From 7a52f890dbc6d4cd5cc2a3799cd5e0d4590345e0 Mon Sep 17 00:00:00 2001
From: GFarage <faragegr@gmail.com>
Date: Mon, 27 Jul 2026 18:50:55 -0500
Subject: [PATCH 1/9] added StableRNGs in docs; updated README badges

---
 README.md         | 2 +-
 docs/Project.toml | 1 +
 2 files changed, 2 insertions(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 7af0566..612bcd6 100644
--- a/README.md
+++ b/README.md
@@ -2,10 +2,10 @@
 
 [![CI](https://github.com/senresearch/MatrixLM.jl/actions/workflows/ci.yml/badge.svg)](https://github.com/senresearch/MatrixLM.jl/actions/workflows/ci.yml)
 [![codecov](https://codecov.io/gh/senresearch/MatrixLM.jl/branch/main/graph/badge.svg?token=uHM6utUQoi)](https://codecov.io/gh/senresearch/MatrixLM.jl)
-[![GNU Affero license](https://img.shields.io/badge/license%20-GNU%20AFFERO%20GENERAL%20PUBLIC%20-green)](https://github.com/senresearch/MatrixLM.jl/blob/main/LICENSE.md)
 [![Stable](https://img.shields.io/badge/docs-stable-blue.svg)](https://senresearch.github.io/MatrixLM.jl/stable)
 [![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://senresearch.github.io/MatrixLM.jl/dev) 
 [![Pkg Status](https://www.repostatus.org/badges/latest/active.svg)](https://www.repostatus.org/#active)
+[![GNU Affero license](https://img.shields.io/badge/license%20-GNU%20AFFERO%20GENERAL%20PUBLIC%20-green)](https://github.com/senresearch/MatrixLM.jl/blob/main/LICENSE.md)
 
 ## Description
 
diff --git a/docs/Project.toml b/docs/Project.toml
index e43e58d..88abe1e 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -3,6 +3,7 @@ DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 MatrixLM = "37290134-6146-11e9-0c71-a5c489be1f53"
 Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
+StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
 StatsModels = "3eaba693-59b7-5ba5-a881-562e759f1c8d"
 
 [compat]

From 91c78eba80b4ce8de30b629df03286a9b95dae96 Mon Sep 17 00:00:00 2001
From: Gregory Farage <faragegr@gmail.com>
Date: Mon, 27 Jul 2026 23:32:27 -0500
Subject: [PATCH 2/9] added show.jl

---
 src/show.jl | 71 +++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 71 insertions(+)
 create mode 100644 src/show.jl

diff --git a/src/show.jl b/src/show.jl
new file mode 100644
index 0000000..80f799c
--- /dev/null
+++ b/src/show.jl
@@ -0,0 +1,71 @@
+"""
+    show(io::IO, data::RawData)
+
+Display a compact summary of a `RawData` object.
+"""
+function Base.show(io::IO, data::RawData)
+    print(
+        io,
+        "RawData(n=$(data.n), m=$(data.m), p=$(data.p), q=$(data.q))",
+    )
+end
+
+"""
+    show(io::IO, ::MIME"text/plain", data::RawData)
+
+Display a readable summary of the matrices and dimensions stored in a
+`RawData` object.
+"""
+function Base.show(io::IO, ::MIME"text/plain", data::RawData)
+    println(io, "RawData")
+    println(io, "  Response matrix Y: $(data.n) × $(data.m)")
+    println(io, "  Design matrix X: $(data.n) × $(data.p)")
+    println(io, "  Design matrix Z: $(data.m) × $(data.q)")
+    println(io, "  X includes intercept: $(data.predictors.hasXIntercept)")
+    print(io, "  Z includes intercept: $(data.predictors.hasZIntercept)")
+end
+
+"""
+    show(io::IO, model::Mlm)
+
+Display a compact summary of a fitted matrix linear model.
+"""
+function Base.show(io::IO, model::Mlm)
+    print(
+        io,
+        "Mlm($(size(model.B, 1)) × $(size(model.B, 2)) coefficient matrix)",
+    )
+end
+
+"""
+    show(io::IO, ::MIME"text/plain", model::Mlm)
+
+Display a readable summary of a fitted matrix linear model.
+"""
+function Base.show(io::IO, ::MIME"text/plain", model::Mlm)
+    data = model.data
+
+    println(io, "Matrix linear model fit")
+    println(io, "  Observations: $(data.n)")
+    println(io, "  Responses: $(data.m)")
+    println(io, "  Row predictors: $(data.p)")
+    println(io, "  Column predictors: $(data.q)")
+    println(
+        io,
+        "  Coefficient matrix B: " *
+        "$(size(model.B, 1)) × $(size(model.B, 2))",
+    )
+    println(
+        io,
+        "  Residual covariance matrix: " *
+        "$(size(model.sigma, 1)) × $(size(model.sigma, 2))",
+    )
+    println(io, "  Weighted fit: $(model.weights !== nothing)")
+
+    if model.targetType === nothing
+        print(io, "  Covariance shrinkage: none")
+    else
+        println(io, "  Covariance shrinkage target: $(model.targetType)")
+        print(io, "  Shrinkage coefficient: $(model.lambda)")
+    end
+end
\ No newline at end of file

From 095031137de448b01b4017f5eb467fb8aa5578fe Mon Sep 17 00:00:00 2001
From: Gregory Farage <faragegr@gmail.com>
Date: Mon, 27 Jul 2026 23:33:49 -0500
Subject: [PATCH 3/9] added test routines for show functions

