Maximum Likelihood - Science topic

bellow this link

https://stats.oarc.ucla.edu/sas/dae/multinomiallogistic-regression/

Bayesian analysis are based on Maximum Likelihood equation but add a multiplier in the numerator describing the prior probability that makes the ML probaility conditioned on the prior probability. This is the subject of and entire course on statistical inference so is difficult to describe unless you have a background in probabilities and Bayes theorem.

Interesting.

Take a look at the attached Google search for your answer. Best wishes, David Booth

You can try this easy to use program:

The help file explains how it works.

Thank You very much Patrice Showers Corneli

Thank you for your answering. I am running 25,000 tips since I am trying to reconstruct the phylogenetics for a virus. I need the starting tree for an additional analysis. The sequences range from 200 to 15,000 bp in length. I don't think using a bayesian method here like mrbayes would work for this since that would be far too computationally intensive. All I need is a MP tree, which should be less intensive than any ML method.

See also the following link that might help: https://www.google.com/amp/s/www.researchgate.net/figure/Cost-function-weights-and-optimal-controllers-with-M-st-159_tbl1_325832470/amp

I will suggest to delete the insertion deletion from the alignments. The analysis based on the alignment may provide similar results.

Dr. Wilhelm is completely correct. I would not go quite as far as he did on hypothesis tests. The important thing here is that pairwise deletion makes it less likely that you are sampling from the population of interest and if asked by some reviewer it's harder to say that you are talking about the population of interest instead of some other. This can defeat your argument for generalizability. Who suggested pairwise deletion? that I believe is from the SPSS literature. I would not suggest that as a good source. Best wishes, David Booth

I general convergence is when there is no meaningful change in the likelihood!

I cannot tell if this is a warning or it has been successful.

You may want to have a look at this:

https://www.ibm.com/support/pages/differences-between-spss-mixed-and-hlm-software-results

This is the HLM 8 Manual ; I suggest you search it for the word "convergence"

Interesting

I don't have access to the 2021 article by Cheung. To my understanding, the quoted section in Jak (2015) was talking about fixed-effects TSSEM proposed by Cheung and Chan in 2005. Fixed-effects TSSEM indeed cannot handle missing correlations as in GLS *in the past*. See the paper by Jak and Cheung in 2018 on how to solve this problem for fixed-effects TSSEM:

Maybe Cheung (2021) is talking about random-effects TSSEM in the quoted section. Random-effects TSSEM use a different approach in stage 1. You can check Chaper 7, section 7.4, of Cheung (2015): Meta‐Analysis: A Structural Equation Modeling Approach:

Hope this helps.

Thank you very much Professor Eliana, I shall read into the article.

Hi! Thank you all for your suggestions. And I would like to ask what do you think about using PLS-SEM in this case? Is the PLS-SEM modeling better option than SEM when most of data are highly skewed?

VAR models can be estimated by regression

I may be misunderstanding your question, but there is no constant variance assumption with logistic regression, so you do not need to worry about heteroskedasticity. In fact, heteroskedasticity is almost guaranteed with logistic regression since the variance of a binomial random variable is a function of the probability of the event happening and the probability of the event not happening, which will usually differ between observations.

A quasi-likelihood incorporates an additional dispersion parameter into a true likelihood for greater flexibility in modeling the variability of the data (think overdispersed Poisson model). A profile likelihood re-expresses nuisance parameters in the full likelihood as a function of the parameters of interest. Under mild regularity conditions after profiling the quasi-likelihood you can differentiate its log transformation and set this equal to zero to solve for the root, which will be a function of the data. This function of the data will be your maximum quasi-likelihood estimate.

For inference you can rely on a Wald, Score, or quasi-likelihood ratio test. For the Wald and Score tests if the parameter space is bounded the performance can be improved by utilizing a link function g{MLE}, e.g. g{ } = log{ } if the parameter space is bounded below by 0. For the score and quasi-likelihood ratio tests the nuisance parameters should be profiled by estimating the nuisance parameters under the restricted null space.

Hi, Thank you. Could you please provide me the reference where I can learn more on this?@arie ten cate

Olarinde Olaiya Muftau see this:

Also check https://www.lesahoffman.com/PSQF7375_Generalized/PSQF7375_Generalized_Lecture6_PathModels.pdf

Dear Marcin

This answer does not address your question exactly. But perhaps you can find some more guidance by looking at the links

Hope this helps

Pablo

You really can't "average" Bayesian and Classical ideas. You pay your money and you make your choice, as they say. David Booth

Maximum likelihood algorithm belongs to a supervised classification, for which the training samples are used to compute their distribution parameters. Further, every sample probability is computed and assigned to the class for which it gets the highest probability.

