the key predictors of survival and their implications in terms of increased or decreased risk (hazard).

library(lme4)

# Load the sleep study data set
data(sleepstudy)

# Fit a linear mixed-effects model allowing for random intercepts and random
# slopes for Days, varying by Subject
fm_sleep <- lmer(Reaction ~ Days + (Days | Subject), data = sleepstudy)
summary(fm_sleep)  # print model summary
#> Linear mixed model fit by REML ['lmerMod']
#> Formula: Reaction ~ Days + (Days | Subject)
#>    Data: sleepstudy
#> 
#> REML criterion at convergence: 1743.6
#> 
#> Scaled residuals: 
#>     Min      1Q  Median      3Q     Max 
#> -3.9536 -0.4634  0.0231  0.4634  5.1793 
#> 
#> Random effects:
#>  Groups   Name        Variance Std.Dev. Corr
#>  Subject  (Intercept) 612.10   24.741       
#>           Days         35.07    5.922   0.07
#>  Residual             654.94   25.592       
#> Number of obs: 180, groups:  Subject, 18
#> 
#> Fixed effects:
#>             Estimate Std. Error t value
#> (Intercept)  251.405      6.825  36.838
#> Days          10.467      1.546   6.771
#> 
#> Correlation of Fixed Effects:
#>      (Intr)
#> Days -0.138

sleepstudy_context <- "
This linear mixed-effects model analyzes data from a sleep deprivation study.
The goal is to understand the effect of days of sleep deprivation ('Days') on
average reaction time ('Reaction' in ms). The model includes random intercepts
and random slopes for 'Days' for each 'Subject', acknowledging that baseline
reaction times and the effect of sleep deprivation may vary across individuals.
We are interested in the average fixed effect of an additional day of sleep
deprivation on reaction time, as well as the extent of inter-subject
variability.
"

# Establish fresh client connection
client <- ellmer::chat_google_gemini(echo = "none")
#> Using model = "gemini-2.0-flash".

explain(fm_sleep, client = client, context = sleepstudy_context,
        audience = "researcher", verbosity = "moderate", style = "text")
#> Here's an explanation of the linear mixed-effects model output, incorporating the context of the sleep deprivation study.
#> 
#> LINEAR MIXED-EFFECTS MODEL INTERPRETATION
#> 
#> The model examines the relationship between days of sleep deprivation (Days) and reaction time (Reaction), accounting for individual differences between subjects.  The formula `Reaction ~ Days + (Days | Subject)` indicates that the model includes a fixed effect of 'Days' on 'Reaction' and random intercepts and slopes for 'Days' varying across 'Subject'.
#> 
#> REML VS. ML
#> 
#> The model was fit using REML (Restricted Maximum Likelihood), which is generally preferred for estimating variance components in mixed-effects models.
#> 
#> RANDOM EFFECTS
#> 
#> This section describes the variability between subjects.
#> 
#> *   Subject (Intercept): Variance = 612.10, Std.Dev. = 24.741. This indicates substantial inter-individual variability in baseline reaction times (i.e., at Day 0 of sleep deprivation).  The standard deviation of 24.741 ms suggests that, even before sleep deprivation, subjects' reaction times vary by approximately ±24.741 ms.
#> 
#> *   Subject Days: Variance = 35.07, Std.Dev. = 5.922. This indicates inter-individual variability in the effect of sleep deprivation on reaction time.  Some subjects' reaction times increase more per day of sleep deprivation than others. The standard deviation of 5.922 ms/day suggests that the effect of each additional day of sleep deprivation varies by approximately ±5.922 ms/day across subjects.