---
 test/show_test.jl | 34 ++++++++++++++++++++++++++++++++++
 1 file changed, 34 insertions(+)
 create mode 100644 test/show_test.jl

diff --git a/test/show_test.jl b/test/show_test.jl
new file mode 100644
index 0000000..2173232
--- /dev/null
+++ b/test/show_test.jl
@@ -0,0 +1,34 @@
+@testset "show methods" begin
+    Y = randn(10, 5)
+    X = hcat(ones(10), randn(10))
+    Z = hcat(ones(5), randn(5))
+
+    response = Response(Y)
+    predictors = Predictors(X, Z, true, true)
+    data = RawData(response, predictors)
+
+    compact_data = sprint(show, data)
+    detailed_data = sprint(
+        show,
+        MIME"text/plain"(),
+        data,
+    )
+
+    @test compact_data == "RawData(n=10, m=5, p=2, q=2)"
+    @test occursin("Response matrix Y: 10 × 5", detailed_data)
+    @test occursin("X includes intercept: true", detailed_data)
+
+    model = mlm(data)
+
+    compact_model = sprint(show, model)
+    detailed_model = sprint(
+        show,
+        MIME"text/plain"(),
+        model,
+    )
+
+    @test compact_model == "Mlm(2 × 2 coefficient matrix)"
+    @test occursin("Matrix linear model fit", detailed_model)
+    @test occursin("Observations: 10", detailed_model)
+    @test occursin("Coefficient matrix B: 2 × 2", detailed_model)
+end
\ No newline at end of file

From 370afc61895dadc894c18bfd9a30ceb5abc6fcf6 Mon Sep 17 00:00:00 2001
From: Gregory Farage <faragegr@gmail.com>
Date: Mon, 27 Jul 2026 23:52:38 -0500
Subject: [PATCH 4/9] updated documentation showing more intermediate results

---
 docs/src/example_ordinal_data.md | 41 ++++++++++++++++++++++++-----
 docs/src/getting_started.md      | 45 ++++++++++++++++++++++++++------
 docs/src/varShrinkage_example.md | 35 +++++++++++++++++++++----
 src/MatrixLM.jl                  |  6 ++++-
 test/runtests.jl                 |  1 +
 5 files changed, 107 insertions(+), 21 deletions(-)

diff --git a/docs/src/example_ordinal_data.md b/docs/src/example_ordinal_data.md
index e608c1a..22fadcc 100644
--- a/docs/src/example_ordinal_data.md
+++ b/docs/src/example_ordinal_data.md
@@ -36,7 +36,9 @@ This matrix is generated as a normally distributed matrix
 
 ```@example
 using MatrixLM, DataFrames, Random, Plots, StatsModels, Statistics
-Random.seed!(1)
+using StableRNGs
+
+rng = StableRNG(2026)
 
 # Dimensions of matrices 
 n = 100
@@ -46,10 +48,10 @@ m = 250
 q = 4
 
 # Generate data with 1 ordinal categorical variable.
-dfX = DataFrame(catvar=rand(1:5, n));
+dfX = DataFrame(catvar=rand(rng, 1:5, n));
 levels_catvar = sort(unique(dfX.catvar));
 
-nothing #hide
+first(dfX, 5)
 ```
 
 To derive the predictor design matrix, we employ the `design_matrix()` function and apply contrast coding using the `SeqDiffCoding()` system. This particular coding system is particularly useful for testing hypotheses related to "sequential differences" between the levels of our ordinal predictor.
@@ -62,7 +64,7 @@ X_ctrst = Dict(
 X = design_matrix(@mlmformula(1 + catvar), dfX, X_ctrst);
 p = size(X, 2);
 
-nothing #hide
+X[1:5, :]
 ```
 
 The design matrix `X` has `p = 5` columns defined as:
@@ -76,14 +78,14 @@ We randomly generate a dataframe `Z` that provides information about whether a r
 The `FullDummyCoding` system generates one indicator (1 or 0) column for each level, including the base level. This technique is sometimes called one-hot encoding and is widely used for categorical variables.
 
 ```@example
-dfZ = DataFrame(attribute= rand(["A", "B", "C", "D"], m))
+dfZ = DataFrame(attribute= rand(rng, ["A", "B", "C", "D"], m))
 Z_ctrst = Dict(
              :attribute => StatsModels.FullDummyCoding(),
           )
            
 Z = design_matrix(@mlmformula(0 + attribute), dfZ, Z_ctrst);
 
-nothing #hide
+Z[1:5, :]
 ```
 
 The design matrix `Z` has `q = 4` columns defined as:
@@ -95,7 +97,7 @@ Z_names = MatrixLM.design_matrix_names(@mlmformula(0 + attribute), dfZ, Z_ctrst)
 The error matrix `E` is obtained as follows:
 
 ```@example
-E = randn(n,m).*4;
+E = randn(rng, n,m).*4;
 
 nothing #hide
 ```
@@ -135,6 +137,18 @@ dat = RawData(Response(Y), Predictors(X, Z, true, false));
 nothing #hide
 ```
 
+We can use the function `show()` and `display()` to respectively 
+display a compact and a readable summary of he matrices and 
+dimensions stored in a `RawData` object.
+
+```@example
+show(dat)
+```
+
+```@example
+display(dat)
+```
+
 ## Model estimation
 
 
@@ -145,6 +159,19 @@ est = mlm(dat; addXIntercept=false, addZIntercept=false); # Model estimation
 nothing # hide
 ```
 
+We can use the function `show()` and `display()` to respectively 
+display a compact and a readable summary of 
+a fitted matrix linear model, i.e. `Mlm` object.
+
+```@example
+show(est)
+```
+
+```@example
+display(est)
+```
+
+
 ## Model predictions and residuals
 
 
diff --git a/docs/src/getting_started.md b/docs/src/getting_started.md
index 5df6f98..7815918 100644
--- a/docs/src/getting_started.md
+++ b/docs/src/getting_started.md
@@ -41,7 +41,9 @@ We generate this matrix as a normally distributed matrix
 