The Maximum Likelihood Estimation (MLE) is a method of estimating the parameters of a specific model. It selects the set of values of the model parameters that maximizes the likelihood function. Intuitively, this maximizes the "agreement" of the selected model with the observed data.

I suppose you use the 'jtools' R package. When you fit the model:

data(movies) fit <- lm(metascore ~ budget + us_gross + year, data = movies) summ(fit)

You get the number of missing observation.

#> MODEL INFO: #> Observations: 831 (10 missing obs. deleted)

see:

https://www.rdocumentation.org/packages/jtools/versions/2.1.2

The capacity region of the uplink two-user channel is achieved by SIC. You can certainly apply joint detection if you want to, but it won't improve the rates since SIC is capacity-achieving. See Section 6.1 in "Fundamentals of Wireless Communications" by Tse et al. for details. All points in the capacity region can be achieved by varying the transmit powers and decoding order.

The capacity/rate is the bit/s that you can deliver with zero BER when using (asymptotically) long coding blocks. The BER is a relevant metric when using short blocks. Here is a video where I discuss that in further detail: https://youtu.be/4nRjsq_P4ZA

You could run a model test to see what substitution profile best suits your data. In my opinion, the easiest way to do that currently is using IQtree ( http://www.iqtree.org/doc/Substitution-Models ), as it returns understandable output when model testing. Their documentation also provides useful summaries of what particular models are suitable for.

Keep in mind that the quality and quantity of your data guides that process. You can then apply the suggested model in RaxML, and compare against IQTree inference.

Also, if I understand you correctly you are inferring a tree from a single tree. Keep in mind that the resulting tree, if resolved, traces the evolution of that gene, which may or may not correlate to species phylogeny.

Hope that helps :)

I too think that it will not make much of a difference which one is used in terms of formality.

The easiest way to think of these is how you calculate the simple descriptive variance - the numerator is the sum of the sum of the squared deviations around then mean , and the numerator is? If you use n - the sample size, this is maximum likelihood and if it is n-1 , it is the restricted version. Fisher by a geometric argument had seen that one degree of freedom had been consumed by fitting the mean. That is the variance is calculated taking account of the uncertainty in the mean. Bayesian analysis which is sometimes known as full uncertainty analysis takes account of the uncertainty in all the parameters of both of the fixed and the random part of the model.

You can introduce joint distribution to pdf. Then differentiate with respect to the parameters.

Parameters that maximize the log likelihood function are the best then.

ML is the basis for CFA, so if you want to maximize consistency, you should use it for your EFA as well. To avoid the "over-fitting" problem (i.e., simply confirming your EFA results by applying both methods to the same data), you can use the EFA on a randomly selected subset of the full data set.

It is not necessary to use ML method.

Hello Mauricio,

The question really isn't a statistical one; the answer depends on how important the 20 variables you propose to discard are to the definition and identification of the construct(s) you seek to assess.

It might be the case that a lot of variables you initially gathered or chose were either inappropriate or of poor technical quality (e.g., unreliable indicators). In such instances, discarding such variables does no harm to your ability to identify the related latent variables. There are certainly many published studies in which the "final" set of indicators retained is far smaller than the original set mustered by the researcher(s).

As a second case, if you had 39 variables which were highly related to one another, you could likely discard variables and not lose appreciable power in identification of the underlying latent variable(s). This is sometimes done when people attempt to develop "short forms" of measures that retain fewer items than the original version. The high intercorrelations pattern doesn't appear to be the case for your data set, based on your query.

If there's no relevant theory to guide you here (and the decision to run an EFA suggests that this could be at least partially the case), It might be useful to confer with domain experts who could advise as to whether the remaining variables appear to still represent a viable set of manifest indicators for the latent variables of interest. As well, other studies may exist in which like factor/s have been identified. You could compare your resultant set of variables to those which others found useful as indicators.

Good luck with your work.

Ahmet Emre Onay, You can click any location and select the data type (Hourly, daily etc.), select dates, then click process, download result. this will give 10m height data, use power law or logarithmic law to convert to 50 m. Also, you can check Global wind atlas

Hi Chee-Seng Tan,

MLR implements a ML estimation approach (e.g., EM) using all available data. Therefore, MLR doesn't:

1) delete incomplete cases (e.g., "listwise deletion"),

2) impute data (e.g., "multiple imputation").

