The Secret Sauce of Five-Star Recipes

Authors: Becca Fu(beccafuu@umich.edu), Yuchen(Wayne) Yang(siriusyc@umich.edu)

Introduction

General Introduction

• The “Recipes and Ratings” dataset provides a comprehensive collection of information about recipes and user interactions with those recipes, based on the data collected from food.com.

• It is split into two main CSV files.

• The “recipes” data set contained metadata about recipes, providing a complete snapshot of the recipes and their attributes, making it essential for understanding what each recipe offers. It includes information like recipe names, preparation times, tags, nutritional content, number of steps, and user-contributed descriptions.

• The “interactions” data set captures user interactions with recipes, including ratings and reviews. The data links users to the recipes they reviewed, allowing for an analysis of trends in user feedback and recipe popularity.

The central question we are interested in is: How average rating could be determined by key attributes of a recipe?

• Understanding how average ratings are determined by recipe attributes has practical applications. By analyzing this data, food bloggers, culinary professionals, and recipe-sharing platforms can tailor their recipes to maximize user satisfaction. For example, a recipe with a shorter preparation time and balanced nutritional value might perform better, which can guide recipe creation and marketing strategies.

Dataset Details Introduction

Recipes

• There exist 83782 rows and 12 columns in the recipes file.
• Here are the relevant columns and their descriptions: ‘minutes’: Time required to prepare the recipe. ‘nutrition’: Nutritional information in the format calories, total fat (%DV), sugar (%DV), sodium (%DV), protein (%DV), saturated fat (%DV), carbohydrates (%DV). For this column, we focus on calories and protein specifically. ‘n_steps’: Number of steps required to prepare the recipe.
• Here are the other columns but not so relevant to our research goal: ‘name’: Name of the recipe. ‘id’: Unique identifier for each recipe. ‘tags’: Keywords describing the recipe, such as cuisine type or dietary restrictions. ‘description’: User-provided description of the recipe.

Interactions

• There exist 83872 rows and 731927 columns in the interactions file.
• Here are the relevant columns and their descriptions: ‘rating’: Numerical score given by the user to rate the recipe (e.g., 1 to 5 stars).
• Here are the other columns but not so relevant to our research goal: ‘user_id’: Unique identifier for the user providing the rating. ‘recipe_id’: Identifier linking the rating to a specific recipe.

Data Cleaning and Exploratory Data Analysis

Part I: Data Cleaning

1. We start with two individual datasets, one for recipes, the other for ratings. To proceed, we need to left merge the recipes and interactions datasets together.
   • We choose left merge because we want to ensure that all the recipes are retained in the merged dataset, even if some recipes have no ratings or interactions.
2. Once we get the combined dataset, we need to deal with 0-star ratings.
   • In this case, we choose to treat all ratings of 0 as missing values first.
   • 0 is likely indicate that no ratings is given, so it currently doesn’t provide meaningful information about user preferences.
3. Before proceeding to any column operations, we want to first deal with missing values:
   • we start by examing which columns contains missing values.
   • then we fill missing values in columns relevant to our analysis, including
     • nutritions
     • rating
     • minutes
     • n_steps
4. Among all columns relevant to our analysis, only rating contains missing value.
   • We decided to use listwise imputation and probabilistic imputation, Imputation section for justification.
     • listwise imputation: we drop all recipe that does not receive any rating.
     • probabilistic imputation, we fill missing value in rating by drawing random sample from all ratings received by that recipe.

5. We will measure a recipe’s popularity by its average rating, so we created a new column that records average rating per recipe.

6. Previously, we notice that calories are stored in the nutrition column.
   • nutrition column contains values that looks like lists, but they are actually strings.
     • [calories (#), total fat (PDV), sugar (PDV), sodium (PDV), protein (PDV), saturated fat (PDV), carbohydrates (PDV)]
   • so we need to extract these information from the list-like string.
   • after that, we create columns that record them per receipe.
7. We define a new categorical column named ‘Time Involved’
   • we categorize recipes into three different categories based on their preparation time
     • less than 30 minutes
     • 4 hours or less
     • 1-day-or-more
8. from now on, we will only focus on relevant columns, including -average_rating
   • minutes
   • time involved
   • calories
   • n_steps
   • total fat(PDV)
   • sugar(PDV)
   • sodium(PDV)
   • protein(PDV)
   • saturated fat(PDV)
   • carbohydrates(PDV)

• more explanation on recipes
  • each row represent a particular recipe, there are 83782 recipes in total
  • each column except average_rating is a feature that we are used to predict average_rating

Below is the head of our league_clean dataframe.

	id	minutes	calories	n_steps	total fat(PDV)	sugar(PDV)	sodium(PDV)	protein(PDV)	saturated fat(PDV)	carbohydrates(PDV)	average_rating	time involved
0	275022	50	386.1	11	34	7	24	41	62	8	3	0.5 hour to 4 hours
1	275024	55	377.1	6	18	208	13	13	30	20	3	0.5 hour to 4 hours
2	275026	45	326.6	7	30	12	27	37	51	5	3	0.5 hour to 4 hours
3	275030	45	577.7	11	53	149	19	14	67	21	5	0.5 hour to 4 hours
4	275032	25	386.9	8	0	347	0	1	0	33	5	less than 30 minutes

