Multiple Imputation is a powerful statistical technique used to address the common problem of missing data in research and analysis. It involves creating multiple imputed datasets, each with plausible values for the missing data, and then combining the results to provide more accurate and robust estimates.
Multiple Imputation is built upon several foundational concepts and principles:
Missing Data Mechanisms: Missing data can occur for various reasons, and understanding the mechanisms behind missingness is essential for appropriate imputation.
Rubin’s Framework: The development of Multiple Imputation is often attributed to Donald Rubin, who introduced the concept of creating multiple imputed datasets and combining them to obtain unbiased estimates.
Plausible Values: Imputed values should be plausible and reflect the uncertainty associated with missing data.
Statistical Models: Multiple Imputation often involves using statistical models to generate imputed values.
The Core Principles of Multiple Imputation
To effectively implement Multiple Imputation, it’s essential to adhere to the core principles:
Randomness: Imputed values should be generated randomly, reflecting the uncertainty associated with missing data.
Multiple Datasets: Create multiple imputed datasets (usually 5 to 20) to account for the uncertainty in the imputed values.
Combining Results: Combine the results from the imputed datasets to obtain valid and reliable estimates.
Modeling: Use appropriate statistical models to impute missing values based on observed data.
The Process of Implementing Multiple Imputation
Implementing Multiple Imputation involves several key steps:
1. Define the Missing Data Problem
Identification: Identify the variables with missing data and understand the mechanisms behind the missingness.
Missing Data Patterns: Determine if the missing data are missing completely at random (MCAR), missing at random (MAR), or missing not at random (MNAR).
2. Data Preparation
Data Exploration: Explore the data to understand the relationships between missing data and other variables.
Variable Selection: Choose variables for imputation and specify the imputation model.
3. Imputation
Model Specification: Specify the imputation model, which may involve using regression models, propensity scores, or other statistical techniques.
Multiple Imputed Datasets: Create multiple imputed datasets, typically using random draws from the imputation model.
4. Analysis
Perform Analysis: Analyze each imputed dataset separately to obtain parameter estimates and standard errors.
5. Combining Results
Combining Estimates: Combine the results from the imputed datasets using Rubin’s rules or other appropriate methods.
Inference: Conduct hypothesis tests and make inferences based on the combined results.
6. Sensitivity Analysis
Sensitivity Checks: Perform sensitivity analyses to assess the robustness of the results to different imputation models or assumptions.
Practical Applications of Multiple Imputation
Multiple Imputation has a wide range of practical applications in various fields:
1. Medical Research
Clinical Trials: Address missing data in clinical trial outcomes, ensuring unbiased treatment effect estimates.
Epidemiology: Impute missing data in epidemiological studies to obtain more accurate estimates of disease prevalence and risk factors.
2. Social Sciences
Survey Research: Handle missing responses in surveys, improving the representativeness of survey data.
Longitudinal Studies: Address missing data in longitudinal studies to retain valuable information on changes over time.
3. Finance and Economics
Economic Research: Impute missing economic indicators or financial data for more accurate economic analyses.
Healthcare Data: Impute missing healthcare data to improve healthcare policy analysis and decision-making.
Health Surveys: Handle missing data in health surveys to assess population health trends accurately.
The Role of Multiple Imputation in Research
Multiple Imputation plays several critical roles in research:
Data Completeness: It ensures that researchers can make the best use of available data, even when missing data are present.
Reduced Bias: By accounting for uncertainty through multiple imputed datasets, it reduces bias in parameter estimates.
Increased Precision: It increases the precision of estimates by incorporating the variability associated with imputed values.
Robust Inference: Multiple Imputation provides robust statistical inference, especially in the presence of missing data.
Advantages and Benefits
Multiple Imputation offers several advantages and benefits:
Reduced Bias: It reduces bias in parameter estimates, ensuring that the imputed values reflect the uncertainty associated with missing data.
Better Precision: Multiple Imputation provides more precise estimates by incorporating variability from imputed values.
Valid Inference: It supports valid statistical inference by accounting for the uncertainty in imputed values.
Handling MNAR Data: Multiple Imputation can handle data that is not missing at random (MNAR) when appropriate imputation models are used.