Roberto

Roland Yonaba Aline de Matos Valerio Roland questioned himself as to whether the method is relevant. It is not. Methods such as SVM or Mahalanobis distance or Random Forest rely on a data distribution, thus the covariance that is derived from the many pixels in a region of interest taken for training. With the endmembers, you have only one example of each endmember spectrum. SAM and other methods can work with the endmembers because they are just calculating a distance in spectral space between each image pixel spectrum and the endmember spectrum.

I recommend to read this

Hi

ML or MLR if you want Logit function (including OR results) on the categorical variables. If no estimator is requested, you will get the WLSMV with probit link function.

Best,

Rolf

Thank you so much. I will check it

Obasanjo Bolarinwa I would not recommend categorizing an outcome variable as it will lose information and therefore statistical power.

Have a look at https://www.ingentaconnect.com/content/asprs/pers/2004/00000070/00000012/art00002?crawler=true&mimetype=application/pdf

https://au.mathworks.com/help/stats/support-vector-machines-for-binary-classification.html

In stata there is an inbuilt maximum likelihood estimator

This will help you out

Here is source code to estimate an ARX model in Python with the Gekko sysid function. You can then use the Gekko arx function to simulate or build a Model Predictive Controller such as https://apmonitor.com/do/index.php/Main/TCLabF

from gekko import GEKKO import pandas as pd import matplotlib.pyplot as plt # load data and parse into columns url = 'http://apmonitor.com/do/uploads/Main/tclab_dyn_data2.txt' data = pd.read_csv(url) t = data['Time'] u = data[['H1','H2']] y = data[['T1','T2']] # generate time-series model m = GEKKO(remote=False) # remote=True for MacOS # system identification na = 2 # output coefficients nb = 2 # input coefficients yp,p,K = m.sysid(t,u,y,na,nb,diaglevel=1) plt.figure() plt.subplot(2,1,1) plt.plot(t,u) plt.legend([r'$u_0$',r'$u_1$']) plt.ylabel('MVs') plt.subplot(2,1,2) plt.plot(t,y) plt.plot(t,yp) plt.legend([r'$y_0$',r'$y_1$',r'$z_0$',r'$z_1$']) plt.ylabel('CVs') plt.xlabel('Time') plt.savefig('sysid.png') plt.show()

Hello Martin,

If you mean (as implied by Alizera's response) that the estimated path coefficients are not significantly different from zero, the most likely reasons would be:

1. There is little or no systematic relationship among the variables for the sample (and possibly the associated population) you are investigating.

2. There is a relationship, but your model is mis-specified (most likely by having omitted one or more important variables).

3. There is a relationship, but the statistical power of the procedure was inadequate to detect it/them (e.g., sample size was likely inadequate).

4. Some combination of the above.

Sorry if that's a bit generic, but your query really didn't furnish much detail about the specific model, variables proposed, and estimated relationships.

Good luck with your work.

Hi Jessica,

the FIML estimator is requested with estimator="fiml" not "ml".

And you should do an attrition analysis: Create a missingness indicator (0 = participant data available for both waves, 1 = missing at T2) and you regress this indicator on all available data (especially your DV's) with a logistic regression. This can help to address whether the data is NRM. The missingness does only have to be MAR for FIML.

Best,

Holger

MrBayes will give you robust results, it's just about finding the best running parameters. And for ML, researches tend to go for RaxML, maybe you could try it and see what happens with the bootstrap values of the output.

Cipres server has various online versions: http://www.phylo.org/

Use table function; is you share the exact breaker you faced, probably I can help you out.

Use the ULS estimator.

Hello Jesua,

So, for items like AP3 and AN1, were these cross-loadings implied by your theory, your instrument construction, or by you paying attention to suggested modification indices from your CFA software? As Cristian notes, choices need to be consistent with the underlying basis for your measure(s). In your case, this would apply to both the cross-loadings and the second-order factor solution.

So, to answer your question, is it possible? Absolutely. Is it mandatory to have these? Not at all. It may be better to modify (and retest) or discard items that do not conform to the theoretical framework than to re-imagine the framework to fit the behavior of the data. The latter approach leads to over-fitting, which tends not to generalize well to other samples and data sets.

So, think carefully about whether each change you make is consistent with the intended basis and behavior of the measure.

