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Statistical help in physiotherapy

Statistical help in physiotherapy

Statistical help in physiotherapy is a normal practice of researchers. Statistical analysis is a commonly used method in physiotherapy research to evaluate the effectiveness of treatment interventions. It involves using statistical tests to determine the significance of differences in outcome measures between different groups, such as a treatment group and a control group. Some commonly used statistical tests in physiotherapy research include t-tests, ANOVA, and linear regression. These tests can help physiotherapists to determine the effectiveness of different treatment approaches and make evidence-based decisions about how to best help their patients.

What is research and experimentation in physiotherapy?

Research and experimentation in physiotherapy refers to the process of conducting studies to investigate the effectiveness of different physiotherapy interventions and techniques. This can include observational studies, randomized controlled trials, and systematic reviews. The goal of these studies is to generate new knowledge and evidence to inform clinical practice and improve patient outcomes.

Studies in physiotherapy can be conducted in various areas like musculoskeletal, neurology, cardio-respiratory, geriatric and pediatric physiotherapy. It can also focus on the investigation of new techniques, technologies, or equipment, as well as the development and testing of new rehabilitation programs. Physiotherapists use the results of research studies to make evidence-based decisions about how to best help their patients and improve the quality of care provided.

Can physiotherapy researchers use statistical help in their research?

Yes, physiotherapy researchers often use statistical methods to help analyze and interpret the data collected in their studies. Statistical analysis allows researchers to determine the significance of differences in outcome measures between different groups, such as a treatment group and a control group. This can help researchers to determine whether an intervention or treatment is effective or not.

Some commonly used statistical methods in physiotherapy research include descriptive statistics, inferential statistics, and statistical modeling. Descriptive statistics are used to summarize and describe the data, while inferential statistics are used to make inferences about a population based on a sample. Statistical modeling is used to identify patterns and relationships in the data and make predictions about future outcomes.

Additionally, Physiotherapy researchers may also use specialized statistical help services or techniques like multivariate analysis, survival analysis, and meta-analysis. These techniques can help researchers to analyze complex data sets and control for potential confounding factors, which can help to increase the accuracy and precision of the results. It is important for physiotherapy researchers to have a good understanding of statistical methods and the appropriate use of statistical tests to ensure the validity and reliability of their research findings.

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Statistical Help in Psychology
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Statistical Help in Psychology

Statistical Help in Psychology

There are a variety of statistical techniques used in psychology research, including descriptive statistics, inferential statistics, and multivariate statistics. Do you search for statistical help in psychology? You can skip this text and click contact. Descriptive statistics are used to summarize and describe data, such as calculating means and standard deviations. Inferential statistics are used to make inferences about a population based on a sample of data, such as t-tests and ANOVA. Multivariate statistics are used to analyze data with multiple variables, such as multiple regression and factor analysis. It is important for psychologists to have a solid understanding of statistical methods in order to design and interpret research studies properly.

Why does a psychologist use statistics?

A psychologist uses statistics to analyze and interpret data collected from research studies. By using statistical techniques, a psychologist can identify patterns and relationships in the data, and make inferences about a population based on a sample. This allows them to draw conclusions and make informed decisions about their research, as well as to test hypotheses and evaluate the effectiveness of interventions. Additionally, statistics can be used to determine the validity and reliability of research findings and to make comparisons between different studies.

Does statistics is useful for psychological survey analysis?

Yes, statistics is very useful for the analysis of psychological surveys. Surveys and questionnaires are commonly used in psychological research to collect data from a large number of participants. Statistics allows psychologists to analyze and interpret this data in a meaningful way, by identifying patterns and relationships, making inferences about the population being studied, and testing hypotheses.

For example, statistical techniques such as correlation and regression can be used to determine the strength and direction of relationships between variables, and t-tests and ANOVA can be used to determine whether there are significant differences between groups. Additionally, statistics can be used to determine the reliability and validity of survey questions, which is important for assessing the quality of the data collected.