 ```@example
 using MatrixLM, DataFrames, Random, Plots, StatsModels, Statistics
-Random.seed!(1)
+using StableRNGs
+
+rng = StableRNG(2026)
 
 # Dimensions of matrices 
 n = 100
@@ -52,11 +54,11 @@ q = 10
 
 # Generate data with two categorical variables and 3 numerical variables.
 dfX = hcat(
-    DataFrame(catvar1=string.(rand(0:1, n)), catvar2=rand(["A", "B", "C", "D"], n)), 
-    DataFrame(rand(n,3), ["var3", "var4", "var5"])
+    DataFrame(catvar1=string.(rand(rng, 0:1, n)), catvar2=rand(rng, ["A", "B", "C", "D"], n)), 
+    DataFrame(rand(rng, n,3), ["var3", "var4", "var5"])
     );
 
-nothing #hide
+first(dfX, 5)
 ```
 
 Let's use the function `design_matrix()` to get the predictor model matrix based on the formula expression, including all the variable terms.
@@ -67,7 +69,7 @@ X = design_matrix(@mlmformula(catvar1 + catvar2 + var3 + var4 + var5), dfX)
 
 p = size(X)[2]; # 5 columns in dfX, but p=7 coefs bc catvar2 has 4 levels
 
-nothing #hide
+X[1:5, :]
 ```
 
 We also have the option to specify contrast coding in our model.
@@ -84,14 +86,14 @@ my_ctrst = Dict(
            
 X = design_matrix(@mlmformula(catvar1 + catvar2 + var3 + var4 + var5), dfX, my_ctrst);
 
-nothing #hide
+X[1:5, :]
 ```
 
 Randomly generate some data for column covariates `Z` and the error matrix `E`:
 
 ```@example
-Z = rand(m,q);
-E = randn(n,m).*4;
+Z = rand(rng, m,q);
+E = randn(rng, n,m).*4;
 
 nothing #hide
 ```
@@ -130,6 +132,20 @@ dat = RawData(Response(Y), Predictors(X, Z));
 nothing #hide
 ```
 
+We can use the function `show()` and `display()` to respectively 
+display a compact and a readable summary of he matrices and 
+dimensions stored in a `RawData` object.
+
+```@example
+show(dat)
+```
+
+```@example
+display(dat)
+```
+
+
+
 ## Model estimation
 
 
@@ -141,6 +157,19 @@ est = mlm(dat; addXIntercept=false, addZIntercept=false); # Model estimation
 nothing #hide
 ```
 
+We can use the function `show()` and `display()` to respectively 
+display a compact and a readable summary of 
+a fitted matrix linear model, i.e. `Mlm` object.
+
+```@example
+show(est)
+```
+
+```@example
+display(est)
+```
+
+
 ## Model predictions and residuals
 
 
diff --git a/docs/src/varShrinkage_example.md b/docs/src/varShrinkage_example.md
index f6814af..cee48e2 100644
--- a/docs/src/varShrinkage_example.md
+++ b/docs/src/varShrinkage_example.md
@@ -48,7 +48,9 @@ correlations.
 
 ```@example varshrinkage
 using MatrixLM, LinearAlgebra, Random, Statistics
-Random.seed!(1)
+using StableRNGs
+
+rng = StableRNG(27072026)
 
 # Matrix dimensions
 n = 100
@@ -57,8 +59,8 @@ p = 5
 q = 4
 
 # Row and column predictors
-X = randn(n, p)
-Z = randn(m, q)
+X = randn(rng, n, p)
+Z = randn(rng, m, q)
 
 # True coefficient matrix
 B = [
@@ -83,8 +85,8 @@ standard_deviations = sqrt.(variances)
 rho = 0.6
 
 # Generate correlated, heteroskedastic errors
-common_noise = randn(n, 1)
-independent_noise = randn(n, m)
+common_noise = randn(rng, n, 1)
+independent_noise = randn(rng, n, m)
 
 E = (
     sqrt(rho) .* common_noise .+
@@ -113,6 +115,18 @@ dat = RawData(
 nothing #hide
 ```
 
+We can use the function `show()` and `display()` to respectively 
+display a compact and a readable summary of he matrices and 
+dimensions stored in a `RawData` object.
+
+```@example
+show(dat)
+```
+
+```@example
+display(dat)
+```
+
 ## Model Estimation Without Variance Shrinkage
 
 Set the positional Boolean argument to `false` to estimate the residual covariance matrix without shrinkage.
@@ -127,6 +141,17 @@ est_no_shrinkage = mlm(
 
 nothing #hide
 ```
+We can use the function `show()` and `display()` to respectively 
+display a compact and a readable summary of 
+a fitted matrix linear model, i.e. `Mlm` object.
+
+```@example
+show(est)
+```
+
+```@example
+display(est)
+```
 
 The fitted object contains the coefficient estimates in `B`, the estimated error covariance matrix in `sigma`, and the coefficient variance estimates in `varB`.
 
diff --git a/src/MatrixLM.jl b/src/MatrixLM.jl
index e0bb545..65eea81 100644
--- a/src/MatrixLM.jl
+++ b/src/MatrixLM.jl
@@ -43,10 +43,14 @@ module MatrixLM
     include("mlm.jl")
     export Mlm, mlm, t_stat
 
-    # # Estimate extraction
+    # Estimate extraction
     include("summary.jl")
     export confint, summary
 
+    # Show methods
+    include("show.jl")
+    export show
+
     # Predictions and residuals
     include("predict.jl")
     export coef, predict, fitted, residuals
diff --git a/test/runtests.jl b/test/runtests.jl
index dd0de4f..be8b24c 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -28,4 +28,5 @@ using Test
     include("contr_test.jl")
     include("calc_sigma_test.jl")
     include("summary_test.jl")
+    include("show_test.jl")
 end