Good luck with your work.

Which Python version did You install? SpedeSTEM needs ver. 2.X

Hi Sarowar,

A good strategy is to run a parallel unsupervised classification and check out the spectral signatures of your training samples. This can inform you about the spectral differences/similarities between your expert classes. You can use this information to split your 'barren lands' and/or 'buildup' into multiple classes. Having more classes might improve the strength of the classification and you can always regroup the classes afterwards.

Regards,

Maarten

If you already tried ICA, try Non-negative matrix factorization (NMF.)

You can use object-oriented classification

I personally wish people would not use undefined terms in these questions. However this link may help you:

https://www.google.com/search?rlz=1C1CHBF_enUS874US874&ei=W3HyXe75DMmsswX6hbjIBQ&q=lg+statistical+model&oq=lg+statistical+model&gs_l=psy-ab.3..33i160l2j33i299.11467.30522..31319...0.2..0.185.1461.1j11......0....1..gws-wiz.......0i71.on5yDu7jDHg&ved=0ahUKEwiuk7iRyrDmAhVJ1qwKHfoCDlkQ4dUDCAs&uact=5

Good luck, D. Booth

Dear Patrice

thank you for your explanation, But I have some other question:

1. Why mega app construct 2 phyogenetic trees: Original tree (attachment no.1) and Bootstrap consensus tree (attachment NO. 2)

which one I can depend on?

2. When I construct a tree using ML is the <50% bs branches will consider as incorrect data?

If I understand well your explanation , these low bs reflect the high relatedness of these species (s1-s10) except s11, s12 and s13, which are slightly different. Although (s1-s13) identified as one same species through BLAST in NCBI.

3. Is it normal when I retry the construction of phylogenetic tree,sometimes , I get different bootstrap value as you can see in attachment No.3 and No.4 .

4. Attachment No.2 the purple branches which are identified as the same species. It was mentioned bellow the bs consensus tree that (less than 50% bs are collapsed). I would be grateful if you explain this point for me

Thank you very much

You are absolutely right. Compared to optical remote sensing where 'adjacency' is a high order effect the signal impact of 'neighbors' is much higher here. A perfect coherence estimator would include dipol distribution, local 3D geometry for ray tracing and radiosity estimation and a gaussian shaped weighting window to 'reflect' the mixing and superimposition of the representing physical process. I was often thinking to compile a paper about all this in connection with a multi stage, alternative phase unwrapping.... Hope it helps. If not you can send me an email: rogass@gfz-potsdam.de

I certainly agree with David Eugene Booth that I do not agree with serially testing each variable in a single predictor LR, then only using those that meet a bivariate p standard to be included in a subsequent multiple predictor LR. This would, of course, be parallel to examining all of the zero order PPM correlations between predictors and a criterion and including only those that met a bivariate p standard in a multiple regression equation. You are missing the joint predictive structure of the variables. Moreover, I am not quite sure how you know that the resultant LR will need to be a Firth LR. This would only be necessary if the LR maximum-likelihood iteration failed to converge due to complete, or quasi-complete separation. The only way one would know this from the bivariate results is if some (or one) of the predictors presented that solution by themselves; perhaps that is the case, I can't tell from what I see.

I presume that disease "positive" and "negative" represent the two groups. As such the very low base rate of 10 for positive, presents a logical and statistical problem. I suggest that you try to prune, or combine, predictors in some way; 20 is problematic given this situation.

Once all of this is settled, I suggest careful consideration of what the criterion of accuracy will be. A long-standing standard of accuracy in the sister-technique of discriminant analysis has been cross-validated classification accuracy -- how well can your model correctly classify Ss (with cross-validation) into the respective groups (postive and negative). My guess is that this would be what is important to you. Indeed, using a matrix simplification due to Bartlett, and introduced for discriminant analysis by Lachenbruch, the "U" method, or "leave-one-out" methop as Huberty deemed it, allows us to get cross-validated classification estimates with the sample at hand. This is, for instance, implemented in discriminant analysis in SPSS. The same round-robin omission of a single subject and prediction of group membership from a model including N-1 Ss is also applicable to LR, but not implemented in that package (no matrix identities to help here). I do have such a program if you are interested.

Finally, I would suggest that you consider discriminant analysis as well as LR as candidate analysis methods; don't toss Fisher out just yet :-) You might be interested in how closely the cross-validated performances of these techniques track in a publication that we wrote a bit back. However, in practice, I have seen LR perform much poorer than discriminant analysis in similar situations with a low base-rate.