#> 
#> *   Corr: 0.07. This is the correlation between random intercepts and random slopes.  A small, positive correlation suggests a weak relationship between a subject's baseline reaction time and how much their reaction time changes with sleep deprivation. Subjects with slightly higher baseline reaction times tend to show a slightly larger increase in reaction time per day of sleep deprivation, although this correlation is very weak.
#> 
#> *   Residual: Variance = 654.94, Std.Dev. = 25.592. This represents the within-subject variability in reaction time that is not explained by the fixed effect of 'Days' or the random effects. This is the variability of reaction time *after* accounting for the subject-specific baselines and slopes. The standard deviation of 25.592 ms represents the typical variation in reaction time for a given subject on a given day.
#> 
#> FIXED EFFECTS
#> 
#> This section describes the average effects across all subjects.
#> 
#> *   (Intercept): Estimate = 251.405, Std. Error = 6.825, t value = 36.838. This is the estimated average reaction time (in ms) at Day 0 of sleep deprivation, across all subjects. The t-value is very large, indicating that this average baseline reaction time is significantly different from zero.
#> 
#> *   Days: Estimate = 10.467, Std. Error = 1.546, t value = 6.771. This is the estimated average increase in reaction time (in ms) for each additional day of sleep deprivation, across all subjects. On average, a subject's reaction time increases by 10.467 ms for each day of sleep deprivation. The t-value is large, indicating a statistically significant effect of days of sleep deprivation on reaction time.
#> 
#> CORRELATION OF FIXED EFFECTS
#> 
#> *   Days -0.138: This is the correlation between the intercept and the slope estimates in the fixed effects part of the model. It's generally less important to interpret than the correlation of random effects. It indicates a slight negative relationship between the estimated average baseline reaction time and the estimated average effect of days.
#> 
#> MODEL APPROPRIATENESS (BASED ON CONTEXT)
#> 
#> Given the repeated measures design (multiple observations per subject), the linear mixed-effects model is appropriate as it accounts for the non-independence of observations within each subject.  The inclusion of both random intercepts and random slopes allows for individual differences in both baseline reaction times and the effect of sleep deprivation, which is a reasonable assumption.  The model assumes linearity between days of sleep deprivation and reaction time.
#> 
#> CHECKING ASSUMPTIONS
#> 
#> To further validate the model:
#> 
#> *   Examine a Q-Q plot of the residuals to assess normality.
#> *   Plot residuals against fitted values to check for homoscedasticity (constant variance).
#> *   Examine Q-Q plots of the random effects for each subject to assess normality of random effects.
#> *   Plot residuals against 'Days' to assess the linearity assumption.
#> 
#> CAUTION: This explanation was generated by a Large Language Model. Critically review the output and consult additional statistical resources or experts to ensure correctness and a full understanding.
#> 