Overall, the use of statistics in the analysis of psychological surveys is essential for drawing valid conclusions and making informed decisions based on the data.

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How statistics help in business?

Statistics can be very useful in business for a variety of purposes. Here are a few examples of how statistics can help in business:

  1. Decision making: Statistics can help businesses make informed decisions by providing data-driven insights. For example, a business might use statistical analysis to compare the effectiveness of different marketing campaigns or to predict future demand for a product.
  2. Customer analysis: Businesses can use statistical techniques to analyze customer data, such as demographics, purchasing habits, and preferences. This can help them better understand their customers and tailor their products or services to meet their needs.
  3. Quality control: Statistics can be used to monitor and improve the quality of products or services. For example, a business might use statistical analysis to identify trends in customer complaints or to identify areas of the production process that may be causing defects.
  4. Market research: Businesses can use statistical analysis to gather and analyze data on their target market, including trends, preferences, and competition. This can help them make informed decisions about how to position their products or services in the market.

Overall, statistics can help businesses make more informed and data-driven decisions, which can ultimately lead to increased efficiency, improved customer satisfaction, and increased profitability.

Why is worth to hire a programmer statistician to develop business solutions?

There are several reasons why it might be worth hiring a statistician who is also a programmer:

  1. Efficient data analysis: A statistician who is also a programmer can write custom code to analyze data in an efficient and automated way, rather than relying on manual analysis or off-the-shelf software. This can save time and resources, and allow for more sophisticated and customized analysis.
  2. Data visualization: A statistician who is also a programmer can create custom data visualizations to communicate findings effectively. This can be especially useful for presenting data to stakeholders or for creating interactive dashboards for ongoing data analysis.
  3. Data automation: A statistician who is also a programmer can create scripts or programs to automate repetitive data tasks, such as data cleaning, transformation, or analysis. This can save time and ensure consistent and accurate results.
  4. Integration with other systems: A statistician who is also a programmer can integrate statistical analysis with other systems or platforms, such as databases or web applications. This can enable real-time data analysis or enable statistical analysis to be part of a larger data workflow.

Overall, hiring a statistician who is also a programmer can bring a combination of statistical expertise and programming skills that can be very useful for data-driven decision making and analysis in a business setting.

Why knowledge about programming is important?

Programming knowledge is important for a variety of reasons. Here are a few examples of why programming is important:

  1. Problem solving: Programming involves breaking down complex problems into smaller, more manageable pieces and finding solutions to them. This can help individuals develop their problem-solving skills and apply them to a wide range of contexts.
  2. Automation: Programming can be used to automate repetitive tasks, saving time and improving efficiency. This can be especially useful in business settings, where data processing and analysis are often required.
  3. Data analysis: Programming is often used in data analysis to manipulate and analyze large datasets. This can be especially useful in fields such as statistics, where programming skills can be used to perform sophisticated statistical analysis and create custom data visualizations.
  4. Web development: Programming skills are essential for web development, which involves building and maintaining websites. Web development is a growing field that is in high demand, and programming skills are often required for web development jobs.
  5. Software development: Programming is a key component of software development, which involves creating and maintaining software applications. Programming skills are essential for careers in software development and can lead to a wide range of job opportunities.

Overall, programming is a valuable skill that can be useful in a wide range of fields and industries. It can help individuals solve problems, automate tasks, and work with data, as well as open up career opportunities in fields such as web development and software development.

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Where to find free statistics help online?