From 44cfdc2fb2ed9052aa9b8e3b4d9548d21f545bdb Mon Sep 17 00:00:00 2001
From: Gregory Farage <faragegr@gmail.com>
Date: Tue, 28 Jul 2026 00:34:28 -0500
Subject: [PATCH 5/9] added real data application example

---
 docs/src/application_to_real_data.md | 46 ++++++++++++++++++++++++++++
 1 file changed, 46 insertions(+)
 create mode 100644 docs/src/application_to_real_data.md

diff --git a/docs/src/application_to_real_data.md b/docs/src/application_to_real_data.md
new file mode 100644
index 0000000..6ea7dc2
--- /dev/null
+++ b/docs/src/application_to_real_data.md
@@ -0,0 +1,46 @@
+# Applications to Real Data
+
+`MatrixLM.jl` has been used to analyze real datasets in metabolomics and high-throughput chemical genetic screening. The repositories below provide code, data-processing workflows, and examples associated with published applications of matrix linear models.
+
+## Metabolomics
+
+The [`mlm-metabolomics-supplement`](https://github.com/senresearch/mlm-metabolomics-supplement) repository contains tools, scripts, and notebooks for preprocessing, analyzing, and visualizing metabolomics data from three studies:
+
+* Statin-Associated Muscle Symptoms (SAMS)
+* Pansteatitis in Mozambique tilapia
+* Chronic Obstructive Pulmonary Disease (COPD)
+
+Each study is organized in a separate directory containing descriptions of the corresponding data-processing and analysis workflow.
+
+These applications demonstrate how matrix linear models can relate individual-level characteristics, such as disease or treatment status, to metabolite measurements while incorporating metabolite-level information, such as chemical composition or metabolite class.
+
+**Reference**
+
+Farage, G., Zhao, C., Choi, H. Y., et al. (2025). Matrix Linear Models for Connecting Metabolite Composition to Individual Characteristics. *Metabolites*, 15(2), 140.
+https://doi.org/10.3390/metabo15020140
+
+## High-Throughput Chemical Genetic Screens
+
+The [`mlm_gs_supplement`](https://github.com/senresearch/mlm_gs_supplement) repository contains code used to reproduce the analyses presented in *Matrix Linear Models for High-Throughput Chemical Genetic Screens*.
+
+The study applies matrix linear models to an *Escherichia coli* chemical genetic screen to examine relationships between mutant strains and experimental conditions. The analyses were primarily performed in Julia, while visualizations were produced in R.
+
+Instructions for obtaining and preparing the data are provided in the supplemental repository.
+
+**Reference**
+
+Liang, J. W., Nichols, R. J., & Sen, Ś. (2019). Matrix Linear Models for High-Throughput Chemical Genetic Screens. *Genetics*, 212(4), 1063–1073.
+https://doi.org/10.1534/genetics.119.302299
+
+## Using These Examples
+
+These repositories contain complete research workflows rather than small introductory examples. Users who are new to `MatrixLM.jl` may wish to begin with the package tutorials before consulting these applications.
+
+The supplemental repositories are useful for understanding how matrix linear models can be incorporated into larger workflows involving:
+
+* data preprocessing;
+* construction of sample- and response-level design matrices;
+* model fitting;
+* extraction of coefficients and p-values;
+* visualization and interpretation of results; and
+* saving analysis outputs.

From b207c756404f713dc7b456a7feb21d60826f5009 Mon Sep 17 00:00:00 2001
From: Gregory Farage <faragegr@gmail.com>
Date: Tue, 28 Jul 2026 13:46:34 -0500
Subject: [PATCH 6/9] updated doc with StableRNGs

---
 Project.toml                     |  5 +++
 docs/Project.toml                |  4 +-
 docs/make.jl                     |  4 ++
 docs/src/example_ordinal_data.md | 18 ++------
 docs/src/getting_started.md      | 49 +++++++++-------------
 docs/src/varShrinkage_example.md | 29 +++++--------
 src/show.jl                      | 70 ++++++++++++++++++++------------
 test/show_test.jl                | 43 +++++++++++++-------
 8 files changed, 118 insertions(+), 104 deletions(-)

diff --git a/Project.toml b/Project.toml
index 7cda4a0..c0c6154 100644
--- a/Project.toml
+++ b/Project.toml
@@ -3,6 +3,9 @@ uuid = "37290134-6146-11e9-0c71-a5c489be1f53"
 version = "1.0.0"
 authors = ["Jane Liang", "Gregory Farage", "Chenhao Zhao", "Harsh Vardhan Dubey", "Saunak Sen"]
 
+[workspace]
+projects = ["docs"]
+
 [deps]
 DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
 Distributed = "8ba89e20-285c-5b6f-9357-94700520ee1b"
@@ -10,6 +13,7 @@ Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 SharedArrays = "1a1011a3-84de-559e-8e89-a11a2f7dc383"
+StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 StatsAPI = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
 StatsModels = "3eaba693-59b7-5ba5-a881-562e759f1c8d"
@@ -23,6 +27,7 @@ GLM = "1.8"
 LinearAlgebra = "1"
 Random = "1"
 SharedArrays = "1"
+StableRNGs = "1.0.4"
 Statistics = "1"
 StatsAPI = "1.8.0"
 StatsModels = "0.6, 0.7"
diff --git a/docs/Project.toml b/docs/Project.toml
index 88abe1e..7b18cfb 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -7,4 +7,6 @@ StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
 StatsModels = "3eaba693-59b7-5ba5-a881-562e759f1c8d"
 