client <- ellmer::chat_google_gemini(echo = "none")
#> Using model = "gemini-2.0-flash".
ex <- explain(fm_sleep, client = client, context = sleepstudy_context,
              audience = "student", verbosity = "detailed", style = "json")

# The 'text' component of the statlingua_explanation object now holds a JSON
# string which can be parsed using the jsonlite package
jsonlite::prettify(ex$text)
#> {
#>     "title": "Explanation of Linear Mixed-Effects Model for Sleep Deprivation Study",
#>     "model_overview": "This is a linear mixed-effects model, fitted using Restricted Maximum Likelihood (REML), examining the impact of sleep deprivation (Days) on reaction time (Reaction). The model accounts for inter-individual variability by including random intercepts and slopes for each subject, allowing for differences in baseline reaction times and how reaction time changes with sleep deprivation across individuals. This type of model is suitable due to the repeated measures design, where we have multiple observations for each subject.",
#>     "coefficient_interpretation": "The fixed effects estimates provide the average effect of each predictor on reaction time across all subjects. The intercept is estimated at 251.405 ms, which represents the average reaction time at Day 0 (the baseline reaction time) across all subjects. The coefficient for 'Days' is 10.467 ms. This indicates that, on average, reaction time increases by 10.467 milliseconds for each additional day of sleep deprivation. So, each day of sleep deprivation increases reaction time by about 10.5 ms.",
#>     "significance_assessment": "The t-value for the intercept is 36.838 and for 'Days' is 6.771. Although the output doesn't directly provide p-values, these t-values can be used to assess statistical significance. Given the large t-values, especially for 'Days', it's highly likely that the effect of days of sleep deprivation on reaction time is statistically significant. The standard error for 'Days' is 1.546, which provides a measure of the precision of the estimated effect of sleep deprivation. Packages like `lmerTest` can be used with this model to obtain p-values for these fixed effects estimates using methods like Satterthwaite or Kenward-Roger approximations.",
#>     "goodness_of_fit": "The REML criterion at convergence is 1743.6. This value is useful for comparing nested models fitted to the same data. Lower REML values indicate a better fit, but only when comparing models with the same fixed effects. Other metrics like AIC and BIC, which can be obtained from the model, are better suited to non-nested model comparisons.",
#>     "assumptions_check": "Several assumptions should be checked to ensure the validity of this model. First, examine the normality of the residuals using a Q-Q plot or histogram of `resid(object)`. Second, assess homoscedasticity by plotting residuals against fitted values (`fitted(object)`), looking for constant variance. Third, check the normality of the random effects using Q-Q plots of the random effects (`ranef(object)`). Additionally, linearity of the fixed effect 'Days' should be checked, possibly by plotting residuals against 'Days'. Finally, it's important to check for influential observations that might disproportionately affect the model results.",
#>     "key_findings": "- On average, baseline reaction time (Day 0) is estimated to be approximately 251.4 ms.\n- Each additional day of sleep deprivation is associated with an average increase of approximately 10.5 ms in reaction time.\n- There is substantial inter-individual variability in both baseline reaction time (Std.Dev. = 24.741 ms) and the effect of sleep deprivation (Std.Dev. = 5.922 ms) across subjects.\n- The correlation between random intercepts and slopes is low (0.07), suggesting a weak relationship between a subject's baseline reaction time and how their reaction time changes with sleep deprivation.",
#>     "warnings_limitations": "The interpretation relies on the assumption that the model is correctly specified and that the assumptions of linear mixed-effects models are met. The absence of p-values in the base output from `lmer` should be addressed using appropriate packages like `lmerTest` to draw firmer conclusions about statistical significance. Also, remember that correlation does not equal causation; while the model suggests a relationship between sleep deprivation and reaction time, it does not prove that sleep deprivation *causes* the change in reaction time."
#> }
#> 

Inspecting LLM Interaction

If you want to see the exact system and user prompts that statlingua generated and sent to the LLM (via ellmer), as well as the raw response from the LLM, you can print the ellmer "Chat" object (defined as client in this example) after an explain() call. The client object stores the history of the interaction.

print(client)