There are several options for finding free statistical help online:
  1. Online tutoring services: Some online tutoring services offer free statistical help to students. These services may be provided by individuals or organizations and may be available for a limited time or on a continuous basis.
  2. Statistical software tutorials: Many statistical software programs, such as SPSS and R, have online tutorials that can help you learn how to use the software and perform statistical analyses. These tutorials are often available for free.
  3. Online forums: There are many online forums where students can ask questions and get answers from other students or experts. Some forums are specific to statistical topics, while others cover a wider range of subjects.
  4. Websites: There are many websites that offer free statistical help to students. These sites may provide explanations of statistical concepts, examples of statistical techniques, and practice problems to help you understand and apply the material.
  5. YouTube: YouTube is a great resource for finding free statistical help online. There are many videos on YouTube that provide explanations and examples of statistical concepts and techniques.

Remember to be careful when using online resources for statistical help. Make sure that the information you are using is reliable and accurate. If you are unsure about the quality of a resource, you may want to consult with your instructor or TA before using it.

How to be careful before using free statistical help in private companies?

There are a few things to consider when using free statistical help from private companies:

  1. Check the company’s reputation: Look for reviews or testimonials from other users to get an idea of the company’s reputation. If the company has a good reputation, it is more likely that the help they provide will be reliable and accurate.
  2. Be wary of guarantees: Some companies may make guarantees about the quality of their help. While these guarantees may be tempting, it’s important to be aware that there are no guarantees in statistical analysis. The results of statistical analyses can depend on many factors, and it’s not always possible to predict the outcome with certainty.
  3. Understand the limitations of free help: Keep in mind that free statistical help is often limited in scope. It may not be as comprehensive as paid help, and you may not be able to get as much individualized attention.
  4. Consider the source of the help: Make sure that the statistical help you are using is coming from a reputable source. If you are unsure about the credibility of a resource, you may want to consult with your instructor or TA before using it.

It’s always a good idea to be cautious when seeking statistical help, especially from private companies. Make sure to do your research and consider all of your options before making a decision.

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How to find statistical help online for students?

There are several options for finding statistical help for students:

Consult your textbook or course materials: Many textbooks and course materials include examples and explanations of statistical concepts and techniques. You can often find solutions to exercises and problems in the back of the book or in the instructor’s manual.

Ask your instructor or TA: Your instructor or teaching assistant is a great resource for statistical help. They can provide clarification on concepts and techniques, and can often provide additional resources or guidance on completing assignments.

Visit your school’s tutoring center: Many schools have tutoring centers that offer free statistical help to students. These centers are staffed by trained tutors who can provide one-on-one assistance with statistical concepts and techniques.

Use online resources: There are many online resources available that can provide statistical help for students. Some options include online tutoring services, statistical software tutorials, and online forums where students can ask questions and get answers from other students or experts.

Consider hiring a private tutor: If you need more individualized attention or have a particularly difficult statistical concept or technique that you are struggling with, you may want to consider hiring a private tutor. Private tutors can provide personalized assistance and can work with you at your own pace.

Remember that it is important to ask for help when you need it. Don’t be afraid to seek out resources or ask for assistance if you are having difficulty understanding statistical concepts or techniques.

What to do when instructor or teaching assistant do not help with statistical analysis?

If you are not getting the help you need from your instructor or teaching assistant (TA) with statistical analysis, there are a few steps you can take:

  1. Communicate your concerns: It’s important to let your instructor or TA know if you are not getting the help you need. Be specific about what you are struggling with and what you need in order to understand the material. Your instructor or TA may be able to provide additional resources or adjust their teaching style to better meet your needs.
  2. Seek additional resources: In addition to your instructor or TA, there are other resources available that can provide statistical help. You can consult your textbook or course materials, use online resources, or visit your school’s tutoring center for assistance.
  3. Consider seeking help from a private tutor: If you are unable to get the help you need from your instructor or TA, you may want to consider hiring a private tutor who can provide personalized assistance and can work with you at your own pace.

It’s important to remember that getting help with statistical analysis can be challenging, and it may take some trial and error to find resources that work for you. Don’t be afraid to seek out additional resources or try different approaches if you are not getting the help you need.

How to seek free statistical help?