Criticisms and Challenges
Multiple Imputation is not without criticisms and challenges:
Model Assumptions: Imputation models rely on assumptions, and violations of these assumptions can lead to biased results.
Computational Complexity: Creating and analyzing multiple imputed datasets can be computationally intensive, especially with large datasets.
Difficulty in Implementation: Proper implementation of Multiple Imputation requires expertise in statistical modeling and data analysis.
Interpretation Complexity: Combining results from multiple imputed datasets can be complex, and interpretation may require specialized knowledge.
Conclusion
Multiple Imputation is a valuable statistical technique for handling missing data in research and analysis. Its systematic approach, involving the creation of multiple imputed datasets and combining results, provides more accurate and robust estimates while accounting for the uncertainty associated with missing data. While it comes with challenges and assumptions, Multiple Imputation is an essential tool for researchers and analysts across various fields, ensuring that missing data do not compromise the validity and reliability of research findings.
Key Highlights on Multiple Imputation:
Foundations: Multiple Imputation is rooted in understanding missing data mechanisms, Rubin’s framework, plausible values, and statistical modeling.
Core Principles: Randomness, creating multiple datasets, combining results, and appropriate modeling are essential principles in Multiple Imputation.
Process: Implementing Multiple Imputation involves defining the missing data problem, data preparation, imputation, analysis, combining results, and sensitivity analysis.
Practical Applications: Multiple Imputation finds applications in medical research, social sciences, finance, economics, public health, and more.
Role in Research: It ensures data completeness, reduces bias, increases precision, and enables robust inference in research.
Advantages and Benefits: Multiple Imputation reduces bias, provides better precision, supports valid inference, and handles MNAR data.
Criticisms and Challenges: Challenges include model assumptions, computational complexity, difficulty in implementation, and interpretation complexity.
Conclusion: Multiple Imputation is a valuable technique for handling missing data, ensuring accurate and robust estimates in research and analysis across various fields.
Convergent thinking occurs when the solution to a problem can be found by applying established rules and logical reasoning. Whereas divergent thinking is an unstructured problem-solving method where participants are encouraged to develop many innovative ideas or solutions to a given problem. Where convergent thinking might work for larger, mature organizations where divergent thinking is more suited for startups and innovative companies.
The concept of cognitive biases was introduced and popularized by the work of Amos Tversky and Daniel Kahneman in 1972. Biases are seen as systematic errors and flaws that make humans deviate from the standards of rationality, thus making us inept at making good decisions under uncertainty.
Second-order thinking is a means of assessing the implications of our decisions by considering future consequences. Second-order thinking is a mental model that considers all future possibilities. It encourages individuals to think outside of the box so that they can prepare for every and eventuality. It also discourages the tendency for individuals to default to the most obvious choice.
Lateral thinking is a business strategy that involves approaching a problem from a different direction. The strategy attempts to remove traditionally formulaic and routine approaches to problem-solving by advocating creative thinking, therefore finding unconventional ways to solve a known problem. This sort of non-linear approach to problem-solving, can at times, create a big impact.
Bounded rationality is a concept attributed to Herbert Simon, an economist and political scientist interested in decision-making and how we make decisions in the real world. In fact, he believed that rather than optimizing (which was the mainstream view in the past decades) humans follow what he called satisficing.
The Dunning-Kruger effect describes a cognitive bias where people with low ability in a task overestimate their ability to perform that task well. Consumers or businesses that do not possess the requisite knowledge make bad decisions. What’s more, knowledge gaps prevent the person or business from seeing their mistakes.
Occam’s Razor states that one should not increase (beyond reason) the number of entities required to explain anything. All things being equal, the simplest solution is often the best one. The principle is attributed to 14th-century English theologian William of Ockham.
The Lindy Effect is a theory about the ageing of non-perishable things, like technology or ideas. Popularized by author Nicholas Nassim Taleb, the Lindy Effect states that non-perishable things like technology age – linearly – in reverse. Therefore, the older an idea or a technology, the same will be its life expectancy.