 [compat]
-Documenter = "1"
+DataFrames = "1.8.1"
+Documenter = "1.17.0"
+StatsModels = "0.7.7"
diff --git a/docs/make.jl b/docs/make.jl
index 1e0371c..46110d9 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -1,5 +1,8 @@
 using MatrixLM
 using Documenter
+# using Pkg
+
+# Pkg.add("StableRNGs")
 
 # copy readme into index.md
 open(joinpath(@__DIR__, "src", "index.md"), "w") do io
@@ -11,6 +14,7 @@ makedocs(; modules=[MatrixLM], sitename="MatrixLM.jl", pages=[
         "Getting Started" => "getting_started.md",
         "Example: MLM for ordinal predictors" => "example_ordinal_data.md",
         "Example: Variance Shrinkage with MatrixLM.jl" => "varShrinkage_example.md",
+        "Example: Application to real data" => "application_to_real_data.md",
         "Types and Functions" => "functions.md",
     ]
 )
diff --git a/docs/src/example_ordinal_data.md b/docs/src/example_ordinal_data.md
index 22fadcc..0b46e6b 100644
--- a/docs/src/example_ordinal_data.md
+++ b/docs/src/example_ordinal_data.md
@@ -137,18 +137,13 @@ dat = RawData(Response(Y), Predictors(X, Z, true, false));
 nothing #hide
 ```
 
-We can use the function `show()` and `display()` to respectively 
-display a compact and a readable summary of he matrices and 
-dimensions stored in a `RawData` object.
+We can use the function `show()` to respectively display 
+a readable summary of the matrices and dimensions stored in a `RawData` object.
 
 ```@example
 show(dat)
 ```
 
-```@example
-display(dat)
-```
-
 ## Model estimation
 
 
@@ -159,18 +154,13 @@ est = mlm(dat; addXIntercept=false, addZIntercept=false); # Model estimation
 nothing # hide
 ```
 
-We can use the function `show()` and `display()` to respectively 
-display a compact and a readable summary of 
-a fitted matrix linear model, i.e. `Mlm` object.
+We can use the function `show()` to respectively display 
+a readable summary of the matrices and dimensions stored in a `Mlm` object.
 
 ```@example
 show(est)
 ```
 
-```@example
-display(est)
-```
-
 
 ## Model predictions and residuals
 
diff --git a/docs/src/getting_started.md b/docs/src/getting_started.md
index 7815918..cb48c30 100644
--- a/docs/src/getting_started.md
+++ b/docs/src/getting_started.md
@@ -39,7 +39,7 @@ We generate this matrix as a normally distributed matrix
 (all values from N(0,σ=4)), adding a layer of randomness to our simulation.
 
 
-```@example
+```@example 
 using MatrixLM, DataFrames, Random, Plots, StatsModels, Statistics
 using StableRNGs
 
@@ -63,7 +63,7 @@ first(dfX, 5)
 
 Let's use the function `design_matrix()` to get the predictor model matrix based on the formula expression, including all the variable terms.
 
-```@example
+```@example 
 # Convert dataframe to prediction matrix
 X = design_matrix(@mlmformula(catvar1 + catvar2 + var3 + var4 + var5), dfX)
 
@@ -77,7 +77,7 @@ For a detailed understanding of how to implement contrast coding,
 please refer to the documentation for [contrast coding with StatsModels.jl](https://juliastats.org/StatsModels.jl/stable/contrasts/#How-to-specify-contrast-coding).
 This provides comprehensive instructions and examples.
 
-```@example
+```@example 
 # Convert dataframe to prediction matrix
 my_ctrst = Dict(
              :catvar1 => DummyCoding(base = "0"),
@@ -91,7 +91,7 @@ X[1:5, :]
 
 Randomly generate some data for column covariates `Z` and the error matrix `E`:
 
-```@example
+```@example 
 Z = rand(rng, m,q);
 E = randn(rng, n,m).*4;
 
@@ -100,7 +100,7 @@ nothing #hide
 
 Next, we will structure the coefficient matrix B following a specific pattern. This approach will facilitate a more effective visualization of the results in the subsequent steps:
 
-```@example
+```@example 
 # (p,q)
 B = [
     2.0   3.0   4.0   5.0  6.0  7.0  8.0  0.0 0.5 -2.0;
@@ -117,7 +117,7 @@ nothing #hide
 
 Generate the response matrix `Y`:
 
-```@example
+```@example 
 Y = X*B*Z' + E;
 
 nothing #hide
@@ -125,50 +125,39 @@ nothing #hide
 
 Now, construct the `RawData` object consisting of the response variable `Y` and row/column predictors `X` and `Z`. All three matrices must be passed in as 2-dimensional arrays.
 
-```@example
+```@example 
 # Construct a RawData object
 dat = RawData(Response(Y), Predictors(X, Z));
 
 nothing #hide
 ```
 
-We can use the function `show()` and `display()` to respectively 
-display a compact and a readable summary of he matrices and 
-dimensions stored in a `RawData` object.
+We can use the function `show()` to respectively display 
+a readable summary of the matrices and dimensions stored in a `RawData` object.
 
 ```@example
 show(dat)
 ```
 
-```@example
-display(dat)
-```
-
-
 
 ## Model estimation
 
 
 Least-squares estimates for matrix linear models can be obtained by running `mlm`. An object of type `Mlm` will be returned, with variables for the coefficient estimates (`B`), the coefficient variance estimates (`varB`), and the estimated variance of the errors (`sigma`). By default, `mlm` estimates both row and column main effects (X and Z intercepts), but this behavior can be suppressed by setting `addXIntercept=false` and/or `addZIntercept=false`. Column weights for `Y` and the target type for variance shrinkage[^1] can be optionally supplied to `weights` and `targetType`, respectively. 
 
-```@example
+```@example 
 est = mlm(dat; addXIntercept=false, addZIntercept=false); # Model estimation
 
 nothing #hide
 ```
 
-We can use the function `show()` and `display()` to respectively 
-display a compact and a readable summary of 
-a fitted matrix linear model, i.e. `Mlm` object.
+We can use the function `show()` to respectively display 
+a readable summary of the matrices and dimensions stored in a `Mlm` object.
 