There are several options for seeking free statistical help:

  1. Consult your textbook or course materials: Many textbooks and course materials include examples and explanations of statistical concepts and techniques. You can often find solutions to exercises and problems in the back of the book or in the instructor’s manual.
  2. Ask your instructor or TA: Your instructor or teaching assistant is a great resource for statistical help. They can provide clarification on concepts and techniques, and can often provide additional resources or guidance on completing assignments.
  3. Visit your school’s tutoring center: Many schools have tutoring centers that offer free statistical help to students. These centers are staffed by trained tutors who can provide one-on-one assistance with statistical concepts and techniques.
  4. Use online resources: There are many online resources available that can provide statistical help for free. Some options include online tutoring services, statistical software tutorials, and online forums where students can ask questions and get answers from other students or experts.
  5. Consider joining a study group: Forming a study group with your classmates can be a great way to get free statistical help. You can work together to understand concepts, review material, and practice problem-solving skills.

Remember to take advantage of all the resources available to you. Don’t be afraid to seek out help when you need it, and be proactive in finding resources that can assist you in your studies.

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How does the statistical help process work?

The process for seeking statistical help can vary depending on the specific needs of the individual or organization seeking assistance and the type of help they are looking for. In general, the process may involve the following steps:

1. Identify the problem or question that needs to be addressed: Before seeking statistical help, it’s important to clearly define the problem or question that needs to be addressed. This will help the statistician understand the scope of the project and determine the appropriate approach to take.

2. Find a statistician: There are many ways to find a statistician, including searching online directories, contacting professional organizations, or asking for recommendations from colleagues or peers. It’s important to choose a statistician who has the necessary expertise and experience to handle the specific problem or question at hand.

3. Discuss the project and agree on terms: Once you have found a statistician, it’s important to have an initial conversation to discuss the project in detail and agree on the terms of the engagement. This may include the scope of the project, the timeline for completion, and the fees for the services.

4. Collect and analyze the data: The statistician will work with you to collect and analyze the data needed to address the problem or question at hand. This may involve developing and implementing statistical models, running analyses, and interpreting the results.

5. Communicate the results: The statistician will help you to understand and interpret the results of the analysis and will provide recommendations based on the findings. They may also help you to communicate the results to others through the use of tables, charts, graphs, or written reports.

Follow-up: Depending on the specific needs of the project, the statistician may provide additional support or guidance as needed, including follow-up analysis or consultation.

How to describe the problem to get professional statistical help?

To get the most benefit from professional statistical help, it’s important to clearly and accurately describe the problem or question that needs to be addressed. Here are a few tips for describing the problem effectively:

1. Be specific: Clearly define the problem or question you need help with, including any relevant details or context.

2. Describe the data: Provide a brief overview of the data you have available and any relevant characteristics, such as the size of the sample, the type of variables, and the level of measurement.

3. Explain your goals: Clearly articulate what you hope to accomplish with the statistical analysis, such as testing a hypothesis or making a prediction.

4. Provide any additional information: If there are any additional details or constraints that may be relevant to the project, such as time or resource limitations, be sure to mention them.

By clearly and accurately describing the problem or question you need help with, you will enable the statistician to better understand your needs and provide the most appropriate assistance.

Can statistical consultations may be free? e.g. before the projects starts?

It’s possible that some statistical consultations may be free, particularly if they are brief and focused on providing general information or guidance. However, it’s important to note that statistical consulting can be a specialized and time-consuming process, and statisticians may need to devote a significant amount of time and effort to a project in order to provide the level of assistance that is needed. As a result, it’s generally not feasible for statisticians to provide extensive consultations for free on a regular basis.

If you are seeking more in-depth statistical consulting or assistance with a specific project, it’s generally a good idea to expect to pay for these services. However, it’s common for statisticians to offer an initial consultation to discuss the project and determine the scope of the work required. This initial consultation may be provided at no cost, or for a reduced fee, as a way to assess the needs of the project and determine the best approach to take.