I would suggest you try one of the methods provided by the "nloptr" package from R. One of them may work to your problem.

Hi Alexandra

1) if the indicators are ordinal and have >=5 categories, it's acceptable. There are estimators such as DWLS or WLMSV that are explicitly designed for categorical indicators but they rely on the (unreasonable) assumption that there is a normally distributed latent response variable which underlies the indicators.

2) Depends on the extend and form of the deviation. Normally, it is easy in nowadays software to apply corrections (e.g., the Satorra-Bentler or Yuan-Bentler correction). Severe kurtosis, especially is problematic. Nonnormality creases if I remember correctly the chisquare and decreases the standard errors.

3) If the factor loading is standardized, then I would view this as a problem. Fit of a model is one thing but plausibility is an important second thing. Unreasonable coefficients or heywoods raise doubt whether the identification and estimation procedure really worked.

Best

Holger

Please see the references.

Himanshu Prasad

The value of the R-Square can not be negative and more than 1.

So your result 3.75 is considered to be not sensable. And I expecte that is because your model is suffering from multiple correation problem. Thath is because high dimention of independent variables (14 variables) that implice nonsingular information matrix that is made suprior regression.

My advise is to use stepwise regression

@ Christopher Imanto ,

p is a parameter. It does not have any distribution.

The MLE of p is a random variable and it has a distribution.

Note that the MLE of p is a function of the random variables

X1, X2 , ............... , Xn .

In the asymptotic distribution of sqrt(n) (p_MLE - p) , p is not a variable . MLE of p is the only variable.

Thus, p can not have quantiles. But MLE of p can have quantiles.

From the asymptotic distribution, you will obtain the quantile of MLE of p as a function of p & I(p).

Still you can not determine the value of the quantile of MLE of p since p is unknown.

The only approximation you can do is

" Substitute the value of the MLE of p, obtained from the observations, in place of p in the formula of the quantile of MLE of p."

Please check this:

Hello Dan,

Yes; different tactics for addressing missing data frequently yield inconsistent results.

Usually the first order of business in trying to select a suitable method is to determine whether the data appear to be missing completely at random (mcar), missing at random (mar), or to have systematic relationships with presence/absence of data points.

Having said that, I suspect the multiple imputation approach you used is likely to be more warmly received than a listwise deletion approach that costs you 60% or more of the data set.

Good luck with your work.

Tray to use matlab mfile

Maximum likelihood estimation works very well for multi-dimensional data. And you are right that singe point estimators are quite useless if the multidimensional space is not orthogonal. In that case the correlations among the parameters must be accommodated,

In other words the parameters that make up the multidimensional space are inaccurate unless the model accommodates any correlations among them.

Certainly if the model is biased by failure to accommodate interactions in the parameter then the estimators will be wrong.

1. Log-likelihood estimates are guaranteed to be unique only if the likelihood function is log-concave in parameters. This is not always the case; see e.g. "

Examples of Nonunique Maximum Likelihood Estimators" by Dharamdhikari and Joag-Dev.

2. Method of moments will not work if your discrete distribution is on infinite support and the sequence of partial sums for one of the moments (say q^th moment) \sum_i p_i x^q_i does not converge.

It's late here to answer. But since v1.6.2, IQ-TREE supports a comma-separated list of outgroup taxa for -o option.

For large samples exact maximum likelihood can be approached reasonably well by faster estimation methods. But I do not understand why you want slow methods. As far as I know, Ait Sahalia code is good. Why do you say "(Unfortunately!)" ?

Thank you Firdos for sharing the article. I have read this and yes, they calculated MLE and not MAP.

But, in other work (Model-Based Clustering and Visualization of Navigation Patterns on a Web Site by Igor V. Cadez et al.) when priors are set using Dirichlet distribution, MAP is computed.

So, my concern is why MAP is not computed in case of K-means priors?

Thank you very much Vincent, a big hug.

Hi Albert,

does this example fit to your question? They used a combination of state and time-varying covariate (serological measure). It allows for absence of measurement event if an individual is captured.

Another possibility is to use as many individual covariates as the number of occasion and to include it in your model in E-SURGE i+t*xind(1_t)

you can try to ask also on https://groups.google.com/forum/#!forum/esurge_ucare

Hope it helps,

Guillaume

Abhijeet Singh Thank you