-```@example
+```@example 
 show(est)
 ```
 
-```@example
-display(est)
-```
-
 
 ## Model predictions and residuals
 
@@ -177,7 +166,7 @@ The coefficient estimates can be accessed using `coef(est)`. Predicted values an
 
 To compare the estimated coefficients with the original matrix `B`, we will visualize the matrices using heatmaps. This graphical representation allows us to readily see differences and similarities between the two.
 
-```@example
+```@example 
 esti_coef = coef(est); # Get the coefficients of the model
 
 plot(
@@ -193,7 +182,7 @@ plot(
 
 Let's employ the same visualization method to compare the predicted values with the original `Y` response matrix. This allows us to gauge the accuracy of our model predictions.
 
-```@example
+```@example 
 preds = predict(est); # Prediction value
 
 plot(
@@ -211,7 +200,7 @@ The `residuals()` function, available in `MatrixLM.jl`, computes residuals
 for each observation, helping us evaluate the discrepancy between
 the model's predictions and the observed data.
 
-```@example
+```@example 
 resids = residuals(est);
 
 plot(
@@ -231,7 +220,7 @@ plot(
 
 The t-statistics for an `Mlm` object (defined as `est.B ./ sqrt.(est.varB)`) can be obtained by running `t_stat`. By default, `t_stat` does not return the corresponding t-statistics for any main effects that were estimated by `mlm`, but they will be returned if `isMainEff=true`.
 
-```@example
+```@example 
 tStats = t_stat(est);
 
 nothing #hide
@@ -243,7 +232,7 @@ a different number can be specified as the second argument
 (by modifying the `nPerms` value).
 By default, the function used to permute `Y` is `shuffle_rows`, which shuffles the rows for `Y`. Alternative functions for permuting `Y`, such as `shuffle_cols`, can be passed into the argument `permFun`. `mlm_perms` calls `mlm` and `t_stat`, so the user is free to specify keyword arguments for `mlm` or `t_stat`; by default, `mlm_perms` will call both functions using their default behavior.
 
-```@example
+```@example 
 nPerms = 500
 tStats, pVals = mlm_perms(dat, nPerms, addXIntercept=false, addZIntercept=false);
 
@@ -286,7 +275,7 @@ The `summary` method has three keyword arguments:
   
 This summary table can be used to identify which row/column covariate combinations are significant and to estimate their effect sizes along with their uncertainty.
 
-```@example
+```@example 
 MatrixLM.summary(est, alpha = 0.05, permutation_test = false)
 ```
 
diff --git a/docs/src/varShrinkage_example.md b/docs/src/varShrinkage_example.md
index cee48e2..085e5cf 100644
--- a/docs/src/varShrinkage_example.md
+++ b/docs/src/varShrinkage_example.md
@@ -50,7 +50,7 @@ correlations.
 using MatrixLM, LinearAlgebra, Random, Statistics
 using StableRNGs
 
-rng = StableRNG(27072026)
+rng = StableRNG(2026)
 
 # Matrix dimensions
 n = 100
@@ -115,16 +115,12 @@ dat = RawData(
 nothing #hide
 ```
 
-We can use the function `show()` and `display()` to respectively 
-display a compact and a readable summary of he matrices and 
-dimensions stored in a `RawData` object.
+We can use the function `show()` to respectively display 
+a readable summary of the matrices and dimensions stored in a `RawData` object.
 
-```@example
-show(dat)
-```
 
-```@example
-display(dat)
+```@example varshrinkage
+show(dat)
 ```
 
 ## Model Estimation Without Variance Shrinkage
@@ -141,16 +137,12 @@ est_no_shrinkage = mlm(
 
 nothing #hide
 ```
-We can use the function `show()` and `display()` to respectively 
-display a compact and a readable summary of 
-a fitted matrix linear model, i.e. `Mlm` object.
 
-```@example
-show(est)
-```
+We can use the function `show()` to respectively display 
+a readable summary of the matrices and dimensions stored in a `Mlm` object.
 
-```@example
-display(est)
+```@example varshrinkage
+show(est_no_shrinkage)
 ```
 
 The fitted object contains the coefficient estimates in `B`, the estimated error covariance matrix in `sigma`, and the coefficient variance estimates in `varB`.
@@ -172,9 +164,10 @@ est_shrinkage = mlm(
     addZIntercept=false
 )
 