It’s always a good idea to discuss the terms of the engagement and any fees upfront with the statistician before beginning a project. This will help ensure that both parties are clear on the expectations and the terms of the arrangement.

 

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Free statistics help online

There are several resources available online that can provide free statistics help. Some options include:

1. Khan Academy: This non-profit educational organization offers a variety of free statistics lessons and exercises, as well as video tutorials and practice problems.

2. Stat Trek: This website provides a variety of free statistics resources, including tutorials, calculators, and problem solvers.

3. OpenIntro: This website offers a range of free statistics textbooks and resources, including interactive tutorials and practice problems.

4. StatisticsHowTo: This website offers a variety of statistics guides, tutorials, and calculator tools.

5. Statistic Brain: This website provides a range of statistics resources, including data sets, calculators, and guides.

It’s also worth checking with your school or university to see if they offer any free tutoring services or online resources for statistics help.

Do statisticians help for free?

It’s possible that some statisticians may be willing to offer free help, particularly if they are volunteering their time or if the topic is of personal interest to them. However, it’s also important to note that statisticians are professionals who have invested a significant amount of time and resources into their education and training, and they may expect to be compensated for their expertise. If you need professional statistical consulting or guidance, it’s generally a good idea to expect to pay for these services.

There are also many free resources available online, such as those mentioned in my previous response, that may be able to provide the assistance you need. It may be helpful to start by exploring these options before considering hiring a statistician.

Why statistical help is sometimes expensive?

Statistical help can sometimes be expensive because statisticians are professionals who have invested a significant amount of time and resources into their education and training. Statisticians are experts in the field of statistics, which involves the collection, analysis, interpretation, presentation, and organization of data. They use their skills and knowledge to help individuals and organizations make informed decisions based on data.

Statisticians often work in a variety of fields, including academia, research, business, and government. They may be employed as full-time employees or may work as independent contractors, offering their services on a consulting basis. In either case, they may charge fees for their services based on their level of expertise, the complexity of the project, and the amount of time and effort required.

It’s also worth noting that statistical consulting can be a specialized and time-consuming process, and statisticians may need to devote a significant amount of time and effort to a project in order to provide the level of assistance that is needed. This can also contribute to the cost of statistical help.

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How does statistics help in decision making?

Statistics can be a useful tool for decision making because it allows you to analyze data and use it to inform your decisions. It can help you identify patterns and trends in the data, make predictions about future outcomes, and assess the likelihood of different events occurring.

For example, if you are trying to decide which marketing strategy to use, you could use statistical analysis to evaluate the effectiveness of different strategies based on past data. This could help you choose the strategy that is most likely to lead to the desired outcome, such as increasing sales or attracting new customers.

Similarly, if you are trying to decide whether to invest in a particular stock, you could use statistical analysis to evaluate the performance of the stock over time and compare it to other investments. This could help you determine the risk and potential return associated with the investment and make an informed decision about whether it is a good choice for your portfolio.

Overall, the use of statistics in decision making can help you make more informed and data-driven decisions, which can increase the likelihood of success and reduce the risk of making poor decisions.

How to gather data to make a statistically based decision?

There are several ways to gather data to support statistical decision making:

1. Surveys: Surveys are a common method for gathering data from a large number of people. Surveys can be administered in person, by phone, or online, and can be used to collect a wide variety of data, including demographic information, attitudes, and behaviors.

2. Experiments: Experiments allow you to manipulate one or more variables and measure the effect on a particular outcome. This can be a powerful way to gather data and identify cause-and-effect relationships.

3. Observations: Observations involve collecting data by watching and recording the behavior of people or other subjects. Observations can be conducted in a natural setting or in a controlled environment, and can be used to collect data on a wide variety of behaviors and outcomes.

4. Secondary data: Secondary data refers to data that has already been collected and is available for analysis. This can include data from government agencies, research studies, or other sources.