Antifragility was first coined as a term by author, and options trader Nassim Nicholas Taleb. Antifragility is a characteristic of systems that thrive as a result of stressors, volatility, and randomness. Therefore, Antifragile is the opposite of fragile. Where a fragile thing breaks up to volatility; a robust thing resists volatility. An antifragile thing gets stronger from volatility (provided the level of stressors and randomness doesn’t pass a certain threshold).
Systems thinking is a holistic means of investigating the factors and interactions that could contribute to a potential outcome. It is about thinking non-linearly, and understanding the second-order consequences of actions and input into the system.
Vertical thinking, on the other hand, is a problem-solving approach that favors a selective, analytical, structured, and sequential mindset. The focus of vertical thinking is to arrive at a reasoned, defined solution.
Maslow’s Hammer, otherwise known as the law of the instrument or the Einstellung effect, is a cognitive bias causing an over-reliance on a familiar tool. This can be expressed as the tendency to overuse a known tool (perhaps a hammer) to solve issues that might require a different tool. This problem is persistent in the business world where perhaps known tools or frameworks might be used in the wrong context (like business plans used as planning tools instead of only investors’ pitches).
The Peter Principle was first described by Canadian sociologist Lawrence J. Peter in his 1969 book The Peter Principle. The Peter Principle states that people are continually promoted within an organization until they reach their level of incompetence.
The straw man fallacy describes an argument that misrepresents an opponent’s stance to make rebuttal more convenient. The straw man fallacy is a type of informal logical fallacy, defined as a flaw in the structure of an argument that renders it invalid.
The Streisand Effect is a paradoxical phenomenon where the act of suppressing information to reduce visibility causes it to become more visible. In 2003, Streisand attempted to suppress aerial photographs of her Californian home by suing photographer Kenneth Adelman for an invasion of privacy. Adelman, who Streisand assumed was paparazzi, was instead taking photographs to document and study coastal erosion. In her quest for more privacy, Streisand’s efforts had the opposite effect.
As highlighted by German psychologist Gerd Gigerenzer in the paper “Heuristic Decision Making,” the term heuristic is of Greek origin, meaning “serving to find out or discover.” More precisely, a heuristic is a fast and accurate way to make decisions in the real world, which is driven by uncertainty.
The recognition heuristic is a psychological model of judgment and decision making. It is part of a suite of simple and economical heuristics proposed by psychologists Daniel Goldstein and Gerd Gigerenzer. The recognition heuristic argues that inferences are made about an object based on whether it is recognized or not.
The representativeness heuristic was first described by psychologists Daniel Kahneman and Amos Tversky. The representativeness heuristic judges the probability of an event according to the degree to which that event resembles a broader class. When queried, most will choose the first option because the description of John matches the stereotype we may hold for an archaeologist.
The take-the-best heuristic is a decision-making shortcut that helps an individual choose between several alternatives. The take-the-best (TTB) heuristic decides between two or more alternatives based on a single good attribute, otherwise known as a cue. In the process, less desirable attributes are ignored.
The bundling bias is a cognitive bias in e-commerce where a consumer tends not to use all of the products bought as a group, or bundle. Bundling occurs when individual products or services are sold together as a bundle. Common examples are tickets and experiences. The bundling bias dictates that consumers are less likely to use each item in the bundle. This means that the value of the bundle and indeed the value of each item in the bundle is decreased.
The Barnum Effect is a cognitive bias where individuals believe that generic information – which applies to most people – is specifically tailored for themselves.
First-principles thinking – sometimes called reasoning from first principles – is used to reverse-engineer complex problems and encourage creativity. It involves breaking down problems into basic elements and reassembling them from the ground up. Elon Musk is among the strongest proponents of this way of thinking.
The ladder of inference is a conscious or subconscious thinking process where an individual moves from a fact to a decision or action. The ladder of inference was created by academic Chris Argyris to illustrate how people form and then use mental models to make decisions.
Goodhart’s Law is named after British monetary policy theorist and economist Charles Goodhart. Speaking at a conference in Sydney in 1975, Goodhart said that “any observed statistical regularity will tend to collapse once pressure is placed upon it for control purposes.” Goodhart’s Law states that when a measure becomes a target, it ceases to be a good measure.