-nothing #hide
+show(est_shrinkage)
 ```
 
+
 The estimator separately shrinks
 
 1. arctanh-transformed sample correlations toward their common mean, and
diff --git a/src/show.jl b/src/show.jl
index 80f799c..2fe1a2d 100644
--- a/src/show.jl
+++ b/src/show.jl
@@ -1,48 +1,53 @@
-"""
-    show(io::IO, data::RawData)
+function row_preview(mat::AbstractMatrix; max_cols::Int=3)
+    if size(mat, 1) == 0 || size(mat, 2) == 0
+        return "[]"
+    end
 
-Display a compact summary of a `RawData` object.
-"""
-function Base.show(io::IO, data::RawData)
-    print(
-        io,
-        "RawData(n=$(data.n), m=$(data.m), p=$(data.p), q=$(data.q))",
-    )
+    ncols = min(size(mat, 2), max_cols)
+    values = [string(mat[1, j]) for j in 1:ncols]
+    preview = "[" * join(values, ", ") * (size(mat, 2) > ncols ? ", …" : "") * "]"
+    return preview
 end
 
 """
-    show(io::IO, ::MIME"text/plain", data::RawData)
+    show(io::IO, data::RawData)
 
 Display a readable summary of the matrices and dimensions stored in a
 `RawData` object.
 """
-function Base.show(io::IO, ::MIME"text/plain", data::RawData)
+function Base.show(io::IO, data::RawData)
     println(io, "RawData")
     println(io, "  Response matrix Y: $(data.n) × $(data.m)")
     println(io, "  Design matrix X: $(data.n) × $(data.p)")
     println(io, "  Design matrix Z: $(data.m) × $(data.q)")
     println(io, "  X includes intercept: $(data.predictors.hasXIntercept)")
-    print(io, "  Z includes intercept: $(data.predictors.hasZIntercept)")
+    println(io, "  Z includes intercept: $(data.predictors.hasZIntercept)")
+    println(io, "  Preview of Y first row (first $(min(3, size(get_Y(data), 2))) columns): " *
+        row_preview(round.(get_Y(data), digits=4)))
+    println(io, "  Preview of X first row (first $(min(3, size(get_X(data), 2))) columns): " *
+        row_preview(round.(get_X(data), digits=4)))
+    println(io, "  Preview of Z first row (first $(min(3, size(get_Z(data), 2))) columns): " *
+        row_preview(round.(get_Z(data), digits=4)))
 end
 
-"""
-    show(io::IO, model::Mlm)
+# """
+#     show(io::IO, model::Mlm)
 
-Display a compact summary of a fitted matrix linear model.
-"""
-function Base.show(io::IO, model::Mlm)
-    print(
-        io,
-        "Mlm($(size(model.B, 1)) × $(size(model.B, 2)) coefficient matrix)",
-    )
-end
+# Display a compact summary of a fitted matrix linear model.
+# """
+# function Base.show(io::IO, model::Mlm)
+#     print(
+#         io,
+#         "Mlm($(size(model.B, 1)) × $(size(model.B, 2)) coefficient matrix)",
+#     )
+# end
 
 """
-    show(io::IO, ::MIME"text/plain", model::Mlm)
+    show(io::IO, model::Mlm)
 
 Display a readable summary of a fitted matrix linear model.
 """
-function Base.show(io::IO, ::MIME"text/plain", model::Mlm)
+function Base.show(io::IO, model::Mlm)
     data = model.data
 
     println(io, "Matrix linear model fit")
@@ -57,15 +62,26 @@ function Base.show(io::IO, ::MIME"text/plain", model::Mlm)
     )
     println(
         io,
-        "  Residual covariance matrix: " *
+        "  Residual covariance matrix sigma(Σ): " *
         "$(size(model.sigma, 1)) × $(size(model.sigma, 2))",
     )
     println(io, "  Weighted fit: $(model.weights !== nothing)")
+    println(
+        io,
+        "  Preview of B first row (first $(min(3, size(model.B, 2))) columns): " *
+        row_preview(round.(model.B, digits=4)),
+    )
+    println(
+        io,
+        "  Preview of sigma(Σ) first row (first $(min(3, size(model.sigma, 2))) columns): " *
+        row_preview(round.(model.sigma, digits=4)),
+    )
 
     if model.targetType === nothing
-        print(io, "  Covariance shrinkage: none")
+        println(io, "  Covariance shrinkage: none")
     else
         println(io, "  Covariance shrinkage target: $(model.targetType)")
-        print(io, "  Shrinkage coefficient: $(model.lambda)")
+        println(io, "  Shrinkage coefficient: (correlation = $(round(model.lambda.correlation,
+         digits=4)), variance = $(round(model.lambda.variance, digits=4)))")
     end
 end
\ No newline at end of file
diff --git a/test/show_test.jl b/test/show_test.jl
index 2173232..bef5ec5 100644
--- a/test/show_test.jl
+++ b/test/show_test.jl
@@ -1,3 +1,15 @@
+
+@testset "row_preview" begin
+    empty_mat = zeros(0, 0)
+    single_row_mat = [1.0 2.0 3.0]
+    wide_mat = reshape(1.0:8.0, (2, 4))
+
+    @test MatrixLM.row_preview(empty_mat) == "[]"
+    @test MatrixLM.row_preview(single_row_mat) == "[1.0, 2.0, 3.0]"
+    @test MatrixLM.row_preview(wide_mat) == "[1.0, 2.0, 3.0, …]"
+    @test MatrixLM.row_preview(wide_mat; max_cols=2) == "[1.0, 2.0, …]"
+end
+
 @testset "show methods" begin
     Y = randn(10, 5)
     X = hcat(ones(10), randn(10))
@@ -7,28 +19,31 @@
     predictors = Predictors(X, Z, true, true)
     data = RawData(response, predictors)
 
-    compact_data = sprint(show, data)
-    detailed_data = sprint(
-        show,
-        MIME"text/plain"(),
-        data,
-    )
+    detailed_data = sprint(show, MIME"text/plain"(), data)
 
-    @test compact_data == "RawData(n=10, m=5, p=2, q=2)"
+    @test occursin("RawData", detailed_data)