Once you have gathered the data, you can use statistical analysis techniques to analyze it and draw conclusions. This may involve calculating measures of central tendency (such as mean, median, and mode), testing statistical hypotheses, or using more advanced techniques such as regression analysis or multivariate analysis. By using these tools, you can gain a deeper understanding of the data and use it to inform your decision making.

Which statistical method is used to data-based decision?

There are many statistical methods that can be used for data-based decision making, and the appropriate method will depend on the type of data you have collected and the questions you are trying to answer. Some common statistical methods that may be useful for decision making include:

1. Descriptive statistics: Descriptive statistics are used to summarize and describe the characteristics of a dataset. This can include measures of central tendency (such as mean, median, and mode) and measures of dispersion (such as range, standard deviation, and variance).

2. Inferential statistics: Inferential statistics are used to make predictions or draw conclusions about a population based on a sample of data. This can include techniques such as hypothesis testing and regression analysis.

3. Bayesian analysis: Bayesian analysis is a statistical method that involves using prior knowledge and data to make predictions or decisions. It involves using probabilities to assess the likelihood of different outcomes and updating those probabilities as new data becomes available.

4. Decision analysis: Decision analysis is a statistical method that involves evaluating the potential outcomes of different decisions and selecting the option that is expected to lead to the best outcome. This can involve techniques such as decision trees and utility analysis.

Overall, the appropriate statistical method will depend on the specific goals and objectives of your analysis, as well as the type and structure of the data you have available.

Who can help in statistical data analysis?

There are several types of professionals who may be able to help with statistical data analysis:

1. Statisticians: Statisticians are trained in the collection, analysis, and interpretation of statistical data. They may work in a variety of fields, including academia, government, research, and business.

2. Data scientists: Data scientists are trained in the use of statistical methods and machine learning techniques to analyze large datasets. They often work in fields such as technology, finance, and marketing.

3. Research analysts: Research analysts are trained in the collection and analysis of data to inform decision making. They may work in fields such as market research, finance, or consulting.

4. Business analysts: Business analysts are trained in the use of data to inform business decisions. They may work in a variety of industries and may be responsible for collecting, analyzing, and interpreting data to help organizations make informed decisions.

There are also many software tools and online resources available that can help with statistical data analysis. These tools may be useful for those who are new to statistical analysis or who are looking for an easy-to-use solution for their data analysis needs. Overall, whether you choose to work with a professional or use a software tool, it is important to have a solid understanding of statistical concepts and techniques to ensure that you are able to effectively analyze and interpret your data.

Cross Lagged Panel Model mediation effect
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Idea and concept of Cross Lagged Panel Model

Many researchers are convinced that structural equation modeling is related to confirmatory factor analysis or simple mediation models, moderation models or a mix of both (mediation and moderation). But there are many established specific models which are oriented toward concrete modeling goals e.g. Latent Growth Models, Autoregressive Latent Trajectory Model with Structured Residuals, Dual Change Score Model, and many more. All of these models answer different questions and relax some strict assumptions nested in data. For example, raised Random Intercepts Cross Lagged Panel Model relaxes assumptions about actual within-person relationships over time and shows that if the stability of constructs is to some extent of a trait-like, time-invariant nature (at least during the course of the study), the autoregressive relationships of the classic Cross Lagged Panel Model fail to adequately account for this. 

 

Cross Lagged Panel Model and Random Intercepts Cross Lagged Panel Model (so-called longitudinal multilevel model) are statistical methods that are related to estimating cause effect in repeated measures study designs. This is the only one non-experimental method that allow to draw of strong inferences about causes (strong as in the experimental studies with experimental and control conditions). These aforementioned statistical methods are very popular in psychology, marketing, management and public health. Cross Lagged Panel Models are know since 1984, but in the 2015 a nice critique appeared (Hamaker, 2015). In this type of causality argument, we can use just two repeated measurements methodology to assess casualty and, therefore, to build the cross-lagged model in “lavaan” (R packages) or MPLUS (allows for very sophisticated estimates).  For example we want to answer the following question: Does parent’s aggression influence on child’s aggression?