#> <Chat Google/Gemini/gemini-2.0-flash turns=3 tokens=2337/887 $0.00>
#> ── system [0] ───────────────────────────────────────────────────────────────────────────────────────
#> ## Role
#> 
#> You are an expert statistician and R programmer, gifted at explaining complex concepts simply. Your primary function is to interpret statistical model outputs from R. You understand model nuances, underlying assumptions, and how results relate to real-world research questions.
#> 
#> You are particularly skilled with **Linear Mixed-Effects Models** created using the `lmer()` function from the `lme4` package in R (producing `lmerMod` objects). You understand their estimation via REML or ML, the interpretation of fixed and random effects (including correlations), and the common practice of using packages like `lmerTest` for p-value estimation.
#> 
#> 
#> ## Intended Audience and Verbosity
#> 
#> ### Target Audience: Student
#> Assume the user is learning statistics. Explain concepts thoroughly but clearly, as if teaching. Define key terms as they arise and explain *why* certain statistics are important or what they indicate in the context of the analysis. Maintain an encouraging and educational tone.
#> 
#> ### Level of Detail (Verbosity): Detailed
#> Give a comprehensive interpretation. Include nuances of the model output, a detailed breakdown of all relevant statistics, and a thorough discussion of assumptions and diagnostics. Be as thorough as possible, exploring various facets of the results.
#> 
#> 
#> ## Response Format Specification (Style: Json)
#> 
#> Your response MUST be a valid JSON object that can be parsed directly into an R list.
#> The JSON object should have the following top-level keys, each containing a string with the relevant part of the explanation (formatted as plain text or simple Markdown within the string if appropriate for that section):
#> - "title": A concise title for the explanation.
#> - "model_overview": A general description of the model type and its purpose in this context.
#> - "coefficient_interpretation": Detailed interpretation of model coefficients/parameters.
#> - "significance_assessment": Discussion of p-values, confidence intervals, and statistical significance.
#> - "goodness_of_fit": Evaluation of model fit (e.g., R-squared, AIC, deviance).
#> - "assumptions_check": Comments on important model assumptions and how they might be checked.
#> - "key_findings": A bulleted list (as a single string with newlines `\n` for bullets) of the main conclusions.
#> - "warnings_limitations": Any warnings, limitations, or caveats regarding the model or its interpretation.
#> 
#> Example of expected JSON structure:
#> {
#>   "title": "Explanation of Linear Regression Model for Car Sales",
#>   "model_overview": "This is a linear regression model...",
#>   "coefficient_interpretation": "The coefficient for 'Price' is -0.10, suggesting that...",
#>   "significance_assessment": "The p-value for 'Price' is very small (< 0.001)...",
#>   "goodness_of_fit": "The R-squared value is 0.87, indicating...",
#>   "assumptions_check": "Assumptions such as linearity and homoscedasticity should be checked by examining residual plots.",
#>   "key_findings": "- Price is a significant negative predictor of sales.\n- Advertising has a positive impact on sales.",
#>   "warnings_limitations": "This model is based on simulated data and results should be interpreted with caution."
#> }
#> 
#> Ensure the entire output is ONLY the JSON object.
#> DO NOT wrap your entire response in JSON code fences (e.g., ```json ... ``` or ``` ... ```).
#> DO NOT include any conversational pleasantries or introductory/concluding phrases.
#> 
#> 
#> ## Instructions
#> 
#> You are explaining a **Linear Mixed-Effects Model** (from `lme4::lmer()`, an `lmerMod` object).
#> 
#> **Core Concepts & Purpose:**
#> This model is used for data with hierarchical/nested structures or repeated measures, where observations are not independent. It models fixed effects (average effects of predictors) and random effects (variability between groups/subjects for intercepts and/or slopes).
#> 
#> **Key Assumptions:**
#> * Linearity: The relationship between predictors and the outcome is linear.
#> * Independence of random effects and errors: Random effects are independent of each other and of the residuals (conditional on covariates).
#> * Normality of random effects: Random effects for each grouping factor are normally distributed (typically with mean 0).
#> * Normality of residuals: The errors (residuals) are normally distributed with a mean of 0.
#> * Homoscedasticity: Residuals have constant variance.
#> * (Note on p-values: `lme4::lmer` itself does not calculate p-values for fixed effects by default due to complexities with degrees of freedom. If p-values are present, they often come from wrapper functions or packages like `lmerTest` using approximations like Satterthwaite's or Kenward-Roger methods.)
#> 
#> **Assessing Model Appropriateness (Based on User Context):**
#> If the user provides context:
#> * Comment on the model's appropriateness based on the data structure (e.g., repeated measures, nesting) and research question.
#> * Relate this to the model's assumptions.
#> If no or insufficient context, state inability to fully assess appropriateness.
#> 
#> **Interpretation of the `lmerMod` Output:**
#> * **Formula and Data:** Briefly reiterate what is being modeled.