The Six Thinking Hats model was created by psychologist Edward de Bono in 1986, who noted that personality type was a key driver of how people approached problem-solving. For example, optimists view situations differently from pessimists. Analytical individuals may generate ideas that a more emotional person would not, and vice versa.
The Mandela effect is a phenomenon where a large group of people remembers an event differently from how it occurred. The Mandela effect was first described in relation to Fiona Broome, who believed that former South African President Nelson Mandela died in prison during the 1980s. While Mandela was released from prison in 1990 and died 23 years later, Broome remembered news coverage of his death in prison and even a speech from his widow. Of course, neither event occurred in reality. But Broome was later to discover that she was not the only one with the same recollection of events.
The bandwagon effect tells us that the more a belief or idea has been adopted by more people within a group, the more the individual adoption of that idea might increase within the same group. This is the psychological effect that leads to herd mentality. What in marketing can be associated with social proof.
Moore’s law states that the number of transistors on a microchip doubles approximately every two years. This observation was made by Intel co-founder Gordon Moore in 1965 and it become a guiding principle for the semiconductor industry and has had far-reaching implications for technology as a whole.
Disruptive innovation as a term was first described by Clayton M. Christensen, an American academic and business consultant whom The Economist called “the most influential management thinker of his time.” Disruptive innovation describes the process by which a product or service takes hold at the bottom of a market and eventually displaces established competitors, products, firms, or alliances.
Value migration was first described by author Adrian Slywotzky in his 1996 book Value Migration – How to Think Several Moves Ahead of the Competition. Value migration is the transferal of value-creating forces from outdated business models to something better able to satisfy consumer demands.
The bye-now effect describes the tendency for consumers to think of the word “buy” when they read the word “bye”. In a study that tracked diners at a name-your-own-price restaurant, each diner was asked to read one of two phrases before ordering their meal. The first phrase, “so long”, resulted in diners paying an average of $32 per meal. But when diners recited the phrase “bye bye” before ordering, the average price per meal rose to $45.
Groupthink occurs when well-intentioned individuals make non-optimal or irrational decisions based on a belief that dissent is impossible or on a motivation to conform. Groupthink occurs when members of a group reach a consensus without critical reasoning or evaluation of the alternatives and their consequences.
A stereotype is a fixed and over-generalized belief about a particular group or class of people. These beliefs are based on the false assumption that certain characteristics are common to every individual residing in that group. Many stereotypes have a long and sometimes controversial history and are a direct consequence of various political, social, or economic events. Stereotyping is the process of making assumptions about a person or group of people based on various attributes, including gender, race, religion, or physical traits.
Murphy’s Law states that if anything can go wrong, it will go wrong. Murphy’s Law was named after aerospace engineer Edward A. Murphy. During his time working at Edwards Air Force Base in 1949, Murphy cursed a technician who had improperly wired an electrical component and said, “If there is any way to do it wrong, he’ll find it.”
The law of unintended consequences was first mentioned by British philosopher John Locke when writing to parliament about the unintended effects of interest rate rises. However, it was popularized in 1936 by American sociologist Robert K. Merton who looked at unexpected, unanticipated, and unintended consequences and their impact on society.
Fundamental attribution error is a bias people display when judging the behavior of others. The tendency is to over-emphasize personal characteristics and under-emphasize environmental and situational factors.
Outcome bias describes a tendency to evaluate a decision based on its outcome and not on the process by which the decision was reached. In other words, the quality of a decision is only determined once the outcome is known. Outcome bias occurs when a decision is based on the outcome of previous events without regard for how those events developed.
Hindsight bias is the tendency for people to perceive past events as more predictable than they actually were. The result of a presidential election, for example, seems more obvious when the winner is announced. The same can also be said for the avid sports fan who predicted the correct outcome of a match regardless of whether their team won or lost. Hindsight bias, therefore, is the tendency for an individual to convince themselves that they accurately predicted an event before it happened.
Gennaro is the creator of FourWeekMBA, which reached about four million business people, comprising C-level executives, investors, analysts, product managers, and aspiring digital entrepreneurs in 2022 alone | He is also Director of Sales for a high-tech scaleup in the AI Industry | In 2012, Gennaro earned an International MBA with emphasis on Corporate Finance and Business Strategy.