How classical Cross Lagged Panel Model can answer this question?

If we allow to observe and measure aggression in dyads (parent vs child) in terms of the word aggression and wrath, then we gather two sources of variation parent t1 -> parent t2, and child t1 -> child t2 (autoregressive element of the model) and parent t1 -> child t2 and child t1 -> parent t2 (cross-lagged element of the model). Then, if we estimate this structure through the SEM technique we can assess what is going on in our casual model. If statistics of our autoregressive paths estimates are significant then we know that our observed time effects are valid, so aggression of both sides are time-related. Although, if the path parent t1 -> child t2 is significant (or has a stronger effect than the opposite path) then the causes of children’s aggression can be attributed to the parents’ aggression, but when path child t1 -> parent t2 is significant (or has a similar effect than the opposite path) then result is inconclusive. This is the classical example of data structure that allows drawing causal inferences from this type of model. Of course, there are other effects that we can estimate e.g. cross lagged mediation effects where mediation components t1->t2 (a path) and t2->t3 (b path) are estimated through subsequent 3 repeated measurements. This model is presented on figure 1. 

Figure 1

Classical Cross Lagged Panel Model examining mediation longitudinally

Cross Lagged Panel Model mediation effect

Random Intercepts Cross Lagged Panel Model can also answer this question.

In this form of the Cross Lagged Panel Model, we can estimate the so-called “within carry-over effect” like fixed effects in the classical panel regression model. We can agree that repeated measurement data can actually be treated as multilevel data, in which measures are nested within individuals. It is clear that in these circumstances we have to somehow separate the within level from the between level variability. spódecomposes observed scores into within-unit dynamics and stable, between-unit differences This situation needs to be treated specially in structural equation model syntax (ref).  

Nevertheless, the time stability has to be treated as trait-like (intraindividual time stability assumption) through the inclusion of a random intercept. Structurally, it is calculated through individual deviations from the group mean. In this context autoregression coefficient (these e.g. xt1 -> xt2) and cross-lagged coefficients (these e.g. xt1 -> yt2) represent so-called “within carry-over effect”. Positive paths values express that the one person scored above the expected score and is likely to be followed by occasions on which is still scored above the expected score a second time. Nevertheless, cross-lagged coefficients indicate the extent to which the two variables influence each other. These statistics express the degree how deviations from the individual expected score on y can be predicted from earlier deviations from the expected score on x (still controlling for deviation of the earlier expected score on y). It seems quite complicated, but we have to change our thinking from the population effect to the within-person (or cluster) carry-over effect. More about this sophisticated method can be read here (Hamaker, 2015). Translating these explanations into the formulated earlier problem of aggression of children and their parents, we can say that aggression of both can be treated as the time-invariant trait of both (a.g. child x’s aggression is 3 units higher than the average in the 1st measurement, and it is also 3 units higher in the second and third measurements). This deviation effect is controlled in both children and parents in the case of aggression in both (autoregressive effect) and their mutual influence (cross lag effect), and their (parents and children) situation can be seen as not separated things but as within dyad effect.

Figure 2

Simple Random Intercepts Cross-Lagged Panel Model 

Do you need help in statistical analysis of this kind of modeling technique? We are ready to act. 

References:

Hamaker EL, Kuiper RM, Grasman RP. A critique of the cross-lagged panel model. Psychol Methods. 2015 Mar;20(1):102-16. doi: 10.1037/a0038889. PMID: 25822208.

Falkenström F, Solomonov N, Rubel JA. How to model and interpret cross-lagged effects in psychotherapy mechanisms of change research: A comparison of multilevel and structural equation models. J Consult Clin Psychol. 2022 May;90(5):446-458. doi: 10.1037/ccp0000727. PMID: 35604748; PMCID: PMC9245087.