     @test occursin("Response matrix Y: 10 × 5", detailed_data)
+    @test occursin("Design matrix X: 10 × 2", detailed_data)
+    @test occursin("Design matrix Z: 5 × 2", detailed_data)
     @test occursin("X includes intercept: true", detailed_data)
+    @test occursin("Z includes intercept: true", detailed_data)
+    @test occursin("Preview of Y first row", detailed_data)
+    @test occursin("Preview of X first row", detailed_data)
+    @test occursin("Preview of Z first row", detailed_data)
 
     model = mlm(data)
 
-    compact_model = sprint(show, model)
-    detailed_model = sprint(
-        show,
-        MIME"text/plain"(),
-        model,
-    )
+    detailed_model = sprint(show, MIME"text/plain"(), model)
 
-    @test compact_model == "Mlm(2 × 2 coefficient matrix)"
     @test occursin("Matrix linear model fit", detailed_model)
     @test occursin("Observations: 10", detailed_model)
+    @test occursin("Responses: 5", detailed_model)
+    @test occursin("Row predictors: 2", detailed_model)
+    @test occursin("Column predictors: 2", detailed_model)
     @test occursin("Coefficient matrix B: 2 × 2", detailed_model)
+    @test occursin("Residual covariance matrix sigma(Σ): 5 × 5", detailed_model)
+    @test occursin("Weighted fit: false", detailed_model)
+    @test occursin("Preview of B first row", detailed_model)
+    @test occursin("Preview of sigma(Σ) first row", detailed_model)
+    @test occursin("Covariance shrinkage: none", detailed_model)
 end
\ No newline at end of file

From 806156efa88b5e2a417adbae906830aae29ec825 Mon Sep 17 00:00:00 2001
From: GregFa <faragegr@gmail.com>
Date: Tue, 28 Jul 2026 14:56:00 -0500
Subject: [PATCH 7/9] fixed testing failures

---
 Project.toml      |  2 --
 docs/make.jl      | 11 ++++++++---
 test/show_test.jl |  4 ++--
 3 files changed, 10 insertions(+), 7 deletions(-)

diff --git a/Project.toml b/Project.toml
index c0c6154..be18c19 100644
--- a/Project.toml
+++ b/Project.toml
@@ -13,7 +13,6 @@ Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 SharedArrays = "1a1011a3-84de-559e-8e89-a11a2f7dc383"
-StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 StatsAPI = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
 StatsModels = "3eaba693-59b7-5ba5-a881-562e759f1c8d"
@@ -27,7 +26,6 @@ GLM = "1.8"
 LinearAlgebra = "1"
 Random = "1"
 SharedArrays = "1"
-StableRNGs = "1.0.4"
 Statistics = "1"
 StatsAPI = "1.8.0"
 StatsModels = "0.6, 0.7"
diff --git a/docs/make.jl b/docs/make.jl
index 46110d9..5e8d762 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -1,8 +1,13 @@
+using Pkg
+
+# Build docs in the docs-specific environment so documentation-only
+# dependencies (for example StableRNGs used in examples) are available.
+Pkg.activate(@__DIR__)
+Pkg.develop(PackageSpec(path=joinpath(@__DIR__, "..")))
+Pkg.instantiate()
+
 using MatrixLM
 using Documenter
-# using Pkg
-
-# Pkg.add("StableRNGs")
 
 # copy readme into index.md
 open(joinpath(@__DIR__, "src", "index.md"), "w") do io
diff --git a/test/show_test.jl b/test/show_test.jl
index bef5ec5..0f69968 100644
--- a/test/show_test.jl
+++ b/test/show_test.jl
@@ -6,8 +6,8 @@
 
     @test MatrixLM.row_preview(empty_mat) == "[]"
     @test MatrixLM.row_preview(single_row_mat) == "[1.0, 2.0, 3.0]"
-    @test MatrixLM.row_preview(wide_mat) == "[1.0, 2.0, 3.0, …]"
-    @test MatrixLM.row_preview(wide_mat; max_cols=2) == "[1.0, 2.0, …]"
+    @test MatrixLM.row_preview(wide_mat) == "[1.0, 3.0, 5.0, …]"
+    @test MatrixLM.row_preview(wide_mat; max_cols=2) == "[1.0, 3.0, …]"
 end
 
 @testset "show methods" begin

From 78c054913418a53281167fa5ef976733679e8f4c Mon Sep 17 00:00:00 2001
From: GregFa <faragegr@gmail.com>
Date: Tue, 28 Jul 2026 16:10:23 -0500
Subject: [PATCH 8/9] added extra testing routines for show()

---
 test/show_test.jl | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/test/show_test.jl b/test/show_test.jl
index 0f69968..c0ba75b 100644
--- a/test/show_test.jl
+++ b/test/show_test.jl
@@ -46,4 +46,12 @@ end
     @test occursin("Preview of B first row", detailed_model)
     @test occursin("Preview of sigma(Σ) first row", detailed_model)
     @test occursin("Covariance shrinkage: none", detailed_model)
+
+    model_shrunk = mlm(data; targetType = "R")
+    detailed_model_shrunk = sprint(show, MIME"text/plain"(), model_shrunk)
+
+    @test occursin("Covariance shrinkage target: R", detailed_model_shrunk)
+    @test occursin("Shrinkage coefficient:", detailed_model_shrunk)
+    @test occursin("correlation =", detailed_model_shrunk)
+    @test occursin("variance =", detailed_model_shrunk)
 end
\ No newline at end of file

From fbecbfd76c595ec493d17bd64e7d8d8ef497eb41 Mon Sep 17 00:00:00 2001
From: GregFa <36859310+GregFa@users.noreply.github.com>
Date: Tue, 28 Jul 2026 16:20:52 -0500
Subject: [PATCH 9/9] Bump version from 1.0.0 to 1.1.0

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index be18c19..abc03af 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "MatrixLM"
 uuid = "37290134-6146-11e9-0c71-a5c489be1f53"
-version = "1.0.0"
+version = "1.1.0"
 authors = ["Jane Liang", "Gregory Farage", "Chenhao Zhao", "Harsh Vardhan Dubey", "Saunak Sen"]
 
 [workspace]