#> * **REML vs ML:** Note if Restricted Maximum Likelihood (REML) or Maximum Likelihood (ML) was used (REML is default and often preferred for variance components; ML for likelihood ratio tests of fixed effects).
#> * **Random Effects (from `VarCorr()` output):**
#>     * For each grouping factor (e.g., `(1 | group_factor)` or `(predictor | group_factor)`):
#>         * **Variance and Std.Dev. (for intercepts):** Quantifies between-group variability in the baseline outcome.
#>         * **Variance and Std.Dev. (for slopes):** Quantifies how much the effect of that predictor varies across groups.
#>         * **Correlation of Random Effects (e.g., `Corr` between random intercept and slope for the same group):** Explain its meaning (e.g., a correlation of -0.5 between intercept and slope for 'day' within 'subject' means subjects with higher initial values tend to have a less steep increase over days).
#>     * **Residual Variance/Std.Dev.:** Within-group or unexplained variability.
#> * **Fixed Effects (from `coef(summary(object))`):**
#>     * For each predictor:
#>         * **Estimate:** The estimated average effect on the outcome for a one-unit change in the predictor (or difference from the reference level for categorical predictors), accounting for random effects.
#>         * **Std. Error:** Precision of the estimate.
#>         * **t-value (or z-value):** `Estimate / Std. Error`.
#>         * **P-values (if available, typically from `lmerTest` via `summary(as(object, "lmerModLmerTest"))` or `anova(object)` from `lmerTest`):** Interpret as the probability of observing such an extreme t-value if the true fixed effect is zero. If p-values are NOT directly in the basic `summary(object)` output, mention they usually come from add-on packages.
#> * **ANOVA Table for Fixed Effects (if provided, typically from `lmerTest::anova()`):**
#>     * Tests the overall significance of fixed effects. For each term: interpret F-statistic, degrees of freedom (NumDF, DenDF), and p-value.
#> * **Model Fit Statistics (AIC, BIC, logLik, deviance):**
#>     * Explain as measures for model comparison. Lower AIC/BIC, higher logLik (less negative deviance) generally indicate better relative fit.
#> 
#> **Suggestions for Checking Assumptions:**
#> * **Normality of Residuals:** Suggest Q-Q plot or histogram of residuals (`resid(object)`).
#> * **Homoscedasticity:** Suggest plotting residuals vs. fitted values (`fitted(object)`). Look for non-constant spread.
#> * **Normality of Random Effects:** Suggest Q-Q plots of the random effects (e.g., from `ranef(object)`).
#> * **Linearity (Fixed Effects):** Check by plotting residuals against continuous predictors.
#> * **Influential Observations:** Mention checking for influential data points.
#> * **Singularity:** If the model is reported as singular (e.g. random effect variances near zero or correlations near +/-1), this often indicates an overly complex random effects structure that the data cannot support.
#> 
#> **Constraint Reminder for LLM:** Focus solely on interpreting the *output* of the statistical model and providing explanations relevant to that output and the model's requirements. Do not perform new calculations or suggest alternative analyses unless directly prompted by assessing the appropriateness based on provided context. **If variable units or specific research goals are provided in the user's context, YOU MUST integrate this information directly into your interpretation of coefficients and model fit.**
#> 
#> 
#> ## Caution
#> 
#> This explanation was generated by a Large Language Model. Advise the user to critically review the output and consult additional statistical resources or experts to ensure correctness and a full understanding, especially given that the interpretation relies on the provided output and context.
#> ── user [2337] ──────────────────────────────────────────────────────────────────────────────────────
#> Explain the following linear mixed-effects model output:
#> Linear mixed model fit by REML ['lmerMod']
#> Formula: Reaction ~ Days + (Days | Subject)
#>    Data: sleepstudy
#> 
#> REML criterion at convergence: 1743.6
#> 
#> Scaled residuals: 
#>     Min      1Q  Median      3Q     Max 
#> -3.9536 -0.4634  0.0231  0.4634  5.1793 
#> 
#> Random effects:
#>  Groups   Name        Variance Std.Dev. Corr
#>  Subject  (Intercept) 612.10   24.741       
#>           Days         35.07    5.922   0.07
#>  Residual             654.94   25.592       
#> Number of obs: 180, groups:  Subject, 18
#> 
#> Fixed effects:
#>             Estimate Std. Error t value
#> (Intercept)  251.405      6.825  36.838
#> Days          10.467      1.546   6.771
#> 
#> Correlation of Fixed Effects:
#>      (Intr)
#> Days -0.138
#> 
#> ## Additional context to consider
#> 
#> 
#> This linear mixed-effects model analyzes data from a sleep deprivation study.
#> The goal is to understand the effect of days of sleep deprivation ('Days') on
#> average reaction time ('Reaction' in ms). The model includes random intercepts
#> and random slopes for 'Days' for each 'Subject', acknowledging that baseline
#> reaction times and the effect of sleep deprivation may vary across individuals.
#> We are interested in the average fixed effect of an additional day of sleep
#> deprivation on reaction time, as well as the extent of inter-subject
#> variability.
#> 
#> ── assistant [887] ──────────────────────────────────────────────────────────────────────────────────
#> ```json
#> {
#>   "title": "Explanation of Linear Mixed-Effects Model for Sleep Deprivation Study",