Part II: Univariate Analysis

1. Difficulty Level

1. We are interested in difficulty level of recipes. Specifically, we wonder if recipes posted are complex in general.
2. We think two features can reflect the difficulty level, time and n_steps.
   • Intuitively, this makes sense because
     • the more complex a recipe is, the longer time it takes to prepare.
     • the more complex a recipe is, the more steps it involves.
3. To get some insights, we decided to draw two histograms to get some insights.
   • Histograms of Time
   • Histograms of n_steps

Preparation Time

we start with summary statistics, and note this a good way to distinguish between recipe’s preparation time:

• recipes taking less than 20 minutes to prepare is in first quartile
• recipes taking 20 to 35 minutes to prepare is in second quartile
• recipes taking 35 to 65 minutes to prepare is in third quartile
• recipes taking longer than 65 minutes to prepare is in the forth quartile

• Findings:
  • The graph above shows that the majority of recipes take less than 65 minutes.

Number of Steps

we continue with analyzing the distribution of steps taken.

• recipes taking within 6 steps to prepare is in first quartile
• recipes taking 7-9 steps to prepare is in second quartile
• recipes taking 11-13 steps to prepare is in third quartile
• receipes taking more than 14 steps to prepare is in the forth quartile

• Findings:
  • Combining two graphs above, we see that most recipes are not much complex, and involves fewer than 14 steps, with very few exceeding 20 steps.
• Conclusion:
  • These patterns indicate that recipes are generally simple and accessible, suggesting that they are not overly time-consuming and complex in terms of number of steps.

2. Energy Provided: Calories

1. We’re also interested in calories of recipes. Specifically, we wonder if
   • there are more recipes associated with high calories, or
   • most recipes tend to have low calories.

• Findings:
  • The histogram for recipe calories shows that the majority of recipes have calorie counts below 1000, with a steep decline in frequency beyond this point.
• Conclusion:
  • It appears that most recipes tend to have lower calories. The distribution is heavily skewed to the left, with the highest frequency of recipes having calorie counts below 1000.
  • This suggests that the majority of recipes are designed to be moderate in calorie content rather than high-calorie content.

Part III: Bivariate Analysis

• Now we want to look at the statistics of pairs of columns to identify possible associations.
• Specifically, we want to further explore what kind of recipes tend to have higher ratings,and we will investigate this question from two perspective similar to previous analysis:
  • difficulty level
  • calorie level
• There are two questions to answer:
  • Do people tend to rate simple recipe higher?
  • Do people rate recipes with lower calorie level higher?
• To answer these questions, we want to create three scatterplot respectively.
  • Average_Rating vs. Preparation Time
  • Average_Rating vs. n_steps
  • Average_Rating vs. calorie

Complexity

• The scatterplot shows that the number of steps does not have a strong visible correlation with the average rating.
• However, if we take a closer look at how ratings differ by different step ranges, we observe that recipes with 6 steps or fewer or more than 14 steps tend to have higher average ratings

• Similarly, the scatterplot shows that preparation time does not have a strong visible correlation with the average rating.
• However, if we take a closer look at how ratings differ by different step ranges, we observe that
  • receips with less preparation time tend to have higher average ratings

Energy Level

• Based on graph, we observe that low-calorie recipes tend to receive slightly higher average ratings compared to medium- and high-calorie recipes. This implies a preference for lower-calorie recipes, possibly due to perceived health benefits.

Recipe Ingredients

• Upon our investigation of original dataset, we noticed one of common tags is low-protein.
• Therefore, we want to see if average rating differs by its protein(PDV)

• The scatterplot shows that protein(PDV) does not have a strong visible correlation with the average rating.
• However, if we take a closer look at how ratings differ by ranges of protein(PDV), we observe that
  • receips with light protein level and moderate protein level tend to receive higher average ratings

Part IV: Interesting Aggregates

Time Involved	Average Rating	Calories	Total Fat (PDV)	Sugar (PDV)	Sodium (PDV)	Carbohydrates (PDV)	Protein (PDV)
Less than 30 minutes	4.64466	345.862	26.4346	57.0829	24.8203	11.0133	25.2582
0.5 hour to 4 hours	4.61538	491.321	37.2619	76.4203	30.8117	15.9859	37.9524
1-day-or-more	4.55493	513.034	37.1742	77.761	46.7199	14.4785	53.9995

Findings:

1. recipes that take “less than 30 minutes”
   • have the highest average rating of 4.64.
   • have the lowest
     • average calories
     • average protein (PDV)
     • average sugar(PDV)
2. receips that takes “1 day or more” have the highest average calories

Conclusion:

1. Preference for Convenience:
   • The high rating for short-preparation recipes suggests that many people value simplicity and speed.
   • This is particularly relevant for recipe developers and food bloggers focusing on gaining popularity; offering easy and quick recipes could attract more users.
2. Trade-off Between Nutrition and Time:
   • Recipes that require more time tend to have richer nutritional content. This suggests a trade-off where users must balance convenience with the desire for more nutrient-dense meals.
   • Consumers who have more time to cook tend to opt for more complex and nutritionally dense dishes

Part V: Imputation Strategy

• In all relevant columns of our analysis, only the rating contains missing value.
• We decided to choose conditional probabilistic imputation and listwise deletion to deal with missing values. The following are justifications:
  • Listwise Deletion:
    • No useful information provided
      • Recipes without any ratings do not provide any feedback about their quality or popularity. Since our analysis is focused on identifying the attributes that contribute to higher ratings, recipes with no ratings have no value in informing this relationship. They are, therefore, not useful in helping us understand the impact of recipe attributes on ratings.
    • Avoid Bias
      • Recipes with no ratings would require imputation based on attributes alone, which risks introducing fabricated or biased information. Since there are no user evaluations to guide this imputation, any values we add would essentially be guesses, reducing the reliability of our analysis.
  • Conditional Probabilistic Imputation
    • Minimizing Bias:
      • By drawing from the existing ratings of the same recipe, this approach minimizes the risk of introducing bias that could come from using values unrelated to the recipe itself. And we analyzed the drawbacks of other strategies as follows
  • (Conditional) mean imputation:
    • Filling missing values with the mean of observed values can reduce variability and introduce bias.
  • Regression imputation.
    • As we are predicting ratings using other features, doing so will produce imputed values that are highly correlated with the predictors, which artificially inflates any relationships detected in subsequent analysis.

Framing a Prediction Problem

• Based on above exploratory data analysis, we see that average rating of a recipes differs by
  • complexity
  • energy level
  • protein level
• Moving forward, we will predict ratings of recipes using its key attributes, including
  • preparation time: measured by minutes
  • number of steps: measured by n_steps
  • calories measured by calories
  • protein level: measured by protein(PDV)

Baseline Model

Model Description and Evaluation

1. Model Description

• Model Type: Ridge Regression
• Predictors (Features): Two quantitative features:
  • minutes: Total preparation time for a recipe (quantitative).
  • n_steps: Number of steps required to prepare a recipe (quantitative).
• Target Variable: average_rating (quantitative).

2. Features Summary

• Quantitative Features:
  • minutes
  • n_steps
• Ordinal Features: None.
• Nominal Features: None.

3. Data Preparation

• No categorical or ordinal features required encoding since all features were numerical.
• Data was split into training and test sets using an 80-20 split.
• Ridge regression was used to mitigate potential multicollinearity between minutes and n_steps.

4. Model Performance

• Mean Squared Error (MSE): ~0.41
• R² (Coefficient of Determination): -0.00002074

5. Evaluation of Model Quality

The current model is not good for the following reasons:

• Low Explanatory Power: The R² value is negative, indicating that the model performs worse than a simple mean baseline (i.e., predicting the average rating for all recipes).
• Limited Predictors: The two predictors (minutes and n_steps) are insufficient to capture the variability in recipe ratings. Additional features such as ingredients, calorie levels, or protein content might better explain the target variable.
• Potential Multicollinearity: Although mitigated with Ridge Regression, the strong correlation between minutes and n_steps may still obscure the contribution of each predictor.

Final Model

1. Predictor Re-selection

• In bivariate analysis, we see that average rating differs by different levels of
  • preparation time,
  • calories
  • protein(PDV)
• To capture these patterns, we want to instead use three categorical variables that we previously defined
  • time_involved
  • calorie_level
  • protein_level
• These features are aligned with the data-generating process as they directly relate to the characteristics users consider when rating recipes.

2. Modeling Algorithm and Hyperparameter Selection

• Algorithm Chosen: Ridge Regression
  • Ridge regression was chosen to mitigate multicollinearity and ensure stable coefficient estimation given the inclusion of potentially correlated features.
• Best Hyperparameters:
  • Regularization strength (alpha): 100
  • Determined using GridSearchCV with cross-validation (cv=5), optimizing for the lowest mean squared error.
• Pipeline Setup:
  • A ColumnTransformer was used for preprocessing:
    • Numerical features (n_steps) were scaled using StandardScaler.
    • Categorical features (time_involved, calorie_level, protein_level) were encoded using OneHotEncoder.
  • Combined preprocessing and regression in a Pipeline to streamline model building.

3. Performance Comparison

• Baseline Model MSE:0.41092464835782266
• Final Model MSE: 0.4103397379674629

Improvement in Performance

1. Reduction in MSE: Improvement = 0.41092464835782266 - 0.4103397379674629 = 0.0005849103903597768
   • The final model has reduced the average squared error by approximately 0.0006.
2. Percentage Improvement:
   • Percentage Improvement = 0.0005849103903597768 / 0.41092464835782266 * 100 ≈ 0.14
   • This indicates that the final model has improved the baseline performance by around 0.14%.