#>   "model_overview": "This is a linear mixed-effects model, fitted using Restricted Maximum Likelihood (REML), examining the impact of sleep deprivation (Days) on reaction time (Reaction). The model accounts for inter-individual variability by including random intercepts and slopes for each subject, allowing for differences in baseline reaction times and how reaction time changes with sleep deprivation across individuals. This type of model is suitable due to the repeated measures design, where we have multiple observations for each subject.",
#>   "coefficient_interpretation": "The fixed effects estimates provide the average effect of each predictor on reaction time across all subjects. The intercept is estimated at 251.405 ms, which represents the average reaction time at Day 0 (the baseline reaction time) across all subjects. The coefficient for 'Days' is 10.467 ms. This indicates that, on average, reaction time increases by 10.467 milliseconds for each additional day of sleep deprivation. So, each day of sleep deprivation increases reaction time by about 10.5 ms.",
#>   "significance_assessment": "The t-value for the intercept is 36.838 and for 'Days' is 6.771. Although the output doesn't directly provide p-values, these t-values can be used to assess statistical significance. Given the large t-values, especially for 'Days', it's highly likely that the effect of days of sleep deprivation on reaction time is statistically significant. The standard error for 'Days' is 1.546, which provides a measure of the precision of the estimated effect of sleep deprivation. Packages like `lmerTest` can be used with this model to obtain p-values for these fixed effects estimates using methods like Satterthwaite or Kenward-Roger approximations.",
#>   "goodness_of_fit": "The REML criterion at convergence is 1743.6. This value is useful for comparing nested models fitted to the same data. Lower REML values indicate a better fit, but only when comparing models with the same fixed effects. Other metrics like AIC and BIC, which can be obtained from the model, are better suited to non-nested model comparisons.",
#>   "assumptions_check": "Several assumptions should be checked to ensure the validity of this model. First, examine the normality of the residuals using a Q-Q plot or histogram of `resid(object)`. Second, assess homoscedasticity by plotting residuals against fitted values (`fitted(object)`), looking for constant variance. Third, check the normality of the random effects using Q-Q plots of the random effects (`ranef(object)`). Additionally, linearity of the fixed effect 'Days' should be checked, possibly by plotting residuals against 'Days'. Finally, it's important to check for influential observations that might disproportionately affect the model results.",
#>   "key_findings": "- On average, baseline reaction time (Day 0) is estimated to be approximately 251.4 ms.\n- Each additional day of sleep deprivation is associated with an average increase of approximately 10.5 ms in reaction time.\n- There is substantial inter-individual variability in both baseline reaction time (Std.Dev. = 24.741 ms) and the effect of sleep deprivation (Std.Dev. = 5.922 ms) across subjects.\n- The correlation between random intercepts and slopes is low (0.07), suggesting a weak relationship between a subject's baseline reaction time and how their reaction time changes with sleep deprivation.",
#>   "warnings_limitations": "The interpretation relies on the assumption that the model is correctly specified and that the assumptions of linear mixed-effects models are met. The absence of p-values in the base output from `lmer` should be addressed using appropriate packages like `lmerTest` to draw firmer conclusions about statistical significance. Also, remember that correlation does not equal causation; while the model suggests a relationship between sleep deprivation and reaction time, it does not prove that sleep deprivation *causes* the change in reaction time."
#> }
#> ```

This transparency is invaluable for debugging, understanding the process, or even refining prompts if you were developing custom extensions for statlingua.

Conclusion

The statlingua package, working hand-in-hand with ellmer, provides a powerful and user-friendly bridge to the interpretive capabilities of Large Language Models for R users. By mastering the explain() function and its arguments—especially context, audience, verbosity, and style—you can transform standard statistical outputs into rich, understandable narratives tailored to your needs.

Important Considerations: * The quality of the LLM’s explanation is heavily influenced by the clarity of the context you provide and the inherent capabilities of the LLM you choose (in this vignette, we’ve focused on Google Gemini). * LLM Output Variability: While statlingua uses detailed prompts to guide the LLM towards the desired output style and content, the nature of generative AI means that responses can vary. The requested style is an aim, and while statlingua includes measures to clean the output (like removing language fences), the exact formatting and content may not always be perfectly consistent across repeated calls or different LLM versions. Always critically review the generated explanations. * For the style = "json" option, which requests JSON output, ensure the jsonlite package is available if you intend to parse the JSON string into an R list within your session.

Remember to critically review all explanations generated by the LLM.

Happy explaining!